LABORATORY IIICalibration of a Venturi Flow Meter

Group Members:

Dustin Harbottle

Taylor Choy

Kevin Ko

Shane McMonagle

Agaton Pasion

University of Hawaii at ManoaDepartment of Civil and Environmental Engineering

CEE 320L Fluid Mechanics

Lab Date: October 27, 2011Report Submitted Date: November 3, 2011

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I Abstract

The objective of this lab was to determine the calibration rate for a Venturi flow meter. In this experiment, the flow rate through the pipe and the pressure difference through the Venturi pipe were measured many times for different flow rates and pressures to help find a calibration factor for the Venturi flow meter. The experimental result for the calibration factor was .101 cfs, which came out to be close to the theoretical prediction of .101 cfs. This means that even with possibilities for error, the experiment closely reflected the theoretical use of using a flow meter in the field.

II Introduction

i. Background

The Venturi meter creates a restricted flow in a pipe, the velocity of the fluid increases as the cross sectional area decreases, with the static pressure correspondingly decreasing. A Venturi meter helps to measure flow rate by measuring a pressure difference between a converging-diverging flow passage. The main advantage of the Venturi meter is that it has a lower head loss then an orifice meter. An equation for the Venturi effect may be derived from a combination of Bernoulli's principle and the continuity equation.

ii. Reason for Experiment

The reason for the experiment it to be able to measure pressure differences between pipes by using the Venturi meter, with a properly calculated Venturi meter it is possible to accurately measure the pressure in any given pipe. Once the calibration for the Venturi meter is recorded then that specific meter will be able to be used in the field. Having a properly calibrated Venturi meter will greatly increase the accuracy of knowing the pressure and flow rate of different pipes.

iii. Theory

According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the principle of continuity, while its pressure must decrease to satisfy the principle of conservation of mechanical energy. Thus any gain in kinetic energy a fluid may gain due to its increased velocity through a constriction is negated by a drop in pressure.

iv. Objective

The objective of this lab was to calibrate a Venturi meter by measuring flow rate along with pressure drop in the Venturi meter. Measuring the two different quantities allows for the calculation of the calibration factor, which will make the calculations for the Venturi meter accurate.

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III Apparatus and Supplies

i. Instruments and Supplies

Figure III.1 – Venturi meter

Figure III.2 – Pressure Gauge Figure III.3 – Weighing Tank

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Figure III.4 – Scale Figure III.5 – Stopwatch (typical of 2)

IV Procedures

A Venturi meter is installed in a length of pipe from a sump pump to a weighing tank with a dump valve. The Venturi meter is, in turn, connected to a pressure gauge. The pump was turned on and a gate valve just downstream of the pump was opened. Water flowed through the piping system from the sump pump, through the Venturi meter and to the weighing tank. The initial pressure gauge reading, in psi, was recorded. The dump valve on the tank was closed and, as water collected in the tank, the initial and final weight of the water in the tank was recorded, along with the time interval, using the stopwatches. The water in the tank was then released via the dump valve, and the gate valve was then closed a certain amount to cause a pressure difference, Δp. This new pressure reading was recorded and the dump valve on the tank was again closed, allowing water to collect in the tank. The initial and final weight, along with the time interval, was again recorded for the new pressure reading. The procedure was repeated for a total of ten trials.

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V Equations/Theory

Experimental Flow Rate: Q= wγt

Theoretical Flow Rate: Q=CK √∆ p

Venturi Constant: K=A2√ 2g

γ [1−(D2D1 )4 ]

Correction Factor: C= Q

K √∆ p

Error Propagation: ∆C=C [ ∆WW + ∆ tt

+∆ (∆ p )2∆ p ]

Relative Error: ∆CC

Derivation of ∆C: Q=CK √∆ P→C= f (W ,t ,∆ P )= W

γtK √∆ P

∴∆C=| ∂ f∂W ∆W|+|∂ f∂ t ∆ t|+| ∂ f∂∆P ∆ (∆ P)|∆C=|( 1

γtK √∆ P )∆W|+|( −WγK √∆ Pt 2 )∆ t|+|( −W

2 γtK (∆P32 ) )∆(∆ P)|

∆CC

=[( ∆WγtK √∆ P )( γtK √∆ P

W )]+[( W ∆t

γK √∆ P t2 )(γtK √∆ PW )]+[( W ∆(∆ P)

2 γtK (∆ P ) (√∆ p ) )( γtK √∆ PW )]

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∴∆C=C[ ∆WW +∆ tt

+∆ (∆ P )2∆ P ]

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VI Experimental Results

Trial t1 (s) t2 (s) tavg (s) W (lbs) ∆P (psi)

1 10.41 10.75 10.58 100 5.52 11.88 12.41 12.145 100 4.33 13.1 13.22 13.16 100 3.44 14.26 14.28 14.27 100 35 15.13 15.34 15.235 100 2.56 17.44 17.69 17.565 100 1.97 18.04 18.81 18.425 100 1.658 20.5 20.57 20.535 100 1.39 22.15 22.69 22.42 100 1.05

10 28.23 29.81 29.02 100 0.5

Table VI-1: Trial Data from the experiment

Trial No.

C Re

1 0.94 231430.772 0.93 201608.693 0.95 186059.094 0.94 171586.385 0.97 160717.926 0.96 139398.677 0.99 132892.138 1.00 119237.289 1.02 109212.2010 1.14 84374.14

Average 0.98

Table VI-2: Correction Factors and Reynolds Number

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60000 80000 100000 120000 140000 160000 180000 200000 220000 240000 2600000

0.2

0.4

0.6

0.8

1

1.2

f(x) = − 1.10803581070823E-06 x + 1.15302328016235R² = 0.675897507578048

C vs Re

Re

C

Figure VI-1: Correction Factor vs Reynolds Number

0.10 1.00 10.000.010

0.100

1.000

f(x) = 0.0186934089773852 x + 0.0534574304338144R² = 0.982202598346408

Q vs Δp

Δp

Q

Figure VI-2: log-Log Graph of Flow Rate vs Pressure

Q=β (∆ p)α β=10 y−intercept α=slope of graph

Q=0.008614 ¿.147

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VII Error Analysis

i. Instrumental Error, Statistical Uncertainty and Random Error

The three instruments used to obtain data for this lab was the pressure gauge, the scale, and the stopwatch. The pressure gauge had markings 1/10 or 0.1 psi, therefore the instrumental error for the pressure gauge was 0.05 psi. The scale that collected the water had an accuracy of 1 lb. so the instrumental error would be 0.5 lb. The stopwatch was a digital stopwatch so its accuracy and instrumental error was .01 sec. Since there was a constant change in pressure, the statistical error was unable to calculate. However, the relative error was able to calculate by using the equation ΔC/C. The average relative error was calculated to be 0.0436.

ii. Other sources of error

Human error must be taken into account mainly with the individuals collecting the time data. Discrepancies in the times may have occurred due the each individual’s reaction time, having to watch the scale until 100 lbs. of water was obtained and then stop the watch. Assuming the water flow was constant throughout the experiment, human error could also be caused due to each person taking times at different weights with a possibility that the water flow could have been different at those weights. One or both persons could have taken the time to early and not allow the flow to become steady enough.

VIII Conclusions and Recommendations

The flow rate through the pipe and the pressure difference through the Venturi pipe were measured many times for different flow rates and pressures to help find a calibration factor for the Venturi flow meter. This in turn helps us understand the flow of the experimental result for the calibration factor, which came out to be close to the theoretical prediction of .101 cfs. We did get a different result for the experimental calibration factor, a flow rate of .101 cfs, which leaves some discussion for error. The experimental value Q of .101 cfs was then compared to the Q value from the log-log plot, which was .147 cfs, which was relatively close to the theoretical value calculated.

If this experiment were to be considered more critically, more trials should be made so there is a decrease in the impact of errors. Another way to achieve more accurate results would be to use a more accurate way of recording the time at which the weight started to increase, such as video recording which would allow frame by frame viewing, and use the same weight difference throughout the entire experiment.

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IX References

Crowe, C.T., Elger, D.F., Williams, B.C., & Roberson, J.A. 2009. Engineering Fluid Mechanics, 9 th Edition . Hoboken, New Jersey: John Wiley & Sons, Inc.

X Appendices

Appendix I – Equations and Sample Calculations

Q=Wγt

= 100(62.4 )(10.58)

=0.151 ft3

s

Q=C K √∆ p = (0.94) (0.00572) √ (5.50 )(12)2 = 0.151 ft3s

K=A2√ 2g

γ [1−(D2D1 )4 ]

=π4 ( 112 )

2

√ 2(32.2)

(62.4 )[1−( 12 )4 ]

=0.00572

C= QK √∆ p

= 0.151

0.00572√5.50 (12 )2=0.9 4

∆C=C [ ∆WW + ∆ tt

+∆ (∆ p )2∆ p ]=.941[ 1100+ 0.0110.58

+ 14.42 (792) ]=.0189

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