Flow Measurement FLUID MECHANICS LAB CIE 321

LAB REPORT # 5

Lebanese American University

Instructor :Mirla AbiAad Done by :Omar Nammour 201300900HadyTouma 201305704Hussein Haidar 201100896Tarek Alhajj 201205768Jerome Jeitany 201302545

Date of submission : 3/10/2015

ContentsAbstract3Introduction4Equipment5Procedure6DATA COLLECTED7CALCULATIONS81- Calculating Q using the definition of volume per unit time :82- Calculating Q using the venturimeter :83-calculating Q using the orifice plate where losses are considered:94- Calculating through the rotameter10RESULTS11DISCUSSION14Conclusion15REFERENCES16

Table 1- readings collected7Table 2-measured flow11Table 3- venturi calculations11Table 4- coefficient of discharge and error11Table 5- head loss in venturi11Table 6-orifice calculations12Table 7- flow calculations from rotameter13Table 8- coefficient of discharge vs. error13

Figure 1-venturi meter , orifice plate,rotameter5Figure 2-piezometric readings6Figure 3-bob of rotameter7

Graph 1- coefficient of discharge vs discharge13Graph 2- rotameter reading vs dischrage14

Abstract

Water flow is measured to assess how much water is available for a supply and to check the quantity of water flowing through a system. Based on Bernoullis principle, flow can be measured using Venturi meters, orifice plates, and rotameters. In this lab work, the flow rate, mass flow rate, velocities and coefficient of discharge of each section of the combined apparatus were computed as well as the head loss due to friction. The results obtained are compared and analyzed in function of the coefficient of discharge and the error and plotting the readings vs. the discharge in order to reach an acceptable conclusion for this experiment.

Introduction

The most important characteristic that distinguishes a fluid from a solid is the capacity of a fluid to flow. The flow rate of a fluid is an important parameter that provides the means to calculate the velocity of the fluid at a point in a tube. The Venturi meter is a device to measure the flow rate along a pipe. The first large-scale Venturi meters to measure liquid flows were developed by Clemens Herschelat the end of the 19th century. The fluid moving through the Venturi meter accelerates in the direction of the tapering contraction with the highest increase in the velocity in the throat. 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 energy. That is, the velocity of the fluid increases as the cross sectional area decreases. This increase in velocity leads to a fall in pressure. The drop in pressure depends on the flow rate. In this experiment, energy losses and flow rates will be analyzed using the Venturi meter, then the continuity equation will be used to compute velocities at several points in the tube. The Bernoulli principle is also essential to be used with the Venturi meter results to determine the discharge. The Bernoulli equation is important because it provides the means to calculate the fluid pressures from the velocity. The principle of the equation was stated by Daniel Bernoulli in the eighteenth century and is based on the conservation of energy. orifice plates are most commonly used to measure flow rates in pipes, when the fluid is single-phase (rather than being a mixture of gases and liquids, or of liquids and solids) and well-mixed. they are also used to reduce pressure or restrict flow, in which case they are often called restriction plates.

Equipment

1. A Venturi meter connected to an orifice plate and a rotameter (Bernoulli apparatus).2. An orifice plate.3. A water supply.4. A chronometer (stop watch).5. A Hydraulic bench, on which the jet apparatus rests.

Figure 1-venturi meter , orifice plate,rotameter

Procedure

1. Set the flow rate.2. Determine the piezometric head by recording the level in the piezometer tubes.3. Measure the flow rate by measuring the time needed to fill 5 L and dividing the volume (5 L) by the time obtained.4. Take the reading of the bob on the rotameter.5. Change the flow rate and repeat the same procedure for three trials in total.

Figure 2-piezometric readings Figure 3-bob of rotameter

DATA COLLECTED

Table 1- readings collectedVolume (m3)Time (s)Manometer levels (m)

ABCDEFGHrotameter

0.00532.280.3280.3040.3220.3260.3280.30.3040.2020.055

0.00522.530.2880.2380.2820.2840.2880.2280.240.2380.098

0.00517.490.2320.1540.2240.2260.2320.1420.1560.1540.111

CALCULATIONS

1- Calculating Q using the definition of volume per unit time :

Q= For trial 1 : V1 = 5 L ; t1 = 32.28 s

Q = = 0.00015489 2- Calculating Q using the venturimeter : Assuming that : z = 0

The Bernoulli equation becomes: h1 + = h2 + where V1= and V2 = h1 + = h2 + 2g (h1-h2) = (-) Q=

For trial 1 between B and C:

Q calculated = = = 0.000129101

Cd =1.199794269

=()*100=(19.97942685

Head loss: H (A) H (D) = = 0.004823805 m

3-calculating Q using the orifice plate where losses are considered:

after similar derivation as above : + H (accounting for losses)

( (V1= ; V2= )

2g (h1-h2) = (-)

Q =

For trial 1 between F and G :

Q = = 5.35 E-05

Cd =2.9

=()*100=(189.5946196

Head loss: H (E) H (G) = = 0.024 m

4- Calculating through the rotameter

Mass flow rate is deduced from graph .

For trial 1:

Manometer scale reading = 5.5cm corresponding to 0.175 kg / m3

Q Rotameter == 0.000175316 m3/s

Cd = 0.883519207

(0.883519207-1)*100= 11.64807931%

RESULTS

Table 2-measured flow

Time (s)

Flow rate: Q measured (m3/s)

32.280.000154895

22.530.000221926

17.490.000285878

Table 3- venturi calculationshc (m)Area B (m2)Area C (m2)g (m/s2)Q calculated venturi (m3/s)

0.3220.0002010620.0005309299.810.000129101

0.2820.0002010620.0005309299.810.000201846

0.2240.0002010620.0005309299.810.000254591

Table 4- coefficient of discharge and errorCoefficient of discharge Cd% Error

1.19979426919.97942685

1.0994842989.948429832

1.12289133912.2891339

Table 5- head loss in venturihD (m)Velocity A (m/s)Velocity D (m/s)g (m/s2)HA(m)HD(m)Head loss HA HD (m)

0.3260.2431605510.0610246229.810.3310136110.3261898070.004823805

0.2840.3801746930.0954102839.810.2953666050.2844639720.010902634

0.2260.4795190720.1203421789.810.2437195990.2267381370.016981463

Table 6-orifice calculationsh at G (m)Area F (m2)Area G (m2)g (m/s2)CQ calculated orifice (m3/s)

0.3040.0003141590.0021155569.810.6015.35E-05

0.240.0003141590.0021155569.810.6019.26E-05

0.1560.0003141590.0021155569.810.6011.00E-04

Graph 1- coefficient of discharge vs discharge

Table 7- flow calculations from rotameterrotameter scale Reading (cm)Mass Flow of Water (kg/s)Density of water (kg/m3)Q rotameter calculated (m3/s)

5.50.175998.20.000175316

9.80.24998.20.000240433

11.10.31998.20.000310559

Graph 2- rotameter reading vs dischrage

Table 8- coefficient of discharge vs. errorQ calculated rotameter (m3/s)Coefficient of discharge Cd% Error

0.0001753160.88351920711.64807931

0.0002404330.9230285557.697144548

0.0003105590.9205260157.947398513

DISCUSSION

Using the venturi meter to measure the flow , we obtained a value of 0.000129101 corresponding to an error of 19.97 % for trial 1. This error increased immensely when we used the orifice plate to calculate the flow , where we obtained for trial 1 a flow of 5.53*10-5 corresping to an error of 189 % .In the rotameterwe reached a flow of 0.000175316 m3/s corresponding to an error of 11.64 % . These results obtained showed that the orifice plate has lead to the highest error percentage. Besides the sources of error during the experiment , which could be reading errors while measuring the flow or instrumental errors from the hydraulic bench itself , the cross section of the orifice is very small whichresults in high error values in the slightest deviations. But when using the rotameter, the acceptable percentage of error is the result of using a theoretical given graph and relatively big values ( 5.5 cm ) .Moreover , only in the rotameter we obtained coefficients of discharge smaller than unity (0.88 , 0.92 and 0.92) while in the other methods the coefficients were larger than one ( 1.19 , 1.09 ,..).Both observations show that the rotameter makes the best way between those three methods to measure the flow. Nevertheless , sources of error must always be taked care of to make this rotameter as accurate as possible taking in consideration the losses in the heads .

Conclusion

Flow measurement is necessary for the transportation of fluid and is nowadays possible due to the invention of the Venturi meter, the Rotameter and the Orifice Plate. Head loss due to viscous effects generated by the surface of the pipe which can be computed using to Bernoullis equation should be taken in consideration in the planning stage, knowing that the losses in vertical pipes are by far higher than in horizontal pipes.The Venturi meter, the orifice meter and the rotameter play important roles in computing several characteristics of fluids such as velocity, head pressures, and flow rates... Taking into account the many types of errors that could have occurred during the experiment, and after comparing the values of coefficient of discharge and percent error, it can be concluded that the results obtained show that the rotameter is the most accurate among all three methods.

REFERENCES

Flow Meters. (2014, 10 29). Retrieved from Gilson Engineering Sales of Florida: http://www.gilsoneng.com/reference/flowmeter.pdf

Kambe, T. (2007). Elementary Fluid Mechanics. World Scientific Publishing.

Abiaad,M. (2014). Instructor. Flow Measurement. LAU.

Street, R. L., Watters, G. Z., & Vennard, J. K. (1996). Elementary FLuid Mechanics. New York: John Wiley and Sons.

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