ME 304
Session # 4, Exp. #7
Venturi and Orifice Flow Meters
Performed by: Team A
John Brown
Mary Power
Mark Smith
Report Evaluation:
Submitted by: Mark Smith
Date: 1/13/2011
Comments:
Technical Content: (%)
Writing (%)
Combined Score:
Background and Theory
This laboratory investigates two types of flow meters that are commonly used in industry:
Venturi flow meter and orifice flow meter. The two flow meters represent so called
obstruction type flow meters, which measure flow rate indirectly by measuring the
pressure loss across a calibrated obstruction. In this way, a more difficult (and more
expensive) flow measurement is replaced with an easier (and less expensive) pressure
measurement. This is especially true for flow in pipes of large diameter.
The objective of this experiment is to measure the pressure drop P across the two flow
meters at various flow rates Q and to determine the calibration curves Q(P).
Principally, any calibrated obstruction could be used as a flow meter by measuring the
pressure drop pm across the obstruction. The most common obstructions used for this
purpose are Venturi nozzle, flow nozzle and orifice [1]. The flow rate through these
devices can be determined from [2]:
Q=
CA2
2p m
1 − ( A2 / A1 ) 2
(Eq. 1)
where A1 is the cross-sectional area before obstruction, A2 is the area at the smallest diameter, and
C is an empirical discharge coefficient.
2
Experimental Setup and Procedure
Schematic of the experimental setup used is presented in Figure 1. In the experiment,
centrifugal pump 5 drew water from water tank 6 and pumped it along the path indicated
with arrows. Valves 10, 11, 12, 16 and 44 remained fully open. Flow rate Q was
adjusted to the desired value using valve 52 and flow meter 5a, and pressure drop across
the orifice flow meter 7 and the Venturi flow meter 8 was measured with differential
pressure gages (not shown). The measurements were collected at eight values of flow
rate, ranging from 2 GPM to 12 GPM.
5a
Figure 1 Schematic of the experimental setup used.
3
Experimental Results
All experimental results are presented in Table A- 1 in the Appendix and the averaged
values for each flow rate are listed in Table 1. All values in Table 1 were converted to SI
units and are presented in Table 2.
Table 1 Averaged Measured Values
Q
(GPM)
2
4
6
7
8
9
10
12
ΔPV
(mbar)
1.0
7.4
18.1
22.9
31.0
39.2
48.3
57.9
Table 2 Averaged Measured Values in SI units
ΔPO
(mbar)
0.4
2.6
6.2
6.6
10.3
12.7
17.3
21.5
ΔPV
(Pa)
Q
(m3/s)
ΔPO
(Pa)
0.000126
100
40
0.000252
740
260
0.000379
1810
620
0.000442
2290
660
0.000505
3100
1030
0.000568
3920
1270
0.000631
4830
1730
0.000757
5790
2150
The data of Table 2 was used to create Figure 2, which graphs two calibration curves:
one for the Venturi flow meter Q(PV) and the other for the orifice flow meter Q(PO).
0.0008
0.0007
0.0005
3
Q (m /s)
0.0006
0.0004
Venturi
0.0003
Orifice
0.0002
0.0001
0
0
1000
2000
3000
4000
5000
6000
P V , P O (Pa)
Figure 2 Calibration curves for the tested Venturi and orifice flow meters.
The two solid lines in Figure 2 represent least square fits of the form Q = a P .
4
Discussion
Examining the data of Figure 2 one can see that the measured flow rate is proportional to
square root of the pressure drop in each device for both flow meters, which is consistent
with Eq. (1). It can also been observed that the proportionality constant a for the orifice
tested is about 100% higher than the corresponding constant for the Venturi flow meter.
It means that at a given flow rate, the pressure difference in the orifice flow meter is
about twice the corresponding pressure drop in the Venturi flow meter. This larger
pressure drop may be beneficial for measuring low flow rates.
The square root fits are not perfect and the measured data shows scatter from the trend
lines, which is within 5% of the measurement value. The deviation does not show any
obvious trend, suggesting random (rather than systematic) error present in measurements.
Indeed, significant variation in both flow rate and pressure measurements was observed
due to fluctuations in the flow. The random error could be reduced by taking more than
three repeats at each flow rate setting.
Conclusion
Calibration curves were determined for two obstruction flow meters. It was shown that
the flow rate through these devices is proportional to the square root of the measured
pressure drop. The calibration allows for the flow rate to be measured indirectly by much
easier measurement of the pressure drop.
References
[1] J.P. Holman, Experimental Methods for Engineers, 7th Edition, McGraw Hill, New York,
2001
[2] F. M. White, Fluid Mechanics, 5th edition, , McGraw Hill, 2003
5
Appendix
Table A- 1 presents all experimental results taken during the laboratory.
Table A- 1 All Experimental Results Taken
Flow rate
(gpm)
P Venturi
(mbar)
P orifice
(mbar)
2
4
6
7
8
9
10
12
Sample Calculations
6
Data Collected During ME-304 Lab
Experiment:
Date:
Team:
1
Angled Plate
Weight
Flow rate
position
(GPM)
(mm)
6
33,0
5,5
28,0
5
23,0
4,5
17,0
4
12,0
3,5
7,0
3
3,0
2,5
1,0
2
0,0
1,5
0,0
Flat Plate
Weight
Flow rate
position
(GPM)
(mm)
6
49,0
5,5
39,0
5
33,0
4,5
28,0
4
19,0
3,5
12,0
3
9,0
2,5
8,0
2
7,0
1,5
5,0
Uncertainty Estimate
Parameter
Unit
Uncertainty
M
(g)
1
g
y
l
2
(m/s )
(mm)
(mm)
0
0,5
0,5
Conical Plate
Weight
Flow rate
position
(GPM)
(mm)
6
63
5,5
57
5
43
4,5
36
4
28
3,5
21
3
16
2,5
11
2
6,0
1,5
3
Hemispherical Cup
Weight
Flow rate
position
(GPM)
(mm)
6
81,0
5,5
73,0
5
56
4,5
44
4
35
3,5
24
3
17
2,5
13
2
7
1,5
4
Data Collected During ME-304 Lab
Experiment:
Date:
Team:
1 gal/min
1m
g
M
l
d
h
ρ
1
=
=
=
=
=
=
=
=
6,31E-05
1000
9,81
0,6
0,15
0,01
0,035
998
Angled Plate
Flow rate
Force F
(Experimental)
Mass flow
rate
Jet exit water
velocity u
(m3/s)
3,79E-04
3,47E-04
3,16E-04
2,84E-04
2,52E-04
2,21E-04
1,89E-04
1,58E-04
1,26E-04
9,47E-05
(N)
1,29
1,10
0,90
0,67
0,47
0,27
0,12
0,04
0,00
0,00
(kg/s)
0,38
0,35
0,31
0,28
0,25
0,22
0,19
0,16
0,13
0,09
(m/s)
4,82
4,42
4,02
3,62
3,21
2,81
2,41
2,01
1,61
1,21
Water
velocity at
vane u o
(m/s)
4,75
4,34
3,93
3,52
3,10
2,69
2,26
1,83
1,38
0,87
Momentum
at vane
entrance L o
(kg-m/s^2)
1,79
1,50
1,24
1,00
0,78
0,59
0,43
0,29
0,17
0,08
Force F
(Theoretical)
(N)
0,90
0,75
0,62
0,50
0,39
0,30
0,21
0,14
0,09
0,04
m3/s
mm
m/s^2
kg
m
m
m
kg/m^3
Flat Plate
Percent
Difference
Flow rate
Force F
(Experimental)
Mass flow
rate
Jet exit water
velocity u
[%]
44%
46%
46%
34%
20%
-7%
-45%
-73%
-100%
-100%
(m3/s)
3,79E-04
3,47E-04
3,16E-04
2,84E-04
2,52E-04
2,21E-04
1,89E-04
1,58E-04
1,26E-04
9,47E-05
(N)
1,92
1,53
1,29
1,10
0,75
0,47
0,35
0,31
0,27
0,20
(kg/s)
0,38
0,35
0,31
0,28
0,25
0,22
0,19
0,16
0,13
0,09
(m/s)
4,82
4,42
4,02
3,62
3,21
2,81
2,41
2,01
1,61
1,21
Water
velocity at
vane u o
(m/s)
4,75
4,34
3,93
3,52
3,10
2,69
2,26
1,83
1,38
0,87
Theoretical Calculations
4,00
y = 2x
Angled Plate
3,50
Flat Plate
3,00
y = 1.5x
Hemispherical Cup
2,50
Force F (N)
Conical Plate
Linear (Angled Plate)
2,00
Linear (Flat Plate)
y=x
1,50
Linear (Conical Plate)
1,00
Linear (Hemispherical Cup)
y = 0,5x
0,50
0,00
0,00
0,50
1,00
1,50
2,00
0,00
0,00
0,50
1,00
Momentum in x-Direction
1,50
(kg-m/s2)
2,00
Conical Plate
Momentum
at vane
entrance L o
(kg-m/s^2)
1,79
1,50
1,24
1,00
0,78
0,59
0,43
0,29
0,17
0,08
Force F
(Theoretical)
Percent
Difference
Flow rate
Force F
(Experimental)
Mass flow
rate
Jet exit water
velocity u
(N)
1,79
1,50
1,24
1,00
0,78
0,59
0,43
0,29
0,17
0,08
[%]
7%
2%
5%
10%
-5%
-20%
-17%
9%
58%
137%
(m3/s)
3,79E-04
3,47E-04
3,16E-04
2,84E-04
2,52E-04
2,21E-04
1,89E-04
1,58E-04
1,26E-04
9,47E-05
(N)
2,47
2,24
1,69
1,41
1,10
0,82
0,63
0,43
0,24
0,12
(kg/s)
0,38
0,35
0,31
0,28
0,25
0,22
0,19
0,16
0,13
0,09
(m/s)
4,82
4,42
4,02
3,62
3,21
2,81
2,41
2,01
1,61
1,21
Angled Plate
Flat Plate
Conical Plate
Hemispherical Cup
Linear (Angled Plate)
Linear (Flat Plate)
Linear (Conical Plate)
Linear (Hemispherical Cup)
onical Plate
He
Water
velocity at
vane u o
(m/s)
4,75
4,34
3,93
3,52
3,10
2,69
2,26
1,83
1,38
0,87
Momentum
at vane
entrance L o
(kg-m/s^2)
1,79
1,50
1,24
1,00
0,78
0,59
0,43
0,29
0,17
0,08
Force F
(Theoretical)
Percent
Difference
Flow rate
Force F
(Experimental)
(N)
2,69
2,25
1,86
1,50
1,17
0,89
0,64
0,43
0,26
0,12
[%]
-8%
-1%
-9%
-6%
-6%
-7%
-2%
0%
-9%
-5%
(m3/s)
3,79E-04
3,47E-04
3,16E-04
2,84E-04
2,52E-04
2,21E-04
1,89E-04
1,58E-04
1,26E-04
9,47E-05
(N)
3,18
2,86
2,20
1,73
1,37
0,94
0,67
0,51
0,27
0,16
Hemispherical Cup
Mass flow rate
Jet exit water
velocity u
Water velocity at
vane u o
Momentum at
vane entrance L o
Force F
(Theoretical)
Percent
Difference
(kg/s)
0,38
0,35
0,31
0,28
0,25
0,22
0,19
0,16
0,13
0,09
(m/s)
4,82
4,42
4,02
3,62
3,21
2,81
2,41
2,01
1,61
1,21
(m/s)
4,75
4,34
3,93
3,52
3,10
2,69
2,26
1,83
1,38
0,87
(kg-m/s^2)
1,79
1,50
1,24
1,00
0,78
0,59
0,43
0,29
0,17
0,08
(N)
3,59
3,01
2,48
1,99
1,56
1,18
0,86
0,58
0,35
0,17
[%]
-11%
-5%
-11%
-13%
-12%
-20%
-22%
-11%
-21%
-5%
Experimental Results
3,50
y = 1,8381x - 0,0591
3,00
y = 1,4055x + 0,0071
2,50
Angled Plate
Flat Plate
y = 1,0298x + 0,0088
Force F (N)
2,00
Conical Plate
Hemispherical Cup
1,50
Linear (Angled Plate)
Linear (Flat Plate)
1,00
y = 0,8214x - 0,1606
Linear (Hemispherical Cup)
0,50
0,00
0,00
-0,50
Linear (Conical Plate)
0,20
0,40
0,60
0,80
1,00
1,20
Momentum in x-Direction (kg-m/s2)
1,40
1,60
1,80
2,00
Data Collected During ME-304 Lab
Experiment:
Date:
Team:
1
1/17/2020
D
Angled Plate
Flow rate
Weight
position
Force F
(Experimental)
Force
Uncetainty
Force F
(Theoretical)
Percent
Difference
(GPM)
6
5,5
5
4,5
4
3,5
3
2,5
2
1,5
(mm)
33,0
28,0
23,0
17,0
12,0
7,0
3,0
1,0
0,0
0,0
(N)
1,29
(N)
0,02
(N)
0,90
[%]
44%
Uncertainty Estimate
Parameter
Unit
Uncertainty
aw/x
M
(g)
1
0,002
0
varies
-0,003
g
y
l
2
(m/s )
(mm)
(mm)
0
0,5
0,5
Flat Plate
Flow rate
Weight
position
Force F
(Experimental)
Force
Uncetainty
Force F
(Theoretical)
Percent
Difference
(GPM)
6
5,5
5
4,5
4
3,5
3
2,5
2
1,5
(mm)
49,0
39,0
33,0
28,0
19,0
12,0
9,0
8,0
7,0
5,0
(N)
1,92
(N)
0,02
(N)
1,79
[%]
7%
Flow rate
(GPM)
6
5,5
Conical Plate
Hemisph
Weight
position
Force F
(Experimental)
Force
Uncetainty
Force F
(Theoretical)
Percent
Difference
Flow rate
Weight
position
(mm)
65,5
33
(N)
2,47
(N)
0,02
(N)
2,69
[%]
-8%
(GPM)
6
(mm)
80,0
Hemispherical Cup
Force F
(Experimental)
Force
Uncetainty
(N)
3,18
(N)
0,02
Percent
Force F
Differenc
(Theoretical)
e
(N)
[%]
3,59
-11%
ME304 Mechanical Measurements II
Experiment 1: Impact of a Liquid Jet
Objective
To investigate the impact force from a water jet striking vanes of various shapes at various flow
rates.
Theoretical Background
When a vane obstructs a liquid jet, it reduces its linear momentum. Per Newton’s second law, the
rate of change of this momentum is equal to the force exerted on the fluid by the vane.
Consider a vane, which is symmetrical about the xaxis, as shown in Figure1. A jet of fluid flowing at the
(kg/s) along the x -axis with the
mass flow rate of m
velocity u0 (m/s) strikes the vane, is deflected and
leaves the vane with the velocity u1 (m/s) directed at
an angle to the x-axis. Changes in elevation from the
striking the vane to leaving it are neglected.
x
F
The rate of x-momentum entering the system is:
u0
L0 = m
(kg m/s2 )
while the rate of x-momentum leaving the system is:
u1 cos
L1 = m
u0
Figure 1
(kg m/s2 )
The force on the vane in the x-direction is equal to the rate of change of the x-momentum:
(u0 - u1 cos )
F= m
(N)
Assuming that the jet velocity does not change so that u0 = u1, one can write:
u0 (1 – cos )
F= m
(N)
The values of angle and the predicted values of the force for the four vanes used in this
experiment are listed in Table 1.
Table 1: Theoretical values of force F for four vanes used in this lab.
Shape
Angled Plate
Flat Plate
Conical Plate
Cup
Experiment description
60o
90o
120o
180o
F
u0
0.5 m
u0
m
u0
1.5 m
u0
2 m
u1
Water is pumped from a water tank through a regulating valve and a flow meter, then discharged
vertically upwards through a nozzle and striking a vane being tested. The vane is supported by a
balance system, which allows for the vertical force acting on the vane to be measured indirectly
by measuring the position of the balance weight. Thus the dependence of the impact force on the
water flow rate through the jet can be established.
Experimental Goal
Experimentally determine the impact force F as a function of the rate of linear momentum at the
u0 for four vanes (hemispherical cup, conical plate, angled plate and flat
vane entrance L0 = m
plate) and compare the findings with the simple theoretical model presented on the first page.
Useful Equations
y
l
1. Force of the water jet:
F = Mg
2. Mass flow rate:
m = V
V
u= 2
d / 4
3. Water velocity at jet exit:
4. Water velocity at vane:
u0 = u 2 − 2 gh
5. Rate of momentum at vane entrance:
u0
L0 = m
Where
M
g
y
l
d
V
h
= mass of the balance weight
= gravitational acceleration
= balance weight position
= distance from the vane axis to the lever pivot (0.15 m)
= water density
= nozzle diameter
= volumetric flow rate
= Height of vane above tip of nozzle
Presentation of Results
Based on the direct measurements recorded, calculate the force F and the rate of momentum in
u0 at the vane entrance.
the vertical direction L0 = m
Compare the experimental curves with the simple theoretical model presented on Page 1.
Discuss possible reasons for the discrepancy between the experimental and theoretical curves.
Consider both the sources of experimental error and the applicability of the theoretical model.
References
(1) J.P. Holman, Experimental Methods for Engineers, 7th Edition, McGraw Hill, New York,
2001
(2) Instructions of “Impact of a jet” by TQ Intelligent Solutions for Education and Training
Purchase answer to see full
attachment