CA1063834A - Apparatus for measuring the flow rate and/or viscosity of a fluid - Google Patents

Abstract

TITLE
AN APPARATUS FOR MEASURING THE FLOW RATE AND/OR VISCOSITY
OF A FLUID

INVENTORS
Helen G. Tucker John W. Tanney William F. Hayes ABSTRACT OF DISCLOSURE

An apparatus for measuring the flow rate and/or vis-cous characteristics of a fluid comprises a casing, having a fluid passage which is elongated in cross-section with two parallel, opposed sides and has a flared entry portion leading to a portion of constant cross-section. Formulae are given, using substantially pure water as a standard, from which a suitable geometry for the flared entry portion can be deduced.
Fluid pressure detectors are provided for detecting a fluid pressure differential in the fluid passage such that the or each fluid characteristic to be measured may be deduced from the pressure differential when laminar flow is maintained in the passage. When laminar flow is maintained the apparatus is capable of measuring a wide range of flow rates and/or vis-cosities of an extensive variety of fluids in a consistent and deducible manner with minimal pressure loss.

Description

. This inventi.on relates to apparatus for measuring the flow rate and/or the visco~ity of a fluid. `j More particularly, in some embodi~ents of the pre- .
sent invention there is provided an apparatus for measuring the flow rate of fluid wherein the fluid flow through the ap- :
paratus is laminar and wherein the excess pressure loss across :. the apparatus relative to the useful output signal indicative .~ -- of flow rate is minimized in contrast with known apparatus.
. Further, according to some embodiments o the-present invention 10 there is provided an apparatus for measuring the viscosity of Newtonian fluids, or for the measurement of viscosi~ of non-. N~wtonian fluids, at a single shear rate with a fixed flow o~
fluid through the apparatus.
In other embodiments, the present invention provides an apparatus for measuring the flow rate of a fluid wherein. a reduction of pressure loss in the fluid is achieved, relative . .
. . .. .
:;.r t~ known apparatus, when entering a constant cross-section la- ~
minar flow portion of a fluid passage such known apparàtus is - :
described for example, by Ricardo in U~S. Patent 2j212,186, 20 Goldsmith in U.S. Patent 3,071,001, Weichbrod in U.S. Patent ;~
39071,160 and 3,220,2569 Millar in U.S. Patent 3,349,619, - Palmer in U~. Patent 767,047 and Brunswick Corp. in U~Ko Pa~
l tent 1,306,161. ;
.. ` In this specification, a fluid may consist of a yas, a liquid, a liquid oontaining a dissolved gas ox dissolved ~:
gases, a mixture of gas and liquid, gas and suspended sol.ids, :.:~
li~uid and suspended solids, where it can be assumed that such . mixtures have the properties of either a compressible or an .. incompressible fluid.
Further, in this specification, fluids considered as being Newtonian are defined as those exhibiting a direct pro-. 2 - :
' ' , ~ ~

' ' ' .~'' ' " ' '' ' ' portionality between shear stress and shea~ Xate in lamin~r flow at a fixed fluid tempexature and pressure.
Further, in this speci~ication~ laminax flow is de-fined as a ~luid flow havin~ insignificant random or irregular .
flow velocity components in contrast with turbulent flow where such irregularities are significant.

The measurement of fluid flow rate is a long standing problem which has been approached with a wide variety o~
techniques, each of which exhibits particular advantages and 10 deficiencies relative to particular applications.
The princlples relative to measuring fluid 10w rates may be classified into five general groupings:
- Heat transfer rate to or from fluids as exempli~
fied by hot wire anemometers or similar devices.
- Transport time of extraneous media suspended in i or driven by the fluid as exemplified by the time displaçement relationship of ion clouds, solid bodies, bubbles, etc.; trans-port time of disturbances within the fluid itself as exempli-fied by the time displacement correlation of inherent or indu-20 ced fluid turbulence noise spectra.
- Fluid momentum detection as exemplified by pitot tubes or venturi meters; fluid momentum utilization as exem-plified by cup anemometers or tubine meters; and fluid momen-tum interaction as exemplified by fluid jet velocity sensors.
~ Fluid disturbance detection as exemplified by vortex shedding flow-meters and vortex generation detecting swirlmeters.
~ Fl~i~ visco~ity induced phenomena as exemplified by lam~nar flo~ pressure drop devi`ce3~
~luid viscosity induced pressure drop apparatus for fluid flow rate measurement is well kno~n as exemplified by , 3'~

the a~ove noted references, wherein the pressure loss due to entrance effects into the laminar flow passages are noted as `~
being proportional to the square of the measured flow rate as is described in standard fluid dynamics texts.
Many types of apparatus are available for measuring the viscosity of fluids (Reference, Viscosity and Flow Measure- -ment-A Laboratory ~andbook of Rheology: Van Wazer, Lyons, Kim, Colwell. Interscience, New York, 1963~. Xnown types of ~ apparatus presently used for the precise measurement of fluid ; io viscosity may be classified into three general groupings:
- capillary-tube type viscometers where the fluid viscosity is directly related to the frictional - pressure drop and laminar flow rate through a long smooth tube.
- rotary type viscometers where the fluid is sheared -~
within an annulus between two concentric cylinders, one of which is rotating, the fluid viscosity ~eing directly related to the reaction torque and speed of the cylinders.
- falling-sphere type viscometers where the fluid viscosity is directly related to the velocity of a sphere free falling through the fluid as ~epen-dent on gravity.
~hese known types of apparatus, with the exception ;~ of the capillary tube viscometer/ are not ~enerally suitable, in ~heir basic configurations, for continuously measuring the viscosity of a flowing fluid. In contrast with known capilla- ;

ry tube viscometers which are difficult to clean and are not capable of adjustment the present invention provides an appa-30 ratus, which can carry out the same function, but with a lower overall pressure drop across the apparatus and additionally ' ' , , , ' ' . ' . ' ':

3~can be dismantled ~or cleaning, and which may be readily adjus-ted by the replacement of a ~ro~ d pl~t~ o~ s~i~ r.ember.
It is one object o~ the present invention to provide an apparatus capable of measuring a wide range of flow rates and/or viscosities of an extensive variety of fluids such that the output differential pressure of the said apparatus can be continuously related to the said fluid characteristics in a consistent and deducible manner while minimizing the pressure . loss across the entire apparatus relative *o the useful out-10 put pressure which is responsive to the fluid characteristic which is be~ng measured, in contrast with the disadvantages of many known types of apparatus for measuring fluid flow rate and/or viscosityO
This invention differs from known apparatus, asexemplified by the above noted references, in tha~ the geome-try of the entry portion into a substantially constant cross-section passage or passages is de~ined in terms o~ a "~igure of merit" by means o~ a test which may be readily conducted by those skilled in the art and where the upstream pressure measu-20 ring location in the fluid passage may be de~ined in terms of another "figure of merit" as- Will become apparent in the follo-wing description-of the present invention~ . ~~' According to the present invention there is provided -an apparatus fox measuring the flow rate and/or viscosity ~
.~ a fluid comprising:
a~ a casing having a fluid passage, which is elonga-:~ ted in cross-section normal to the mean direction ~or fluid flow therein with two parallel~ opposed major boundary surfa-ce portions wh.ich are parallel in a plane normal to the mean 3~ direction for fluid flow therebetween, the fluid passage com-prising a flared entry portion and a portion having, in the .~

:
'' : ~.

mean direction for fluid flow therein, continuous bvundary surface and a substantially constant cross-section, the ~lared entry portion being flared to decrease in width, without in-creasing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the portion .
having, in the mean direction for fluid flow therein, a con-. tinuous boundary surface and a substantially constant cross- :- .
section, a fluid inlet to the casing and forming a substan- -. ~ tially unobstructed flow path for fluid to the whole of an io inlet area to the flared entry portion of the fluid passage, .
said inlet area being normal to the mean direction for flow of fluid at an inlet end of the flared entry portion, and fluid . outlet from the casing and forming a substantially unobstructed flow path for fluid from the whole area of an outlet end of . :~:
the fluid passage said outlet area being normal to the mean ~.
direction for flow of fluid at the outlet end o~ the fluid passage, and wherein b) the portion of the 1uid passage having conti- .
nuous boundary surface and a substantially constant cross-sec-20 tion in the mean direction for fluid flow therein has a magni-tude of mean breadth which is at least as large as that given by a mean breadth to meàn width ratio of 1.~ to 1, and an area in any plane normal to the mean direction for fluid flow therein which does not vary more than in the region of 2~ from the mean area calculated in this manner for substantially the -.
whole length of the said portion having continuous boundary ~:
surface and a substantially constant cross-section, and wherein c) the geometry of the flared entry portion o~ the fluid passage is such that, with laminar flow being m~intained in the whole of the iluid passage, using substa~tially pure .. . ..
, , . , , : : , : . , : , water at 70F as a standard, the flared entry portion has a "figure of merit", M which is calculated using consistent units from the relationship: -M = 1 -where, G2 = the mass flow rate of the substantially pure water through the fluid passage when'the Reynold~ nu~er, Re~

is at least 20~.0-.in-the':.port~on o.t~e:fl~d pas~ge ~aving 10 continuous boundary sur~ace and a substantially constant cross-section in the mean direction for fluid flow therein, and the Reynolds number, Re~ in the portion o the fluid passage having continuous boundary surface and a substantially constant cross-section is de~ined in consistent units by the relationship:

,~
hU~
Re = ~ ~ whexe h ~ the width separating the paralle~ opposed major boundary surface portions, of the portion of the ~luid passage . ' 20 '.laving ecntinuous boundary surfac~ and a su~stanti~.ally cons~tant cross-section in the mean direction for fluid flow therein, U = the mean velocity of the substantially pure . water through the portion of the fluid passage having conti-nuous boundary surface and a substantially constant cross-' section in the mean direction for fluid flow therein, p = the density of the substantially pure water, ' ~:
~ = the absolute viscosity of the substantially ~.
-~ pure water, ~E~ ~ a ~tatic pres~uxe di~erential ~etween the subs~

': - 7 ~ :.
': , ~, ".. ~

tantially pure wat~r at ox upstream of t~e fluid inlet to the casing and the su~stantially pure ~ater with;n the fluid passa-:~ ge at a position ~ithin the portion having continuous boundary surface and a substan~ially constant cross-section in the mean ::
direction for fluid flow therein and where the flow rate is G2 as previously defined immediately above and which is downstream of an outlet end of the flared entry portion by at least an :
: amount Le and is determined in consistent units by the rela- ~ -tionship:
Le = 0-04 Re h when the ~eynolds number, Re~ is ~:
that where the flow rate is G2 as previously defined immediate-ly above in the portion of the fluid passage having continuous boundaxy surface and a substantially constant cross-section in the mean direction for fluid flow therein, : K2 is a constant and is defined in consistent units by, (.Gl ) K2 - aEl - aE~_G2 / w~ere . ~ Gl (Gl~ ' '' : G2 Gl ~ the ~s flow x~te of the substantiall~ pure ~ater th~ough the fluid passa~e when the Reyno.lds num~er Re~
is less than G2 and is at least 1000 in the portion of the ~luid passage having continuous boundary surface and a sub-stantially constant cross-section in the mean direction for . . flow thereln, and aEl = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to .
- the casing and the substantially pure water within the fluid passage at a position within the portion having continuous : , boundary surface and a substantially constant cross-section in 30 the mean direction for fluid flow therein and where the flow :. rate is Gl as previously defined immediately above and which 8 - :
, .' ' ' ~' . . ~ '':,, '- '''' ' ' .' :' ' ' ' . . ' , .' ' . ' 3~
is downsk~eam of the outlet end o~ the flared entr~ portion by at least an amount Le as previously defined, and where the flared entry portion "f;gure of merit", M, is with;n the limi~s determined ~y the relationship in con-sistent units:
M < 1.36 h dh ~ where dh = the hydraulic diameter o the portion of the fluid passage having continuous boundary surface and a subs-10 tantially constant cross-section in the mean direction for the flow of fluid therein, and is defined in consistent units by, dh = 4C ~ where ` A = cross-sectional area of the portion of the fluid passage having continuous boundary surface, and a sub~-tantially constant cross-section, normal to the mean direc-~ tion for fluid flow therein, .~ .
:. C = wetted perimeter of the portion of the fluid passage having continuous boundary surface, and a substantially constant cross-section, in a plane normal to the mean direc-:: 20 tion for fluid flow therein, `. and where h is a~ previously defined, and d) fluid pressure detecting means in the casing for detecting a fluid pressure differential in the fluid passage, between spaced positions in the mean direction for fluid flow . therein, a~ least one of the positions being in the portion .
having continuous boundary surface and a substantially cons- :
tant cross-section, whereby ~ :
;~ . e) the or each fluid characteristic to be measured . :
is related to the pressure differential indicated by the fluid . :
: 30 pressure detecting means and is deducible therefrom in a con-sistent manner for any given fluid when laminar flow is main~ ~::
_ 9 ~
.,. ~ ;:
.. ... ... .
' , '"" ~:~.

:' ' ' ' :
: . , . , . -. ~

.

.V~ 3~
. tain2d in the w~ol~ o~ ~he ~luid pas~ag~
:' ' Furt~er, according to the ~r~sent invention there is provided an apparatus for measuring the flow rate and/or the ~.:
viscous characteristics of a fluid, comprising.
a) a casing having a pluraiit~ of substantially iden- :

tical fluid passages, which are elongated in cross-section normal to the mean direc~ion for fluid flow therein with each -:
passage having two parallel, opposed major boundary surface portions, which are parallel in a plane normal to the mean 10 direction for fluid flow therethrough, each fluid passage com-prising a flared entry portion and a portion having, in the : .
mean direction for fluid flow therein, continuous boundary sur-face and a substantially constant cross-section, the flared en-try portion of each passage being flared to decrease in width, without increasing in breadth, in the mean dire~tion for 1uid flow therein and forming an unobstxucted ~low path to the portion, having in the mean direction ~or ~luid flow therein, continuous boundary surface and a substantially constant cross-section, a fluid inlet to the casing forming a substantially 20 unobstructed flow path for fluid to the whole o~ an inlet area to the flared entry portion of each fluid passage, for each fluid passage said inlet area being normal to the mean direc~
~: tion for flow of fluid at an inlet end of the 1ared entry : : .
portion, a fluid outlet from the casing forming a substan-tiall~ unobstructed ~low path for fluid from the whole area of an outlet end of each fluid passaget for each fluid passa-ge, said outlet area being normal to the mean direction for . ~:
.
flow of fluid at the outlet end of that fluid passage, and :~ wherein , . : .
b) the portion of each fluid passage having conti-nuous boundary surface and a substantially constant cross~sec-, - 1 0 - ` "' '" ' '', .
..

tion in the mean direction for fluid flow therein has a magni-tude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 1.5 to 1, and an area in any plane normal to the mean direction for fluid flow there-in w~ich doe~ not Yary more than in t~e region of 2~ from the mean area calculat~d ~n th~s manner for the whole length of the said portion of that fluid passage having continuous boun--dary surface and a substantially constant cross--section, and wherein 10 c) the geometry of the flared entry portion of each fluid passage is such that, with.laminar flow being maintained in the whole of each fluid passage, using substantially pure water at 70F as a standardy the flared entry portion of each fluid passage has a "figure of merit", M which is substantially the same for each fluid passage and which is calculated using ! consistent units from the relationship:

K G .

. where, G2 ~ the mass ~low rate of the substantially pure water through each of the fluid passages when the ReYnolds num- .... `.
b~r Re~ is at ieas~.2~n.0 ~n t~e port~on of eac~ fluid pas~
sage having continuous boundary surface and a substantially ~ :
: . .
constant cross-section in the mean direction for fluid flow therein, and ~:
the Re~nolds number~ Re~ in the portion o~ each of ~:
the fluid passages having continuous boundary surface and a .
substantially constant cross-section is defined in consistent units by the relationship~
3C ~
Re - h~p s where ' ::. :. : '' , ..... : :'` " . ' '' ' ~ ``
, ." , : ,' . ' - ' ' ' : ~ , : ' : . ' 3~ :
h ~ th.e ~id~h s~paratin~ th~ parallel opposed -major ~oundary ~urface port;~.ons, of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean di.rection for ~luid flow therein, U = the mean velocity of the substantially pure water through the portion of each of the fluid passages having continuous boundary surface and a substankially constant cross-: . section in the mean direction for fluid flow therein r p = the density of the su~stantially pure water, ~ ~ the absolute viscosity of the substantially pure water, .
~E2 = a static pressure differential between the suhstan~ially pur~ ~atex at or up~tream of the fluid inlet to the casin~ and the su~stanti`all~ pure water ~ithïn each fluid passage at a pos~tion w~thin t~e`portion having continuous ~ boundary surface and a substantially constant cross~section in ; the mean direction for fluid flow t:herein and where the`flow rate is G2 as previously defined in~ediately above and which 20 is downstream of an outlet end of the flared entry portion by ::
. at least an amount Le and is determined in consistent units by : the relationship: -:
; Le = 0-04 Re h when the Reynolds number, Re~ is :: -that where the flow rate is G2 as previously defined immediate~
ly above in the portion of each fluid passage having continu~
- ous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, K2 is a constant and is defined in consistent units, K2 = ( 2 2~ , where ~

G2 .. . :

- 12 - :-.

:

3'~

Gl - the m~ss flo~ rate of the substantially ~ure water through each of the ~luid passages when the Reynolds num-ber Re, is less than G2 and is at least 1000 in the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and . .
~El = a static pressure differential between the .
su~stantially pure water at or upstream of the fluid inlet to - the casing and the su~s~antially pure ~ater within each fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is Gl as previously defined ilmmediately above and which is downstream of the.outlet end of the flared entry portion by ~: .
at least an amount Le as previously defined, and where the flared entry portion "figure of merit", `: .
. :
M, is within the limits determined by the relationship in con-: sistent units~
M < 1.36 h dh ' where . dh = the hydraulic diameter of the portion of each ~.
; . fluid passage having continuous.boundary surface and a subs~
tantially constant cross-section in the mean direction for the .
flow of fluid therein, and is defined in consistent units by~
~; - . . .
d~ = 4CA ~ where A = cross-sectional area of the portion of each fluid passage having continuous boundary surace, and a subs- :
tantially constant cross-section, normal to the mean direction : for fluid flow therein, . . .
C -. w~ted perim~ter o~ t~e portion of each fluid ..
passage ~aving continuous~ ~oundary surface and a substantial- ;
ly constant cross-section, in a plane normal to the mean di-rection for fluid flow therein, and ~here h is as previously defined, and d) fluid pressure detecting means in the casing for detecting a fluid pressure differential in at least one of the fluid passages between spaced positions in the mean direc-tion for fluid flow therein, at least one of the positions, being.~
in a. portion of that fluid passage having continuous boundary ¦-surface and a substantially constant cross-section, whereby e3 the or each fluid characteristic to-be measured ~0 is related to the pressure differential indicated by the pres-sure detecting means and is deducible therefrom in a consistent manner for any given fluid when laminar flow is maintained in . the whole of each fluid passage.

Once a particular fluid passage geometry has been : . .
. numerically evaluated by a static pressure differential measu- .
.' rement to meet the limiting criteria given above it will be .;
.. appreciated that it is not necessary to numerically evaluate any other apparatus in this manner which has substantially .: :.
the same fluid passage geometry. Thus any apparatus having :.
substantially the same fluid passage geometry as a geometry so tested, may have fluid pressure detecting means provided solely - for the purpose o providing a pressure differential from which the fluid characteristic to be measured may be deduced. It ..
will be appreciated that once a particular fluid passage geo- .
metry has been tested, either static or total pressure detec-ting means may be provided for the purpose of providing a pressure differential from which the fluid characteristic to :
be measured may be deduced without invalidating the intent of the present invention~
Further, a fluid passage flared end geometry may be ..
evaluated by different pressure measurements than those used - 14 - :

:
, to obtain a pxessure differential to determine a.fluid flow rate and/or viscosity. For example, for a prototype it may be conYenient to ~aluat~ the g~o~try from ei.ther a known entry or exit velocit~ ~o t~e fluid passage ln ~hic~ case only one pressure pro~e is necessary and this is disposed in the portion of the fluid passage having continuous ~oundary surface and a substantially constant cross-section, however, when apparatus ; using that flared entry geometry is to measure fluid flow rate and/or viscosity it may be advantageous for two pressure probes .:
10 to be used in the fluid passage with at least one located in ..
the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section. :.
~ .
.; The apparatus according to the present invention en~
sures that:
1) a pressure dif~erential is generated between two detector locations by means of wall boundary layer induced vis~
cous shear energy dissipation in thle fluid passage~

2) the pressure di~ferential between the two sui- ~
tably located pressu.re detectors is a large portion o~ the ~ .
20 pressure differential as measured between the inlet to the . :
fluid passage and the outlet from the fluid passage by mini-.
mizing viscous entry losses.

-~ 3) repeatable performance results are obtalned in re~

. lation to well known manufacturing techniques such as metal pres- .~

~ sing, die.. casting, plastic molding, powder metal orming, etc. .

In some embodiments of the present invention the . portion of the or each fluid passage having continuous boun-dary surface and a substantially constant cross-section has a ; magnitude of mean breadth which is at least as large as that 30 given by a mean breadth to mean width ratio of 2 In other embodiments of the present invention the ;~
' ' ' - 15 ~
, .

portion o~ th~.or each flui~ passage h.aYing continuous boun dary surface and a substantially constant cross--section has a magnitude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 3.0:1. In which case Gl = the mass flow rate of th~ substantially pure water through the or each fluid passage when the Reynolds number~ Re~
is preferably 1500 in the portion of the or each fluid passage having continuous boundary surface and a substantially constant - cross-section in the mean direction for fluid flow therein, and .; 10 G2 - the mass flow rate of the substantially pure water through the or each fluid passage when the Reynolds num- .
ber, Re, is preferably 3000 in that portion of the or each .: .
fluid passage having continuous boundary surface.and a substan- ..
tially constant cross-section in the mean direction for fluid flow therein.
In other embodiments of the present invention the : portion of the or each fluid passage having continuous bounda-ry surface and a substantially constant cross-section has a ` magnitude of mean breadth which .is at least as large as that `~ 20 g.iven by a mean breadth to mean width ratio of 5:1. In which .
case Gl - the mass flow rate of the substantially pure water through the or each fluid passage when the Reynolds number, Re~
is preferably 2000 in the portion of the or each fluid passage .. :
having continuous boundary surface and a substantially constant ~
cross-section in the mean direction for fluid flow therein, and G2 ~ the mass flow rate of the substantially pure water through the or each fluid passage when the Reynolds num- :
ber, Re~ is preferably 4000 in that portion of the or each fluid passage having continuous boundary surface and a substan-30 tially constant cross-section in the mean direction for fluid flow therein.

-~ 3 Y~

In ot~8x emhodiments o~ the present invention the portion of the or each fluid passage h.av;ng continuous bounda-ry surface and a substantially constant cross-section has a magnitude of mean breadth which is at least as large as that : :
given by a mean ~readth to mean width ratio of 10:1. In which .
case Gl = the mass flow rate of the substantially pure water thxough the or each fluid passage when the Reynolds number, R
, ~
is preferably 3000 in the portion of the or each fluid passage - having continuous boundary surface and a substantially cons~

10 tant cross-section in the mean direction for fluid flow there- - :

'!. in, and :

G2 ~ the mass flow rate of the substantially pure .. ~-water through the or each fluid passage when the Reynolds num- :

: bex, Re/ is preferably 6,000 in that portion of the or each ~ fluid passage having continuous ~oundary surface and a subs-.~ tantially constant cross-section in the mean direction for :

fluid flow therein.

In the accompanying draw.Lngs which illustrate, by ~` way of example, embodiments of the present invention as well : 20 as unsuitable flared entry portions, :

Figure 1 is a diagrammatic view of an apparatus for . measuri.ng the flow ratè and/or viscosity of a fluid, :

Figure 2 is a sectional side view along B-B, Figure . .

3, of an apparatus for measuring the flow rate and/or viscosity . of a fluid and having a fluid passage comprising a flared en-try portion leading to a single, laminar fluid flow portion, Figure 3 is a sectional plan view along A-A, Figure .. .

` 2, . ..

Figure 4 is a sectional end view along C-C, Figure 30 3, ~ ...... ... .. .

: Figures 5 to 16 are sectional side view of different ~.

. - 17 :
: .
' ' :' 3i~
, entry portions. ~o that ~h~wn in F~ure 2, some of which are suitable and others of which are unsuita~le for use in the present invention, : . Fi~ure 17 i~ a partl~ sectional pl~n view of a.n apparatus similar to that shown in Figures 2 to 4, but having five fluid passages, along F-F, Figure 18, Figure 18 is a sectional side view along E-E, Figu- ;
. re 17, Figure l9 is a sectional end view along G-G, Figu- :-io re 18, Figure 20 is a sectional side view of an apparatus similar to that ~hown in Figure 18, but with enlarged static pressure taps extending to all of the fluid passages, Figure 21 is a sectional side view of an apparatus similar to that shown in Figure 18, but with total pressure probes, Figure 22 is a sectional side view of a porti~n of the apparatus shown in Pi~ure`18 kut showing a total pressure probe, Figure 23 is a sectional view along J-J, Figure 22, -~
: of the total pressure probe, Figuxe 24 is a sectional view along J-J, Figure 22, of a different shape o~ total pressure probe, Figure 25 is a diagrammatic view of an apparatus for measuring the flow rate and/or viscosity of a fluid having a ;`
matrix of fluid passages, Figure 26 is a sectional end ~iew along K-K, Figu-- re 25~ . :
Figure 27 is a sectional side view along L-L, ~` 30 Figure 26, of a flared entry portion~ .
Figure 28 is a sectional end view along K-K, Figure 25, but showing trapezoidal fluid passag~s, Figure 29 is a pictorial view of a portion of the :
apparatus shown in Figure 18, showing a different construction ~ .
for rectangular ~luid passages, ~ -Figure 3a is a pictorial Yiew of a portion of the . apparatus along J-J, Figure 29, with a top plate removed, --; Figure 3I is a plan view of a portion of an appara-: tus similar to Figures:29 and 30, but with integral shim members, i0 ~'igure 32 is a side sectional view along M-M, Figu-re 31, Figure 33 is an isometric view of a portion of an ~ ~
apparatus which is similar to that shown in Figure 29, but with ~.
shims and spacers integral and with the mean directions for fluid flow in the fluid passages radiating from a central posi~
I tion, Figure 34 is a sectional end view alon~ N-N, Figure 33, Figure 35 is an isometric view o~ an apparatus which is similar to that shown in Figures 31 and 32, but with a shim : :
- ring member upstream of the passage inlet and joining all of the shims, . - . .
Figure 36 is a sectional end view along P-P, Figu~
re 3~, Fi~r~ 37 is a pictori.al v~e~ of apparatus similar . .
to that si~o:wn in ~igures 31 and 32, Put w~th a shim ring mem-- ber downstream o~ the passage outlet and ~oining all of the shims, Figure 38 is a sectional end view along R-R, Figu- : -: 30 re 37, .. . . .. .
Figure 39 is a sectional side view of an apparatus ~'',, : -.. . ..
.. .. . .

: similar to that shown in Figures 17 to 19 but having inlet and outlet cavities in the casing, Figure 40 is a graph of the pressure drop/flow rate cha- ~
racteristic of a fluid passage of rectangular cross-section ::
and having a square entry portion as shown in Figure 8, Figure 41 i.s a similar graph to that shown in Fiyu-re 40 for a similar fluid passage but having a radiused entry portion as shown in Figure 10, and ; . Figure 42 is a similar graph to that shown in Figu-10 re 40 for a similar fluid passage but having a chamfered inlet as shown in Figure 11.

Referring no~ to Figure 1 there is shown an appara-tus:for measuring tne flow rate and/or viscosity of a fluid comprising: .
a) a casin~ 1 having a fluid passage 2, which is elongated in cross-section normal to the mean direction, arrow 14, for fluid flow therein with two parallel, opposed major ~ :
boundary surface portions 21 and 22, which are parallel in a plane normal to the mean direction for fluid flow therebetween, 20 the fluid passage comprising a flar.ed entry por~ion 12 of length L~ and a portion 13 of length Lc having, in the mean direction ~or fluid flow therein, continuous boundary surface :-. and a substantially constant cross-section, the flared entry portion 12 being flared to decrease in width, without increa-. sing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the portion 13 having, in the mean direction for fluid flow therein, a continuous boundary surface and a substantially constant cross-section, : a fluid inlet 3 to the casing and forming a substantially 30 unobstructed flow path for fluid to the whole area at an inlet end 4 to the flared entry portion 12 of the fluid passage 2, : .

.:

said inlet area being normal to the mean direction for flow of ; fluid through that end 4 of the flared entry portion 12, and -~ a fluid outlet 5 from the casing and forming a substantially unobstructed flow path for fluid from the whole area at an outlet end 6 of the fluid passage 2 said outlet area being : normal to the mean direction for flow of fluid at the outlet end 6 of the fluid passage 2, and wherein, .b) the portion 13 of the fluid passage 2 having con- ::
tinuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein has a magnitude of mean breadth b which'is at least as large as that giYen by a mean hreadth b to mean width h ratio of 1.5 -' to 1, (shown having a mean breadth to mean width ratio of . ~
about'3:1) and an area in any plane normal to the mean direction . :
~or fluid flow therein which'does not vary more than in the re-.' gion of 2% from the mean~area calculated in this manner for the ..
wh.ole length Lc of thb sai~ portion having continuous boundary surface'ana a su~s~ant~all~ con~tant".aross~sec~'ion~ and w~erein . c) the geometry of the flared entry portion 12 of ' 20 the fluid passage 2 is such that, when laminar flow is maintai-ned in the whole of the ~luid passage 2, using substantially ~' pure water at .70F as a standard, the f1arad entry portion 12 . .' :~
has a "figure of merit", M which is calculated using consistent units from the relationship: ' .. M = 1 ~ '-'a-E2 . where, . G2 = the mass flow rate of the substantially pure water through the fluid passage 2 when the Reynolds num~er, 30 Re~ is at least '2~ n th-~ por~on :~3''of''tn~ f-lu~d pas~sage 2 having continuous boundary surface and a substantially cons~

. tant cross~section in the mean direction for fluid flow there-::

;

. in, and .~ the Reynolds number, Re/ in the portion 13 of the ~luid passage having continuous boundary surface and a subs-tantially constant cross-section is defined in consistent units by the relationship:

- hUD c where R,~ -. ~ 11 ' h = the width separating the parallel opposed .

major boundary surface portions, of the portion of the fluid : .
..
10 passage having continuous boundary surface and a substantially :
constant cross-section in the mean direction for fluid flow .-:~ therein,.

. U - . the mean veIocity o~ the substantiall~ pure - -water through the portion 13 of the fluid passage having con-tinuous boundary surface and a substantially constant cross- :
~l section in the mean direction for fluid flow therein, : p ~ the densit~ of the substantially pure water, ~ = .the a~s~lute YisCosity o~ the.substantiall~ !
pure.water, 20. AE2 ~ a static pressure differential between the subs- .

tantially pure water at or upstream of the fluid ;nlet 3 to the casing 1 and the substantially pure water within the ~luid pas-sage 2 at a position within the portion 13 having continuous .~; boundary surface and a substantiall~ constant cross-section in the mean direction for fluid flow therein and where the fluid flow rate is G2 as previously defined immediately above and which is downstream of an outlet end 23 of the flared entry por-tion by at least an amount Le and is determined in consistent units by the relationship:

.

r- ~~
' ', . ~"
. . ~, -Le - 0.04 R~ h when the Reynolds number, Re~ is ' - .
~ that where the flow rate is G2 as previously defined immediate-ly above~in the portion 13 of the fluid passage having conti-. nuous boundary surface and a substantially constant cross-sec- :'~
' 'tion in the mean direction for 1uid flow therein, . 10 K2 is a constant and is defined in consistent units '. by: ' (Gl) : :
: ~El aE2 G .-K2 - 2~ d where ':~ Gl .(.G~
' ' ~ ' '' ~-.
~ Gl = the mass flow rate of the substantially pure ~' water through the fluid passage 2 when the Reynolds number - .
Re~ iS a~ least lO~.~. in t~e.port~on 13'of t~ fluia passage ha- ~' ving continuous boundary surface and a substantially constant ':
' cross-section in the mean direction for fluid flow.therein, and `~ 20 ~El - a ~tatic ~re~sux~ differential between the . --:.
;. sub~tantially p~re ~ater at or upstream of the fluid inlet 3 ':
.' '''to the ca~ing 1 and tha''su~stant~ally pure water within the :" fluid passage at a position ~ithin t~e portion 13 having con-tinuous boundary surface'and a substantially constant cross- ' section in thè mean direction for fluid flow therein and where .
........... the flow rate is Gl as previously defined immediately above and -''~ which is downstream of the outlet end of the flared entry por~
. . . .
tion 12 by at least an amount Le as previously defined, ` ' .: and where the flared entry portion "figure of ~eritn, .'~
':'.................................................................... ''",' ' ' - 23 - ''' '~
'': '';

: ' . ' ~
' :,~, '..

M, is within ~h~ lLmi.~s determined by t~e. relationship in consi.stent units: -< 1.36 h , where . .

dh = the hydraulic diameter of the portion 13 of the fluid passage 2 having continuous boundary surface and a -.. :
substantially constant cross-section in the mean direction or -~
the flow of fluid therein, and is defined in consist~nt units - by: .
dh ~ 4A
C ~ where . . ~ = cross-se~ctional area of th.e portion 13 of the- fluid passage 2 ~avi`ng cont~nuous-~oundary s~rface, and a subs-tantially constant cross~section, normal to the m~an direction for fluid flo~ therein, C = wetted perimeter of the portion 13 of the ~luid passage 2 having continuous boundary sur~ace and a substan-tially constant cross section, in a plane normal to the mean ; direction for fluid flo~ t.herein, and ~here h is as pre~iousl~ defined, and dl ~luid pxessure detecting means, in thi:s embodi-ment in the form of static pressure probes 10 and 11 in the ca-sing 1, connected to a differential pressure gauge 24, for detecting a fluld pressure differential in the fluid passage 2, between spaced positions in the ~ean direction, arrow 14, for fluid flow therein~ at least one of the positions being in the portion 13 having continuous boundary surface and a substan tially constant cross-section, whereby e3 the or each fluid characteristic to be measured is related to tha pressure differential indicated by the fluid pressure means9 that is static pressure probes 10 and 11, and is deducible therefrom in a consistent manner for any given - ~4 -lY3~

flwid when laminar ~lo~Y is maintained in the w~ole of fluid passaye 2.
When the fluid pressure detecting means comprises static pressure probes 10 and 11, the static pressure is measu- .
- red preferably at the boundary surface of the fluid passage 2 and preferably at the centre of the ~luid passage breadth.
However, when the fluid pressure detecting means de-tects fluid total pressure, as will become apparent with fur-; ther description of other embodiments of tne present invention, 10 the total pressure is preferably measured in the vicinity of ~ -the center of the fluid passage breadth with detecting means oriented so as to have maximum sensitivity in the local mean direction of flow as shown by arrows 14 in Figure 1. When the entrance to the total head detecting means is less than the pas- : -sage width such entrance should be preferably located in the vi-cinity of the centre of the passage width and breadth and should be oriented to have maximum sensitivity.
The fluid pressure tap 10 is located within the fluid passage 2 and upstream of fluid pressure tap 11 and preferably 20 at a minimum distance from the inlet end 3 of the fluid passa-ge 2 such that when using substantially pure water at 70F as a standard, then a figure o~ merit, T, for a suitable upstream .: :
position, but not necessarily the only position, for the pressu-:: re probe 10 may be evaluated from the following relationship in ~ consistent units~
. ~. . . ~ ' - where, in consistent uni~s, (G )2 .
acl ~ ~C2 G2 . '; ' '~ ' ' Gl - (Gl)2 ~2 : :

where Gl and G2 are as ~reviousl~ defined for the a~propriate ,. '~.

:' ' ' :' ' . . ' . ' . ' ; . ' :, ' . :' :

~ v~
mean breadth, ~,. to ~h.e mean ~Ldth4 h, ratio 6Cl = pressure di.fferential ~etween the upstream . .
pressure pro~e, such as 10 shown in Figure 1, and the down-stream pressure probe, such as 11 as shown in Figure 1, when the flow rate in the portion:13 of the fluid passage 2 having substantially constant cross-section is Gl defined immediately above, .
~ C2 ~ pressure differential between the upstream pressure probe 10 and the downstream pressure pro~e 11 and when the flow rate in.the portion 13 of the fluid passage-having substantially constant cross-section is G2 as d~ ed immediately above, and where, in consistent units:
.

Fl o C2,, - F2 ~ G ;? ) '''` . (G2) : where ~C2, F2 and G2 are as previously defined immediately above.
In applications ~here linearity o~ output pressure differential on the measured characteristic is important the calculated upstream pressure tap figura of merit may.suitably be lLmited by the relationship:
T ~ .001~ .
If T exceeds O.~anl5, the upstream pressure pro~e 10 may be moved further downstream in order to reduce the calculated value of T to less than 0.0015. However, in applications where output differential pressure sensitivity to the measured fluid charac-teriskic is important, it may be advantageous to locate the upstream pressure probe 10 such that the figure of merlt will exceed 0.0015.
This apparatus in accordance with Figure 1, uses the flared inlet portion 12 ko the substantially constant cross-~ 26 -; : :
: ` :
33~-~
s~cti.on l~minar flow portion 13 to r~duc~ the pressure loss across the entire fluid passage, from the area of inlet end 3 to the area of the outlet end 5 such t~at this pressure loss tends to approach the usable output differential pressure ma- : ~
; gnitude. T~is differentiates the laminar flow measurement ap- . .
paratus of the present invention from other known laminar flow measurement devices which do not define a flared inlet portion 12 to the or each fluid passage 2 ~or the laminar flow of .. -.
fluid therein.
, 10 The operational principle of the present invention . can be most easily understood by considering the constant area :~
portion 13 of fluid passage 2~ In the absence of a flared inlet portion 12, it is known that a pressure loss is .induced over an inlet portion of the fluid passage 2 which is in ex-.j cess of the pressure loss induced over any equivalent length of substantially identical fluid passage downstream of the 1, . .
inlet portion. It will be appreciated that this excess of .
~ pressure loss, which is commonly referred to as "the entrance pressure loss", is additional to the static pressure loss (~p) ..

20 resulting from the ~onversion of static pressure upstream o~ the 1.
1 . .
fluid passage inlet to 1uid velocity within the fluid passage in ~
- accordance with the well-Xnown Bernoulli relationship. in consis- ..
tent units: 1 ~2 :~ :
~ 2- P g L
where.
p ~ densi:t~ of the fluid flowing through the pas- ~.
sage, . V - mean velocity of the fluid flowing through .
the constant area portion o~ the passage, :

g _ acceleration due to gravity In the apparatus according to the present invention, :
the inlet portion 12 is flared such that the la~inar flow ve-. - 27 -.. , , ;
.

locity profiles in planes normal to the mean direetion for fluid flow tend to reduce the ~luid acceleration gradients within the inlet portion 12 and consequently reduce the asso-ciated fluid viscous shear induced pressure losses which arein addition to those fluid viscous shear induced pressur~
losses which would be generated over an equivalent length of .
substantially constant cross-section fluid passage having identical geometry, but being downstream of the inlet portion ; 12.
It is there~ore possible with the present invention to measure the flow rates of fluids wherein the usable output differential pressurej which is the measure of the laminar fluid flow rate through the apparatus, tends to more closel~
approach in magnitude, the pressure loss induced by the com-plete apparatus than for other known laminar flow rate measu-rement apparatus. Accordingly, an advantage of the present invention is the limited pressure loss imposed on the laminar fluid flow whose rate is being measured while an adequate out-put signal sensitivity to flow rate is ensured.
20. This advantage is particularly useful in applications-where the power loss, as indicated by the product of the pres-sure loss across the complete àpparatus and the flow rate through the apparatus, must be maintained small due to parti-cular application ~er availa~ilit~ constr~ints and where sizeable flow rate dependent output signal differential pressure is required for purposes of reducing the sensitivity re~uire-- ment of associatad indicating and slgnal transmitting appara-tus.
Typical applications where the use o~ the present : 3Q .invention has particular advantages are:
1) ~as pipeline flow rate measurement .

~U~3~ :

2) cooling fluid flow ra~e measurement in combus-tion and power generation applications 3) intake air ~low ra-te measurement to internal ' combustion engines

4) process industry fluid transfer pipeline flow :- ' rate measurement Additionally, it has been found in practice that ':
;' minor boundary surface imperfections such as scratches~ burrs~ :
! ' dents, etc. in the immediate inlet region of a laminar flow 10 passage result in disproportionately large pressure drops additional to the pressure drop occuring when using a boundary ,' surface without such imperfections. In the present invention, :' the ~lared inlet portion has been found to have the effect of ~: very substantially reducing the pressure drop associated with . such inlet boundary wall imperfections as may occur as a result ' of practical apparatus fabrication and application. '.
The present invention, when used as a viscometer, '. .' provides a di~ferential pressure output signal that 'is propor~
tional to fluid viscosity for a given constant volumetric flow ';
20 rate of fluids on either a continuous or intermittent basis. . .:
- , Further, the larger wetted surface area of the lamlnar flow pas~age compared to the wetted surface area of laminar flow . passages having subst~ntiall~ circular cross-sections such as capillary tube viscometers~ facilitates fluid temperature re~ulation.
Further, it will ~e appreciated that the per~ormance ' ', of apparatus according to the present in~ention is not in general dependent upon the orientation of the'apparatus with respect to gravity or other accelerations in that compensation : 30 for orientation will not be required ,unless hydrostatic head , 29 '`

. .. . .

~ffects Y~ry si~nificantl~ eith.er along or across the flow length of the flu.id passage 2. For example, suc~ hydrostatic head variations might ~e encountered in the particular case of a large scale apparatus, according to tne present invention, operating with a high density fluid and oriented with the direction for fluid flow in the passage 2 being Yertical. An apparatus according to the present invention and having a plurality of similar fluid passages, such as will be described later with reference to.other figures, may also be affected by hydrostatic head variations in the same manner.
It will be further appreciated, and will become more apparent with following description of particular embodi-` ments of the present invention, that the apparatus may b~ very : economically fabricated using a suitable.assembly comprising plates, strips, discs and/or rings which have been edge pro-I filed by such well-known manufacturing techniques as rolling, extruding, coining, turning, milli:ng, tumbling, etc.
In Figures 2 to 4 similar parts to those shown in Figure 1 are designated by the same reference numerals and the previous description is relied upon to describe them.
In Figures 2 to 4 the casing 1 comprises a top plate 7 affixed to a bottom plate 8 by screws 9 which are screwed into threaded holes in the bottom plate 8. The top plate 7 is suitably sealed to the botto~ plate 8 to provide.ade~uate sealing of the fluid passin~ th~ough the fluid passage 2.
The apparatus according to the present invention, -: has been found in practice to have a useful output differential pressure dependency upon flow rate through the apparatus while exhibiting decreased pressure loss across the en~ire fluid 2~ passage 2 relative to other known laminar flow rate and/or viscosity measurement apparatus, such as the apparatus descri- :

- 30 - ~ :

.

. bed in the above noted patents, provided that:
1) portion 13, of the fluid passage 2, downstream and connected without discontinuity to the entry portion 12, has a substantially constant cross-section as previously de-fined, 2) the entry portion 12, of the fluid passage 2, leading to the substantially constant cross-section portion 13 of the fluid passage, is flared such that when usiny substan~
tiall~ pure water at 70F, for example distilled water, as a :; .
` 10 standard, the flared entry figure of merit, M, previously ~ -.. defined, shall meet the limiting criteria previously defined .
as per c) 2bove.
It has ~een found convenient in practice to numeri-cally evaluate the geometry of the flared inlet portion 1~ of the fluid passage 2 in terms of the limiting criteria as per provision c) above when the output differential pressure is .
measured by two static pressure taps, one of which is in com-munication with the inlet 4 to the flared entry portion 12 of :
fluid passage 2 and is arranged to measure the static pressure 2.' at or upstream of the inlet 4 and the other is located within the substantially constant cross-section fluid passage 13 at - ~ the p.reviou~ly defined distance Le downstream of the outlet :.
end of the flared portion of the said passage by means of the -: following procedure.

- . The ~ass 1O~ rate.oX substantiall~ pure water, such - as distilled water, at 7aF corresponding to Reynolds numbers of 1000 and 2000 within the substantially constant cross-section portion 13 of fluid passage 2 is determined using any ~ well known measurement means, such as a rotameter, or by ..
30 volumetric accumulation of the water flowing from the fluid passage 2 over a known time, for the particular geometry of ~ 31 - ;

. , . : ~

f~
fluid passage 2 where the viscosity and density of substantially pure water, for example distilled water at 70F may be taken, in English units to be 0.210 x 10 4 lbs. sec/ft2 and 62~4 lbs./ft3 respectively.
The output differential static pressures for water mass flo~ rates corres~onding to two Re~nolds nu~bers, in 'he substantially constant cross-section portion 13 of the fluid passage 2, for the appropriate breadth b to mean width h ratio, - are determined using well known precision pressure measurement 10 means such as manometers, pressure ~ransducers or similar means as will be known to those skilled in the art.
The entry portion figure of merit, M, is numerically evaluated from the output differential static pressure measure-ment and corresponding mass flow rate corresponding to the two Reynolds numbers for the appropxiate mean breadth b to mean width h ratio in accordance with the previously defined rela-tionship.
~ Should the magnitude of the previously defined fi~
gure of merit, M, violate the limi.ting criteria, then the said 20 criteria could be satisfied b..yl enlar~ing t~e profile defining t~e flar~d entr~-por~on 12 ei~èr ~lt~ `or wl~th-out alter;ng . the shape of the contour of the ~lared entrance portion 12.
The fluid static pressure tap 11 is located within the substantially constant cross-section portion 13 of passage 2 and downstream of fluid pressure tap 10 and preferably as close as possible to the vutl~t. end 6 o~ the.constant cross-section poxtion 13 of fluid passage 2 wlthin the. constraint of practical fabrication limitations. The position of the fluid static pressure tap 10 is chosen to be within the laminar 30 flow ~luid passage 2 as pre~iously described with reference . .
to Flgure 1. ~
... . .
In Figures 5 to 16 there are shown cross-sectiona~ ~ ~

: - 32 - i :
.' ',' ~ .
.. , . : . .

~t3~

side views of a number o~ laminar fluid flow passages, each having a different conflguration of entry portion and wherei;n . .
: similar parts to those sho~n in Figure 1, are designated by the same reference numbers and the previous description is relied upon to describe them.
- In Figure 5, there is shown a fluid passage 2 having ~ :

an inlet portion which has an inwardly extending lip 90 such as might be produced by a metal shearing process and which would not meet the criteria or figure of merit, (M), due in part to .;~
0 excessive flow velocity gradients in the immediate vicinity of the lip and due in part to the non-symmetry of the entran- . :
`ce ~low. . ; ~.
In Figures 6 and 7 the lip 90 has been rounded but ; would still not meet the criteria for the figure of merit, M, for the same reason as given for Figure 5.
.1 In Figure 8 there is shown a fluid passage 2 having a squared inlet portion, and which would not meet the criteria for the figure of merit, M, even though the flow velocity gradient~ in the vicinity o:E the squared corners are reduced relative to those gradients associated with the inlet por-tion shown in Figure 5 and the entrance ~low is symmetrical.
In Figure 9 there is shown a ~luid passage 2 having an inlet portion with the lower portion of the lip rounded and ~:~ the upper portion o~ the lip squared and which would not meet the cxiteri~ or the fi~ure of merit~ M, due in part to non-symmetry. of entrance flo~ and in part due to the high flow velocity gradients in the vicinity of the squared corner~ .
..
In Figure 10 there is shown a fluid passage 2 in accordance with the present invention having a radiused flared ~ 30 entry portion. Any radii r will give an improvement over the squared inlet portion shown in Figure 8. -1:

In Figure 11 there is shown a fluid passage 2 in - - 33 - .:~
.
., .. , . , . . . ~ , ,: . . ~
. . . : ', ' . ' ' . . '' , :' . ' :, ' ': '. '' ' , ' accordance wi.th~t~e present inyention having a chamfered inlet portion. Any dept~ d wi.ll gi~ve an i`mprovement over the squared inlet portion shown in Figure 8.
In Figure 12 there is shown a fluid passage 2 acc~r-ding to the present invention having a chamfered inlet portionwith the upstream end of the chamer rounded. Such rounding o~ the inlet end of the entry portion would further improve the figure of merit relative to an entry portion of the type - shown .in Figure 11 having the sa~e chamfer~
`10' . In Figure 13 there is shown a fluid passage 2.in accordance with the present invention having a chamfered outlet portion with the downstream end of the chamfer rounded. Such rounding o~ the outlet end o~ the entry portion would further improve the figure of merit relative to an entry portion of the type shown in Figure 11 having the same chamfer.
In Figure 14 there is shown a fluid passage 2 accor-ding to the present invention having a chamfered inlet portion . .
which is rounded on both the upstream and.downstream ends.
Such rounding of the inlet and out]Let end o the entry portion 20 would further improve the fi.gure of merit relative to entry portions of both of the types shown in Figure 12 and 13 and having tXe same chamfer~
In Pigure 15 there is shown a fluid passage ~ accor- .
ding to the present invention having a double chamfered inlet ~:
portion with the upstream angle having a steeper angle than the downstream chamfer. Such double chamering of the inlet :
portion would also improve the figure of merit relative to the entry portion in Figure 11 pro~ided that the angle o the ~
second chamfer is not steeper than the angle of the sin:gle ::

. -3~ chamfer of Figure 11.

.. In Figure 16 there is shown a flared entry portion ~'~

...
: :

3~
in accordance with the presen-t invention, where the radius of curvature of the flare chanyes in magnitude over at least a portion of the inle-t length. The flow velocity gradients throughout the flared entry portion may be minimized by appro-:.pri~tely contouring the inlet portion in this ~anner, the contour of which may be determined by tests.
In practice it has been found that a gradual and continuous increase in the radius of curvature of the flare in - the direction for fl~id flow gives good results in terms of 10 the figure of merit, M.
In Figures 17 to 19 similar parts to those shown in Figure 1 are designated by the same reference numerals and the previous description is relied upon to describe them.
There is shown in Figures 17 to 19 three views of an apparatus for flow rate and~or YiSCosity measurement of fluid having a plurality of substantially identical flow passages.
The apparatus comprises a casing generally designated 31, a plurality of fluid passages typically designated 2, a whole fluid inlet area 33 which may be exposed to a source of pres-20 surized fluid, which may be an ambient fluid such as the at-mosphere, and forming a substantially unobstructed flow path ~or fluid to the whole area of the individual inlet ends 4 to the said fluid passage where the said inlet area 33 is nor-mal to the mean direction, as shown ~y arrows 14r of flow in the fluid passages 2, and a whole fluid outlet area 35 for-ming a substantially unobstructed flow path for fluid from the whole of the individual outlet ends 6 of the fluid passages 2 where the said outlet area 35 is normal to the mean direction for flow of fluid 14 in fluid passage 2, the whole outle~
3D area 35 which is exposed to a sink for fluid that is at a pressure lower than that of the pressurized fluid at the fluid .
.: . . : - : . ~ -...................... . . .
.

-inlet area 33, such that there is a flow o~ fluid through passage 2 in the direction of arrows 14, ànd having a top co-ver plate 32, a bottom cover plate 34 and alternate shims 36, and separator plates 37, which together form inlet area 33 and outlet area 35 and the pluralit~ of fluid passages 2 for lami-nar flow of fluid therethrough in the direction shown by arrows 14. The cover plates 3~ and 34, shLms 36 and separator plates 37 are located relative to each other, as shown in Figures 17, 18 and 19 and are cl~mped together in ~ fluid 10 tight manner b~ means o screws 38 threaded into bottom plate 34.
In operation, pressurized fluid from a source (not :~ shown) is supplied to the whole of thè inlet area 33 of the casing 31 and fiows through thè individual inlet ends 4 of the ~luid passages 2, through the inlet portion12 o the fluid passages 2 and through the substantially constant cross-section portions 13 of the fluid passage 2 and through the individual passage outlet ends 6 to the whole outlet area 35 and to a fluid sink (not shown~
~ , . . ;
.~ 20 The separator plates 37 are pro~iled along their ~ -upstream edges 39 to form, the flared entry portion 12 to the ~.~
.
substantially constant cross-section portion 13 of the fluid :
passages 2; as shown in Figure 18. It will be appreciated that although the profile of the inlet portion 12 of the fluid passage 2 is, in general, similar to that shown in Figure 1, : : :
: the profile o the flared inlets could be any other suitable : :

shape provided the flared entry portion 12 of the fluid passages 2 meets the ~igure of merit M, criteria previously definedO : ~
~here is shown in Figures 17, 18 and 19 an upstream : -stati~ pressure tap 1~ and a ~ownstream static pressure tap 11 -.

- 36 - : ;

and wherein the downstream static pressure tap 11 is located ' ..
as close as possible to the outlet end 6 o~ one o~ the constant '~
cross-section portions of one of the fluid passages 2 within the constraint of practical fabrication limitations. ~ :
The upstream fluid static pressure tap 10 is located :. within the fluid passage 2 and upstream of fluid static pressure .
.; tap 11 and preferably at a minimum distance from the inlet end . 4 of the fluid passage 2 such that when using su~stantiall~
pure'water, for example distilled water~ at 70F as a.standard 10 then the upstream pressure tap figure of merit,. T, previously ~ defined, conforms with the previously given limit.
. .
In the apparatus shown in Figures 17, 18 and 19 the differential pressure between static pressure taps 10 and 11 as measured by a differential pressure sensing means (not shown~ is a proportional ~easure o~ the fluid flow rate ~r viscosi~y of the fluid passing through the apparatus from the ; whole inlet' area 33.to the whole'outlet area 35. Additionally~ .
in this multipassage'emb.odLment of the present invention the . ' .
pressure loss across the entire apparatus from inlet area 33 to 20- outlet area 35 is appreciably reduced relative to apparatus without such a flared inlet section by the use of the flared inlet section in accordance with the present invention.
:In Figure 20 similar parts to those shown in Figu- .:
~res 17, 18 and 19 are designated by the same reference nume~
'~ rals and the same description is relied upon to describe them. ^' :
~ Figure 20 is a cross-sectional side view of an appa-.. ratus similar to that shown in Figures 17, 18 and 19 except .
that the static pressure taps 45 and 46 have a diameter several ~: -times the lesser dimension of the cross-section o~ the subs-3~ tantially constant cross-section portion 13 of fluid passage 2 normal to the direction for fluid flow therethrouc~h and both ' ~:
' ' , ' ' ' ' , ~ ', ~. '': . ' ''' "

pressure taps are shown extending through the separator plates 37 such that each passage 2 .is in communication with the adja-cent passage at each of the pressure taps. Such communication of the pressure taps with all of the fluid passages 2 minimizes the efects of manufacturing tolerance deviations between the flared inlet portions and substantially constant cross-section portions of the fluid passages 2. Further, each of the pressure taps may be in communication with from one to all of the fluid passages 2.

: 10 In Figure 21 similar parts to those shown in Figures 17 to l9 are designated by the same `reference numerals and the previous description is relied upon to describe them.
In Figure 21 there is shown an apparatus similar to that shown in Figures 17 to 19 except that there is shown an upstream total pressure probe 50 and a downstream total pressu- : -re probe 51 whose inlets are located within at least one of the fluid passages 2 in accordance with the same criteria used :
to locate the static pressure probes 10 and 11 describèd with ;~

reerence to and shown in Figures 17 to 19. .
The embodiment shown in Figure 21 operates in the ; ;
same manner as the.embodiment described with reference to ." . .. , ~ - .
. Figures 17 to 19 and the output differential pressure is mea~
~.
sured in the same.manner and gives the same output propor~
~ionality to measured characteristic as the apparatus descri~
.~ bed with reference to Pigures 17 to 19~ .:
It will be appreciated that with any of the apparatus shown in Figures 17 to 19, 20 or 21~ or with an apparatus similar to that shown in these figures but having a different number of parallel and identical fluid passages 2~ the static :-.. 30 pressure taps or total pressure probes could be located within any one or any number of the flow passages 2 in a particular - 38 - .:
. .

.

:
3'~

apparatus because both the static pressure gradient an~
the total pressure gra d ie n t in the direction for flui~
flow 14 within all the fluid passages will be essentially the same.
The embodiments of the present invention described with reference to any of Figures 17 to 21 when used as a vis-cometer provides a differential pressure output signal that is proportional to the absolute viscosity of the fluid passing therethrough for a g.iven volumetric flow rate of fluids. Fur-10 .ther the large surface area of the fluld passage 2 of the present invention, in.contact with the fluid~ facilitates temperature regulation of the fluid flowing therethrough.
In Figure 22 similar parts to those shown in Fiyure .. . . . . . . ~
; . 21 are designated by the same reference numerals and the pre-.. vious description is relied upon to describe them. : -,.
A specific total head pressure probe configuration is shown in Figures 22 and 23. A total head probe 52, .:
is fixed within the apparatus by some suitable means such as a screw threaded plug. 54, threaded into the aperture 53 in . 2~ cover plate 32, and sealed therein by an 'O'-ring 55, and :
.. passing through separator plates 37 so-as to -traverse the ~:
~ . .
.~. fluid passages 2. A narro~ longitudinal slot 56 is cu~ along a portion o~ the length of probe.52 z~d a ~ectLon tnr.ough the slotted tube is shown in Figure 23. The probe ~2 is lo-cated such that the slot 56 is oriented towards and is essen- .
tially perpendicular to the fluid flow direction within the fluid passages 2, as shown by the arrows 14. Two such probes are particularly useful in detecting the total pressure di~fe- :

rential between any given locations within one or more identi-30 cal flow passages with configurations of the apparatus as shown in Figure 21~ or in configurations similar to t.hat shown _ .

in Fi~ure 21 but hav:ing a d.ifferent .nu~ber of identlcal fluid passages than are shown in Figuxe 2l It will be appreciatecl tha~ total }lead probe 52 need not be circular in cross~section as s~own in ~'igure 2~, but ma~ have other cross sections such as the ellj.ptical sec tion as shown in Figure 24, where ~imilar pa.~.s as shown in Figure 22 are rlesigna~ed b~ the same xeference numerals and the pxe~vious descripti.o.n .is rel.iecl upon to descri~e them~
In Figures ~5 ~nd 2~ I.here is shown an apparatus or measuring the viscosit,y or elOw xa-te of a fluid flowlng ther~
through comprl.sing a matxix of cons-~ant cx~ss--section fluid '~
passages ~9, which are rectanyular in cro~s--section, as defined -by boundar.,~ walls 67 and 68 suitah.ly bonded, fixed, or clamped together'and locatecl w:ithi.n a ci.rcular ,pipe 62 provi.ded for the entr,y and exhaust of flui.d elOwing ~hrou~h the rnatrix 60.
The upstream edges o the sepa:ra~o.r plates 67 and the hat sec- :
tioned spacer plates 68 ha~e an ed~e contour 70 as shown in .
enlarged view in E'igure 27 to provicle a flared inlet simi.lax to the flared inlet 12 shown in Fi.gure l~ leading to each of ,:~.
the substantiall~ co.nstant cross--~ect.io~ poxtion of fluid pas~
., , ,,. sages 69~ Two suitab.le pressuxe pxobes ~, which are similar ~.
' to one another, are located a:l.ollg -the l~n~th of the matrix 60 :~ :
in the direct.ion fo.r lami.nar'lu.i.c1:~ow t~erethrou~h in a man ner similar to those p.ressure proh~s ~e~c.rihed with referen ce to Figures 17 to 24 and are prov.ided for the measurement of " differential. pressuxe which is propox~ional to the viscosîty or fluid flow xate of ~he fluid flow.i.ng through the matrix.
It will be :I'.urther app.rec.ia~ed ~hat a 1uid passage matrix such as that shown in F.i(~lre ~5 and deslgnated 60 may 30 comprise su~ a'hly shapecl plates and~o.r ~pacers so as to deine fluid passages havi.ng ~i~'exe.~;: cross~sectlons to the ross~

~ ~1 0 ~

.

sections shown in Figure 26, such as the fluid passages 73 having trapezoidal cross-section shown in Figure 28 where the fluid passage defining plates have an edge contour 70 such as shown in Figure 27 to provide the flared inlet to each of the fluid passages.
~ t will be ap~reciated that the fluid passage matrix 60 shown in Figure 25 mast comprise suitable edge profiled and formed spacers and/or plates so as to defi.ne f.l~id passages having two parallel opposed major boundary sur~ace portions ; 10 but with cross-sections other than those designated 69 in Figure 26 and 73 in Figure 28.
There is shown in Figures 29 and 30 a portion o~ à :
matrix of small fluid passages, such as that designated 60 in Figure 25, comprising spacer plates ~0 separated by shims 81 :,.......... . .
.where such shims are located relative to the plates 80 and to each other by pins 82 so as to form thin rectangular fluid .-~
passages 83 ~or the laminar flow of fluid therethrough. The upstream edges of spacer plates 80 are sui.tably contoured and : the upstream ends 84 of the shims 81 are suitably profile~d as shown in Figures 29 and 30 so as to form a flared inlet region `~ 85 of the fluid passage 83 in accordance with the present in- ~-vention. It will be appreciated that the shims 81 need not necessarily be profiled~
In Figures 31 and 32 sLmilar parts to those shown in Figures 29 and 30 are deslgnated by the same reference numerals ~:
and the previous description is relied upon to describe them.
In Figures 31 and 32, a portion of a matr.ix of small fluid :~
passages is shown which has passages similar to those shown in Figures 29 and 30 but where the shims 81 are posltioned one . :
relative to another by means of interconnecting member 86 which - may be suitably attached to or may be integral with shims 81, 3~
the integral embodiment of the interconnecting member 86 and shims 81 being shown in Figures 31 and 32. The shims are pro-filed at the inlet o~ the passages such that, when combined ...
with the edge contoured spacer plates'80, the resultant pàss,a-ges for laminar fluid flow therethrough are in accordance with-the present invention. It will be further appreciated that the interconnecting member 86 when sufficiently thin relative to the '~
plate~ 80 so as not to impede the inlet flow to the passages 83, .' . may be located upstream of the fluid flow passages as shown in 10 Figures 31 and 32 or may be located downstream of the outlet from the fluid passages as shown in ~igure 37. .
- In Figuxe 33 ~nd 34 si,,mil~r p~rts to tho~e shQ~n .. in Figures 3I and 32 are designated by the same reference numerals. ' ' and the previous description is relied upon to describe them. ' :~
In Figures 33'and 34 there are shown portions o~ plates 80 ,' for forming an annular matrix of small fluid passages in '.. ' ';' contrast to the parallel location of the fluid passages shown in Figures 31 and 32 and where the shLms 81 are integral with . -:
the spacer plates 80 in contrast with the separate shims and plates shown in Figures 31 and 32. The shims are contoured ' ; at the inlet o the passages to provide flared entry poXtiQnS.

.. . . : ~ ', .
: The spacer plates 80 shown in Figures 33 and 34 may '' b~ a strip member which is substantially straight in plan view '~. ' .' or may be a segment of an annulus in plan view as shown in ~ .

; Figure 33, or may be a complete annulus in plan view such that -.' the matrix of fluid passages will have the form of a hollow .~. cylinder when the plates 80 are stacked in layers about a com-. mon axis of symmetry.

' In Figures 35 to 38 similar parts to those shown in ; 30 Figures 31 and 32 are designated by the same reference nume-rals and the previous description is relied upon to describe_ .''. ' . . . .
- 42 - : .

..
.. . . ~ . . . . . .

them. In the embodiments shown in Figures 35 to 38 both the shims 81 with their integral interconnecting ~ember 86 and the spacer plates 80 are shown as a sector o~ an annulus in plan view, wherein the shim portions 81 are tapered in plan view such that the rectangular fluid passage 83 formed by the shLms 81 and spacer plates 83 are o~ substantially constant . cross-section downstream o the entry portion of the passagP.
- In Figures 35 and 36 there is shown apparatus having the interconnecting member 86 for shims 81 upstream o~ the inlet to 0 fluid passage 83. In Figures 37 and 38 there lS shown appa-ratus having the interconnecting member 86 for shims 81 downs~ ~ :
tream of the inlet to the fluid passage 830 It will be appre-ciated that the spacer plates and shim ring assemblies could have the shape of a complete annulus in plan view such that the matrix o~ fluid passages will ;lave t~e form o a hollow cy-lind~r w~en spacer plates 30 ana sh.ims &l with interconnecting mel~er 86 are:stacked in layers a~out a com~on axis of symmetry.
In Figure 39 similar parts to those shown in Figu-res 17, 18 and 19 are deslynated by the same reference numerals 20 and the previous description is relied upon to describe ~hem. :~
There is shown in Figure 39 a cross-sectional side ~ :
. .
view o~ an apparatus si~ilar to that shown in Figures 1,~ 18 ;:
and 19 having the substan~ially unobstructed inlet area 33 enclosed by an inlet cavity 47 and having the substantially unobstructed outlet area 35 enclosed by the outlet cavity 48.
The top cover plate 41 and the bottom cover plate 42 carry out the same function and are located relative to shims 36~
separator plates 37, by screws 38 to form a casing generally designated 49p which is similar ~o casing 31 described with ; 30 reference to Figures 17, 18 and 19. The top cover plate 41, bottom cover plate 42, shims 36, screws 44, and inlet plate 45 - 43 - :

combine to form an inlet cavity 47 wi~h inlet port 95 connected to a source of pressurized fluid (not shown~ The top coyer plate 41, bottom cover plate 42, shims 36, screws 44 and out~
. let plate 43 combine to form an outlet cavity ~8 with outlet - port 46 connected to a sink for fluid inducing a ~low of flui.d through casing 49.
In operation pressurized fluid from a source (not ~
shown~ is supplied to the inlet port 95, flows through the :
inlet cavity 47 to the unobstructed inlet area 33, through .
10 the fluid passages 2 to the unobstructed outlet area 35, :~ through the outlet cavit~ 48 and to the fluid sink through outlet port 46.
It will be appreciated that apparatus such as that ~ -described with reference to any of Figures 2, 3, 4, 17, 18, 19, 20, 21, 25, 29, 30, 31, 32, 33, 35 and 37 can have an in-! let cavity 47, and an outlet cavity 48 or either an inlet ca-vity 47 or an outlet cavity such as that shown in Figure 39. .:~
Referring to Figures 40 to 42 there are shown graphs ~:
of test results showing the pressure drop/flow rate characte- .
20 ristics of fluid passages having different entries. For all ~:
of the fluid passages b = 0.200 inches, h - 0.008 inches and Lc ~ 0.98 inches. The fluid used was air.
The fluid passage for Figure 40 had a square entry ~ .
as shown in Figure 8 and a figure of merit M of 0.729 was obtained.
The fluid passage for Figure 41 ~ad a radiused lnlet as shown in Fi.~re. 10 ~i~th a x~ s of 0.016 inches and a fi- ..
: gure of meri.t ~ of Q.417 was o~t~ined~
The fluid pas~age for Flgure 42 ~ad a chamfered in-30 let as shown in Figure 11 with a depth d of 0.0694 inches and a figure of merit M of 0.584 was o~tained. : :
... . .

For fluid passages having the rectangular cross-sec-tion of those used for the characteristics given in Figures 40 to 42 the figure of merit is given by .: M < 1.36 h which is 0.707 dh :
and it will be seen that this is exceeded by the figure of merit obtained for the squared inlet of Figure 40 while the -figures of merit obtained for the appropriately profiled en-tries of Figures 41 and 42 are less than 0.707 and so fall 10 within the scope of the present invention.
- It has been found in practice that to obtain the -most useful output differential pressure sensitivity for a gas such as air, the width h of the constant cross-sectional area portion of the fluid is typically less than 0.02 inches and the length is preferably at least twenty five times the . .
width h. However, the dimensions may be selected as required !- to provide adequate sensitivity for a particular application and a particular working fluid. :

~: :

.
~ .~

Claims (11)

CLAIMS:

1. An apparatus for measuring the flow rate and/or viscosity of a fluid comprising:
a) a casing having a fluid passage, which is elonga-ted in cross-section normal to the mean direction for fluid flow therein with two parallel, opposed major boundary surfa-ce portions which are parallel in a plane normal to the mean direction for fluid flow therebetween, the fluid passage com-prising a flared entry portion and a portion having, in the mean direction for fluid flow therein, continuous boundary surface and a substantially constant cross-section, the flared entry portion being flared to decrease in width, without in-creasing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the portion having, in the mean direction for fluid flow therein, a con-tinuous boundary surface and a substantially constant cross-section, a fluid inlet to the casing and forming a substan-tially unobstructed flow path for fluid to the whole of an inlet area to the flared entry portion of the fluid passage, said inlet area being normal to the mean direction for flow of fluid at an inlet end of the flared entry portion, and fluid outlet from the casing and forming a substantially unobstructed flow path for fluid from the whole area of an outlet end of the fluid passage said outlet area being normal to the mean direction for flow of fluid at the outlet end of the fluid passage, and wherein b) the portion of the fluid passage having conti-nuous boundary surface and a substantially constant cross-sec-tion in the mean direction for fluid flow therein has a magni-tude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 1.5 to 1, and an area in any plane normal to the mean direction for fluid flow therein which does not vary more than in the region of 2% from the mean area calculated in this manner for substantially the whole length of the said portion having continuous boundary surface and a substantially constant cross-section, and wherein c) the geometry of the flared entry portion of the fluid passage is such that, with laminar flow being maintained in the whole of the fluid passage, using substantially pure water at 70°F as a standard, the flared entry portion has a "figure of merit", M which is calculated using consistent units from the relationship:

where, G2 - the mass flow rate of the substantially pure water through the fluid passage when the Reynolds number, Re, is at least 2000 in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, and the Reynolds number, Re, in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section is defined in consistent units by the relationship:

, where h = the width separating the parallel opposed major boundary surface portions, of the portion of the fluid passage having continuous boundary surface and a substantially cons-tant cross-section in the mean direction for fluid flow therein, ? = the mean velocity of the substantially pure water through the portion of the fluid passage having conti-nuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, ? = the density of the substantially pure water, µ = the absolute viscosity of the substantially pure water, .DELTA.E2 = a static pressure differential between the subs-tantially pure water at ox upstream of the fluid inlet to the casing and the substantially pure water within the fluid passa-ge at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G2 as previously defined immediately above and which is downstream of an outlet end of the flared entry portion by at least an amount Le and is determined in consistent units by the rela-tionship:
Le = 0.04 Re h when the Reynolds number, Re, is that where the flow rate is G2 as previously defined immediate-ly above in the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, K2 is a constant and is defined in consistent units by , where G1 - the mass flow rate of the substantial-ly pure water through the fluid passage when the Reynolds number Re, is less than G2 and is at least 1000 in the portion of the fluid passage having continuous boundary surface"
and a substantially constant cross-section in the mean direction for fluid flow therein, and .DELTA.E1 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within the fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G1 as previously defined immediately above and which is downstream of the outlet end of the flared entry portion by at least an amount Le as previously defined, and where the flared entry portion "figure of merit", M, is within the limits determined by the relationship in consistent units:

, where dh = the hydraulic diameter of the portion of the fluid passage having continuous boundary surface and a subs-tantially constant cross-section in the mean direction for the flow of fluid therein, and is defined in consistent units by, , where A = cross-sectional area of the portion of the fluid passage having continuous boundary surface, and a substantially constant cross-section, normal to the mean direction for fluid flow therein, C = wetted perimeter of the portion of the fluid passage having continuous boundary surface and a substantially constant cross-section, in a plane normal to the mean direc-tion for fluid flow therein, and where h is as previously defined, and d) fluid pressure detecting means in the casing for detecting a fluid pressure differential in the fluid passage, between spaced positions in the mean direction for fluid flow therein, at least one of the positions being in the portion having continuous boundary surface and a substantially cross-section, whereby e) the or each fluid characteristic to be measured is related to the pressure differential indicated by the fluid pressure detecting means and is deducible therefrom in a con-sistent manner for any given fluid when laminar flow is main-tained in the whole of the fluid passage.

2. An apparatus according to claim 1, wherein the flared entry portion is continuously curved in the direction for fluid flow.

3. An apparatus according to claim 2, wherein the flared entry portion has a gradual and continuous increase in radius of curvature in the direction for fluid flow.

4. An apparatus according to claim 2, wherein the flared entry portion is radiused.

5. An apparatus according to claim 1, wherein the flared entry portion is chamfered.

6. An apparatus for measuring the flow rate and/or the viscous characteristics of a fluid, comprising:
a) a casing having a plurality of substantially identical fluid passages, which are elongated in cross-section normal to the mean direction for fluid flow therein with each passage having two parallel, opposed major boundary surface portions, which are parallel in a plane normal to the mean direction for fluid flow therethrough, each fluid passage com-prising a flared entry portion and a portion having, in the mean direction for fluid flow therein, continuous boundary sur-face and a substantially constant cross-section, the flared en-try portion of each passage being flared to decrease in width, without increasing in breadth, in the mean direction for fluid flow therein and forming an unobstructed flow path to the por-tion, having in the mean direction for fluid flow therein, continuous boundary surface and a substantially constant cross-section, a fluid inlet to the casing forming a substantially unobstructed flow path for fluid to the whole of an inlet area to the flared entry portion of each fluid passage, for each fluid passage said inlet area being normal to the mean direc-tion for flow of fluid at an inlet end of the flared entry portion, a fluid outlet from the casing forming a substan-tially unobstructed flow path for fluid from the whole area of an outlet end of each fluid passage, for each fluid passa-ge, said outlet area being normal to the mean direction for flow of fluid at the outlet end of that fluid passage, and wherein b) the portion of each fluid passage having conti-nuous boundary surface and a substantially constant cross-sec-tion in the mean direction for fluid flow therein has a magni-tude of mean breadth which is at least as large as that given by a mean breadth to mean width ratio of 1.5 to 1, and an area in any plane normal to the mean direction for fluid flow there-in which does not vary more than in the region of 2% from the mean area calculated in this manner for the whole length of the said portion of that fluid passage having continuous boun-dary surface and a substantially constant cross-section, and wherein c) the geometry of the flared entry portion of each fluid passage is such that, with laminar flow being maintained in the whole of each fluid passage, using substantially pure water at 70°F as a standard, the flared entry portion of each fluid passage has a "figure of merit", M which is substantially the same for each fluid passage and which is calculated using consistent units from the relationship:

where, G2 = the mass flow rate of the substantially pure water through each of the fluid passages when the Reynolds num-ber Re, is at least 2000 in the portion of each fluid passage having continuous boundary surface and a substantially cons-tant cross-section in the mean direction for fluid flow there-in, and the Reynolds number, Re, in the portion of each of the fluid passages having continuous boundary surface and a substantially constant cross-section is defined in consistent units by the relationship:

, where h = the width separating the parallel opposed major boundary surface portions, of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, ? = the mean velocity of the substantially pure water through the portion of each of the fluid passages having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, ? = the density of the substantially pure water, µ = the absolute viscosity of the substantially pure water, .DELTA.E2 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within each fluid passage at a position within the portion having continuous boun-dary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G2 as previously defined immediately above and which is downstream of an outlet end of the flared entry portion by at least an amount Le and is determined in consistent units by the relationship:
Le = 0-04 Re h when the Reynolds number, Re, is that where the flow rate is G2 as previously defined immediate-ly above in the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein, K2 is a constant and is defined in consistent units, , where G1 = the mass flow rate of the substantially pure water through each of the fluid passages when the Reynolds num-ber Re, is less than G2 and is at least 1000 in the portion of each fluid passage having continuous boundary surfaces and a substantially constant cross-section in the means direction for fluid flow therein, and .DELTA.E1 = a static pressure differential between the substantially pure water at or upstream of the fluid inlet to the casing and the substantially pure water within each fluid passage at a position within the portion having continuous boundary surface and a substantially constant cross-section in the mean direction for fluid flow therein and where the flow rate is G1 as previously defined immediately above and which is downstream of the outlet end of the flared entry portion by at least an amount Le as previously defined, and where the flared entry portion "figure of merit", M, is within the limits determined by the relationship in con-sistent units:

, where dh = the hydraulic diameter of the portion of each fluid passage having continuous boundary surface and a subs-tantially constant cross-section in the mean direction for the flow of fluid therein, and is defined in consistent units by, , where A = cross-sectional area of the portion of each fluid passage having continuous boundary surface, and a subs-tantially constant cross-section, normal to the mean direction for fluid flow therein, C = wetted perimeter of the portion of each fluid passage having continuous boundary surface and a substantially constant cross-section, in a plane normal to the mean direc--tion for fluid flow therein, and where h is as previously defined, and d) fluid pressure detecting means in the casing for detecting a fluid pressure differential in at least one of the fluid passages between spaced positions in the mean direc-tion for fluid flow therein, at least one of the positions, being in a portion of that fluid passage having continuous boundary surface and a substantially constant cross-section, whereby e) the or each fluid characteristic to be measured is related to the pressure differential indicated by the pres-sure detecting means and is deducible therefrom in a consistent manner for any given fluid when laminar flow is maintained in the whole of each fluid passage.

7. An apparatus according to claim 6, wherein each flared entry portion is continuously curved in the direction for fluid flow.

8. An apparatus according to claim 7, wherein each flared entry portion has a gradual and continuous increase in radius of curvature in the direction for fluid flow.

9. An apparatus according to claim 8,wherein the flared entry portion is radiused.

10. An apparatus according to claim 6, wherein the flared entry portion is chamfered.

11. An apparatus according to claim 6, wherein the flared entry portion has a double chamfer.