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Lab #2
Experiment #3 Venturi Meter
Fluid Mechanics Lab
Abstract Flow rate is a common measurement which often needs to be performed. A venturi meter allows the flow rate in a pipe to be determined from a pressure differential. A venturi narrows the diameter of the pipe for a short duration, converting pressure head to velocity head. Through this pressure differential, Bernoulli’s equation, and the known dimensions of the venturi, the flow rate of the incompressible fluid can be determined.
I h1 hthroat
ntroduction
Q
Figure 1: Venturi Meter Concept
Pressure is measured at the point h1 and hthroat. As seen in Figure 1, the point hthroat is known as the vena contracta – this is where the velocity is at its maximum. Listed in Table 1 are the venturi dimensions. Athroat is the cross-sectional area of the throat, where hthroat is measured; A1 is the area at the point where h1 is measured.
Table 1: Venturi Data
A1 (d1)
Athroat (dthroat)
0.0021 m2 (0.026 m)
0.00080 m2 (0.016 m)
Because the amount of energy in the flowing fluid must be conserved, the pressure drop occurring is easily used to measure the velocity of the fluid in the throat. This is converted to volumetric flow rate by multiplying the cross-sectional area.
Procedure
The venturi meter experiment is initiated by closing the valves on the hydraulic bench, turning on the pump, and slowly opening them to ensure that water is flowing. Open the air valve atop the manometer bank and adjust the flow control valve and/or the air valve to develop a difference of at least 100 mm of head between manometers A and D. Place weight on the balance lever and begin timing and weighing. When the balance tips, the time is recorded and used to calculate the actual mass flow rate. Mass flow rates are calculated five times for each adjustment in flow on the hydraulic bench. Five flow adjustments are to be made, with an average time calculated. Additional mass may be added if the time is too short to accurately measure. The head loss between manometers A and D is also recorded for each flow rate.
Results and Discussion
The venturi meter constant k, calculated from equation 1, is a reformulation of Bernoulli’s equation, taking into account the change in velocity head between the inlet and the throat of the venturi.
(1) Venturi meter constant This constant is then multiplied by the square root of the differential head observed on the manometers (Equation 2). This will give the theoretical discharge, which assumes an ideal fluid with no energy loss due to viscosity/friction. In order to determine a more realistic value, a coefficient determined either empirically or from charts of Reynolds Numbers and venturi materials must be used. The coefficient will always be less than 1, as in the real world energy is always lost. This coefficient is multiplied (Equation 3).
(2) Theoretical Discharge
(3) Actual Discharge
The flow rate is related logarithmically to the differential head (See Figure 2). In the case of this experiment, the discharge coefficient C is calculated graphically using empirical data – measured volumetric flow rate and change in head. By plotting the logarithmic measured discharge and measured head loss data points (see Figure 3) and determining the linear trend line equation, two constants – α and β – can be found. Rearrangement of Equation 3 can also be used to determine C:
(4) Determination of C from measured flow rate
Table 2: Venturi Constants k (Equation 1)
Discharge Coeff. C (Equation 4)
0.0039
0.041
Table 3: Venturi Meter Test data Trial
Time
Mass (avg. kg)
(avg. s)
Δh
Qmeas
Qtheo
Qactual
(avg. m)
(m3/s)
(m3/s)
(m3/s)
% error
1
48.892
6
0.1138
0.0003682
0.0012984
4.19E-05
11.38
2
27.782
4
0.1332
0.0004319
0.0014048
5.75E-05
13.32
3
26.912
4
0.1398
0.0004459
0.0014392
6.23E-05
13.98
4
7.188
2
0.1898
0.0008347
0.0016769
0.00016
18.98
Figure 2: Calibration Curve – relationship between discharge and head loss.
Figure 3: Determination of C – Flow rate vs. Head Loss y = 1.6543x – 4.5197
While five different flow rates were tested, one of the flow rate tests contained several outliers and skewed the graph, bringing the R2 value to 0.78 versus 0.96 without that particular data point. Hence, it was removed.
Conclusions The results seemed to be more error-prone that expected, in reality there will be variations from theory as friction/viscosity result in energy loss in the system and slightly different heads in each part of the venturi. Also pulsation of the water being pumped made it difficult to read some of the manometer readings; these were either discarded or averaged with others in order to obtain a more consistent result. If the pump is turned off, extra air enters the system and needs to be purged prior to proceeding, or else it will produce error in the manometer readings.
References
1. Crowe, Clayton T., Donald F. Elger, Barbara C. Williams, and John A. Roberson. Engineering Fluid Mechanics. 9th edition. John Wiley & Sons, 2009.
