## Abstrict A flow meter includes a variable area obstruction mounted in a
conduit and a differential pressure transducer having its two ports
mounted on opposite sides of the obstruction in fluid communication
with the fluid flowing through the conduit. The variable area obstruction
is formed of one or more flexible leaves which extend into the flow
stream and are deflectable under the influence of fluid pressure,
such that an increased flow rate increases the deflection of the
leaves and decreases the area of the obstruction.
## Claims The invention claimed is:
1. A flow meter comprising:
a. transducer means for sensing a pressure differential between
a first port thereof and a second port thereof,
b. a conduit with said first port of said transducer means connected
at a first location in said conduit and in fluid communication with
fluid flowing therethrough, the fluid at a second location in said
conduit being connected to and in fluid communication with said
second port, and
c. an obstruction mounted in said conduit between said first location
and said second location, said obstruction comprising a plurality
of independently flexible spring fingers extending initially in
a plane transverse to the flow of fluid in said conduit each of
said fingers being compliant to said fluid flow and deflected in
response to one parameter of said fluid flow whereby said obstruction
to said fluid flow varies in response to said one parameter.
2. The flow meter of claim 1 wherein said element is subject to
flexure in response to the velocity of the fluid in said conduit.
3. The flow meter of claim 1 wherein the spring constant of said
spring fingers is of a value to provide a flow rate-differential
pressure relationship which is approximately linear.
4. The flow meter of claim 1 wherein the spring constant of said
spring fingers is of a value to provide a flow rate which is approximately
proportional to the square of the differential pressure.
## Description BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates generally to a flow meter, and more particularly
to a variable area obstruction in a conduit for use with a pressure
transducer to measure the flow rate of a fluid in that conduit.
2. Prior Art
A number of different types of flow meters are presently available
for measuring the flow rate of a fluid in a conduit. These flow
meters can be classified broadly into two groups; namely, the group
which presents little or no interference to the flow stream and
the group which has a significant influence on the flow stream.
The first group of devices which present relatively little or no
interference to the flow stream are relatively elaborate and expensive
systems. The present invention is concerned with the second group
of flow meters which are less elaborate and considerably less expensive,
but present some significant amount of interference to the flow
stream.
This second group of flow meters includes the type which is position
and/or displacement oriented and the type having no moving parts.
The position and/or displacement type of flow meter includes some
movable part which changes its position, displacement or velocity
in response to the flow of fluid with respect thereto. Examples
of such compliant type of flow meters are the turbine flow meters,
the variable capacitance flow meters, and the oscillating vane flow
meters. These compliant type of flow meters all have the usual problems
associated with moving parts. Furthermore, because of the relatively
large pressure drop produced by these flow meters, they are normally
not employed in a closed flow system, but rather in an open flow.
The second group of flow meters having no moving parts employ some
type of obstruction in the flow stream and a differential pressure
transducer for measuring the difference in fluid pressure across
the obstruction. The obstruction in this type of flow meter has
been formed in the past of either a plate having a fixed area orifice
therein, a venturi, or a flow nozzle. The pressure differential
across the obstruction is a measure of the flow rate of the fluid
passing through the conduit. Under constant pressure and enthalpy
conditions, this pressure differential is proportional to the square
of the flow rate of the fluid in the conduit. This square law relationship
is highly undersirable, since the error at the lower flow rates
is a greater percentage of the flow rate than the error at the higher
flow rates. It is generally desirable, when measuring flow rates,
to have an error which is equal at both the lower flow rates and
the higher flow rates. When flow rate is to be employed for measuring
accumulated volume, it is desirable to have an error at the lower
flow rates which is less than that at the higher flow rates, such
that the error associated with accumulated volume is constant with
changes in the flow rate.
SUMMARY OF THE INVENTION
It is, therefore, an object of the present invention to provide
a flow meter of the type employing an obstruction in a conduit and
a pressure differential connected across the obstruction, in which
the area of the obstruction in a plane transverse to the flow of
fluid in the conduit is variable with fluid pressure exerted thereon.
Another object of the present invention is to provide such a flow
meter in which the area of the obstruction in a plane transverse
to the flow of fluid in the conduit is directly proportional to
the fluid pressure exerted thereon.
Still another object of the present invention is to provide such
a flow meter in which the flow rate of the fluid in the conduit
is approximately linearly proportional to the pressure differential
across the obstruction.
A further object of the present invention is to provide such a
flow meter in which the flow rate of the fluid in the conduit is
approximately proportional to the square of the pressure differential
across the obstruction.
These and other objects of the present invention are attained by
a flow meter which includes an obstruction mounted in a conduit
and a differential pressure transducer connected to that conduit
to measure the pressure differential across the obstruction, with
the obstruction having an area in a plane transverse to the flow
of fluid in the conduit which is variable in response to the fluid
pressure exerted thereon.
The invention, however, as well as other objects, features and
advantages thereof will be more fully realized and understood from
the following detailed description, when taken in conjunction with
the accompanying drawings, wherein:
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a view partially in section of a flow meter of the type
which the present invention is concerned with.
FIG. 2 is an elevational plan view of a variable area obstruction
which can be employed in the flow meter illustrated in FIG. 1 and
which is constructed in accordance with the principles of the present
invention.
FIG. 3 is a sectional view taken generally along line 3--3 of FIG.
2.
FIG. 4 is a sectional view similar to that illustrated in FIG.
3 but with the obstruction in a partially flexed state.
FIG. 5 is an elevational plan view of another embodiment of the
variable area obstruction which can be employed in the flow meter
illustrated in FIG. 1 and which is constructed in accordance with
the principles of the present invention.
FIG. 6 is a sectional view taken generally along line 6--6 of FIG.
5.
FIG. 7 is a sectional view similar to that illustrated in FIG.
6 but with the obstruction in a flexed state.
FIG. 8 is a graph illustrating the pressure versus voltage relationship
of the pressure transducer illustrated in FIG. 1.
FIG. 9 is a graph illustrating the pressure versus flow rate relationship
of a prior art flow meter of the type illustrated in FIG. 1.
FIG. 10 is a graph illustrating the pressure versus flow rate relationship
of a flow meter constructed in accordance with the principles of
the present invention.
FIG. 11 is a graph illustrating the pressure versus flow rate relationship
of another flow meter constructed in accordance with the principles
of the present invention.
Like reference numerals throughout the various views of the drawings
are intended to designate the same or similar elements.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
With reference to FIG. 1 there is shown a flow meter for measuring
the flow rate of a fluid passing through a conduit 10. An obstruction
12 is mounted in the conduit and is formed of a circular plate having
a central aperture 14 therein. A differential pressure transducer
16 has a pair of ports 18 and 20 mounted on opposite sides of the
obstruction 12 and in fluid communication with the fluid passing
through the conduit 10. As is well known, the pressure transducer
16 provides an output which is directly proportional to the flow
rate of the fluid passing through the conduit 10. Briefly, however,
this type of flow meter operates in the following manner.
When the obstruction 12 is provided in the stream of a fluid passing
through the conduit 10 as shown in FIG. 1 a boundary condition
will result in the downstream portion of the fluid stream, as represented
by the phantom lines designated with the reference numeral 22. The
pressure of the fluid between the phantom lines 22 will be equal
to the pressure of the fluid upstream of the obstruction 12. However,
the pressure of the fluid between the phantom lines 22 and the obstruction
12 in an area called "curl" and designated with the reference
numeral 24 will be equal to the pressure of the fluid at the opening
14 in the obstruction 12.
It will be noted that the port 18 of the differential pressure
transducer 16 is in fluid communication with the fluid upstream
of the obstruction 12 and that the port 20 of the transducer 16
is in fluid communication with the curl portion of the fluid in
the conduit 10. The differential pressure transducer 16 provides
an output corresponding to the difference between the pressure of
the fluid at the port 18 and the pressure of the fluid at the port
20. This output is measured and displayed by a meter 26 which can
be calibrated to read in units of flow rate, such as gallons per
minute. Examples of differential pressure transducers are disclosed
in the first edition of a catalog and handbook of Integrated Pressure
and Temperature Transducers published by National Semiconductor,
Inc., and dated August 1974.
Under constant temperature and enthalpy conditions, the differential
pressure, .DELTA.P, measured by the transducer 16 can be expressed
by the following expression. ##EQU1## where V.sub.1 is the velocity
of the fluid at the opening 14 V.sub.2 is the velocity of the fluid
at the port 18 and g is the acceleration of gravity, 32.2 fps.sup.2.
The flow rate, Q, can be expressed by the equation,
where A.sub.1 is the transverse cross sectional area of the opening
14 and A.sub.2 is the transverse cross sectional internal area of
the conduit 10 or the area of the fluid in a plane transverse to
the flow stream at the port 18.
By substituting equation (2) into equation (1) and rearranging,
the flow rate Q can be expressed as, ##EQU2##
Since the two areas A.sub.1 and A.sub.2 are known, the flow rate,
Q, of the fluid passing through the conduit 10 can be determined
by measuring the pressure differential between the ports 18 and
20.
It can be appreciated from the equation (3) that the flow rate
is proportional to the square root of the differential pressure
across the obstruction 12. This square law relationship between
the flow rate and the differential pressure produces an undesirable
condition in most applications of the flow meter, as will be explained
below.
FIG. 8 is a graph illustrating the pressure versus voltage relationship
of the pressure transducer 16 illustrated in FIG. 1 with the differential
pressure represented on the axis of abscissas and the voltage output
of the transducer 16 represented on the axis of ordinates. The line
28 represents the ideal pressure versus voltage relationship of
the pressure transducer 16 and the dotted lines 30 and 32 represent
the upper and lower limits of the error which can be expected. If,
for example, a voltage V.sub.1 is generated at an output of the
pressure transducer 16 under certain constant flow rate conditions,
because of the tolerances of the pressure transducer 16 that voltage
may represent a pressure differential having a range from P.sub.1
to P.sub.2. If, under different, but constant flow rate conditions,
a voltage V.sub.2 is generated at an output of the pressure transducer
16 such voltage may represent a range of differential pressures
from P.sub.3 to P.sub.4. Because of the linear relationship of pressure
and voltage illustrated in FIG. 8 and the constant error across
the linear plot, the range from P.sub.1 to P.sub.2 is equal to the
range from P.sub.3 to P.sub.4. Accordingly, if an operator observes
a reading of V.sub.1 on the meter 26 he can expect the pressure
differential to be between the values P.sub.1 and P.sub.2 because
of this error. In a typical differential pressure transducer, the
output may have an error of plus or minus 0.15 volts, with an output
of 2.5 volts at the lower end of the curve and an output of 12.5
volts at the upper end of the curve.
FIG. 9 is a graph of the pressure versus flow rate relationship
expressed by equation (3) of a prior art flow meter of the type
illustrated in FIG. 1. The differential pressure sensed by the pressure
transducer 16 is represented on the axis of abscissas and the flow
rate of the fluid flowing through the conduit 10 is represented
on the axis of ordinates. The plot of the relationship represented
by equation (3) is shown by a curve 34.
The differential pressure P.sub.1 corresponds to a flow rate Q.sub.1
the differential pressure P.sub.2 corresponds to a flow rate Q.sub.2
the differential pressure P.sub.3 corresponds to a flow rate Q.sub.3
and the differential pressure P.sub.4 corresponds to a flow rate
Q.sub.4. It can be appreciated from FIG. 9 that the error of the
differential pressure transducer 16 will generate a relatively large
error at the lower end of the curve 34 and a relatively small error
at the upper end of the curve 34 since the range Q.sub.2 -Q.sub.1
is greater than the range Q.sub.4 -Q.sub.3. This condition is not
satisfactory for any known application of a flow meter. If it is
desired to measure flow rate, the preferred error profile is one
in which the flow rate error is constant along the entire range
of pressures. If it is desired to convert flow rate to accumulated
volume, the preferred error profile is one in which the flow rate
error is relatively small at the lower end of the pressure-flow
rate curve and relatively large at the upper end of that curve.
More particularly, when accumulated volume is desired, the percentage
of error along the entire range of pressures should remain constant.
The present invention overcomes this disadvantage of the fixed
area orifice of the prior art by providing an obstruction in the
conduit 10 which has an area in a plane transverse to the fluid
stream which is variable in response to fluid pressure exerted thereon.
As shown in FIG. 2 the obstruction 12 of the present invention
is formed of an outer rim portion 36 and a plurality of flexible
leaves 38 extending radially inwardly therefrom. The rim portion
36 is disposed for being secured to the inner surface of the conduit
10. The leaves 38 are flexible, such that when fluid pressure is
exerted thereagainst, they flex as shown in FIG. 4. It will be noted
in FIG. 2 that the ends of the leaves 38 form an opening 40. When
the fluid pressure exerted against the obstruction 12 is relatively
small or nonexistent, the leaves 38 are in their relaxed, unflexed
state, as shown in FIG. 3. Under such conditions, the opening 40
is relatively small and therefore, the area of the obstruction in
a plane transverse to the fluid stream is relatively large. However,
as the pressure of the fluid increases, with increased velocity
thereof, the leaves 38 begin to flex, thereby decreasing the area
of the obstruction in a plane transverse to the fluid stream.
If, for example, ##EQU3## then, from equation (3),
it can be appreciated that if the left hand side of equation (4)
is proportional to fluid flow, then a linear relationship exists
between fluid flow and differential pressure as expressed in equation
(5). Since fluid flow is variable, one of the quantities on the
left hand side of equation (4) must also be variable in accordance
therewith. This is accomplished by the variable area obstruction
of the present invention in which the area A.sub.1 varies with fluid
pressure.
A plot of equation (5) is illustrated in FIG. 10. As shown therein,
the error along the entire length of the linear curve is constant,
since Q.sub.8 -Q.sub.7 is equal to Q.sub.6 -Q.sub.5.
If, on the other hand, ##EQU4## then, from equation (3),
the plot of equation (7) is illustrated in FIG. 11. As shown therein,
the error at the lower end of the curve is considerably smaller
than the error at the upper end of the curve. It can be appreciated
from the above, therefore, that the area of the opening through
the obstruction 12 can control the relationship between flow rate
and differential pressure. By properly dimensioning the size of
the leaves 38 the area of the opening presented to the flow stream
by the obstruction 12 can vary to provide either a constant error
with changes in fluid velocity or a constant percentage of error
with changes in fluid velocity.
In a theoretical analysis of an obstruction in a flow stream, an
obstruction similar to that illustrated in FIG. 2 was analyzed,
with the exception that it had only four leaves, with each leaf
occupying one quadrant of the area circumscribed by the rim 36
and each leaf terminated in a flat end, such that the opening 40
was square. Also, the leaves had a thickness of 0.005 inch and a
Young's modulus of 3.times.10.sup.7 pounds/inch.sup.2. The inside
diameter of the rim 36 was assumed to be one inch and the inner
end of each leaf was assumed to be 0.03 inch. The obstruction was
analyzed on the basis of each leaf representing a cantilever beam.
In this respect, therefore, several assumptions were made in the
analysis. However, it is not believed that these assumptions produced
any drastic change in the results of this analysis.
The results of this analysis are shown in Tables I and II.
TABLE I ______________________________________ DIFFERENTIAL AREA,
A.sub.1 PRESSURE, .increment.P, PSI SQUARE INCH, .times.10.sup.-.sup.3
______________________________________ 0 0.900 1 0.904 2 0.948 3
1.013 4 1.109 5 1.239 6 1.407 7 1.619 8 1.882 9 2.202 10 2.588 11
3.049 12 3.595 13 4.237 14 4.986 15 5.852 20 12.405 25 23.882 30
41.942 35 68.010 40 103.043 ______________________________________
TABLE II ______________________________________ DIFFERENTIAL FLOW
RATE, Pressure, .DELTA.P, PSI Q, GAL/MIN ______________________________________
0 0 1 .04285 2 .06355 3 .08317 4 .10513 5 .13132 6 .16336 7 .20304
8 .25231 9 .31312 10 .38792 11 .47933 12 .59029 13 .72412 14 .88429
15 1.07431 20 2.62960 25 5.66003 30 10.88900 35 19.07151 40 30.89064
______________________________________
It can be appreciated that the plot illustrated in FIG. 11 closely
approximates the values given in Table II. Scaling can be accomplished
by employing a "look-up" table, such as a read only memory,
when the flow meter of the present invention is used in a digital
readout system.
A second embodiment of the present invention is illustrated in
FIGS. 5 6 and 7 wherein the obstruction 12 includes an outer rim
portion 42 and a pair of rectangularly shaped leaves 44 and 46 secured
thereto. When the leaves 44 and 46 are in their relaxed, unflexed
state, they are shown in FIG. 6. However, under increased fluid
velocity and, therefore, increased fluid pressure, the leaves 44
and 46 flex as shown in FIG. 7 to increase the size of the opening
48 presented to the fluid stream.
It can be appreciated that the leaves 38 and the leaves 44 and
46 can be appropriately dimensioned to provide any desired result.
For example, the thickness of these leaves may vary from one end
to the other end thereof, such that a varying spring constant is
presented as flexure occurs. Also, any number of leaves may be provided
to form the obstruction 12. It can also be appreciated that the
openings 40 and 48 can vary considerably in size and in relationship
to the diameter of the rim portion 36. In this respect, the openings
40 and 48 can be reduced to zero by extending the free ends of the
leaves to a center point of the obstruction 12. The leaves 44 and
46 may also be extended to overlap one another, if desired. Also,
the edges of the leaves can be curled to any desired configuration
to control the spring constant thereof. The leaves can be fabricated
of any suitable material or layers of several material. It is to
be understood, of course, that a large variety of sizes and shapes
of leaves can be employed to provide the desired spring constant
thereto. Also, these leaves can be dimensioned such that the spring
constants thereof vary with changes in pressure exerted thereon. |