FLOW MEASURING APPARATUS

PAGE REF. NO.TU/ENG/LS-Y1S1

REV. DATE07-SEP-2011

FLOW MEASURING APPARATUS

OBJECTIVES:

1. To demonstrate the characteristics of several different commonly used methods of measuring fluid flow rates.2. To determine the head losses associated with each flow measuring methods.

APPARATUS:1) Flow measuring apparatus 2) Volumetric Hydraulic Bench/Water3) Stop Watch1. INTRODUCTION

The flow measuring apparatus is designed to accustom students to typical methods of measuring the discharge of an essentially incompressible fluid, whilst at the same time giving applications of the Steady Flow Energy Equation (Bernoulli's Equation). The discharge is determined using a venturi meter, an orifice plate meter and a rotameter. Head losses associated with each meter are determined and compared as well as those arising in a rapid enlargement and a 90-degree elbow. The unit is designed for use with the Hydraulic Bench, which provides the necessary liquid service and gravimetric evaluation of flow rate.

2. DESCRIPTION OF APPARATUSFigure 1 shows the Flow Measuring Apparatus. Water from the Hydraulic Bench enters the equipment through a venturi meter, which consists of a gradually-converging section, followed by a throat, and a long gradually-diverging section. After a change in cross-section through a rapidly diverging section, the flow continues along a settling length and through an orifice plate meter. This is manufactured in accordance with BS1042 from a plate with a hole of reduced diameter through which the fluid flows.

Following a further settling length and a right-angled bend, the flow enters the rotameter. This consists of a transparent tube in which a float takes up an equilibrium position. The position of this float is a measure of the flow rate.

After the rotameter the water returns via a control valve to the Hydraulic Bench and the weigh tank. The equipment has nine pressure tapings as detailed in Fig. 2 each of which is connected to its own manometer for immediate read out.

Figure 1. Flow Measuring Apparatus.

Figure 2. Explanatory diagram of flow measuring apparatus.

3. BACKGROUND

An effective way to measure the flowrate through a pipe is to place some type of restriction within the pipe and measure the pressure difference between the low-velocity, high-pressure upstream section (1) and the high-velocity, low-pressure downstream section (2) as shown in Fig. 3. So the principle is an increase in velocity results in a decrease in pressure as the famous Bernoullis equation states.

Figure 3. The steady-flow energy equation.

For steady, adiabatic flow of an incompressible fluid along a stream tube, as shown in Fig. 3, Bernoulli's equation can be written in the form;

(1)

wherep/(g

is termed the hydrostatic head.

is termed the kinetic head ( is the mean velocity i.e. the ratio of

volumetric discharge to cross-sectional area of tube).

z

is termed potential head.

represents the total head.

The head loss (H12 may be assumed to arise as a consequence of vorticity in the stream. Because the flow is viscous a wall shear stress then exists and a pressure force must be applied to overcome it. The consequent increase in flow work appears as increased internal energy. Also, because the flow is viscous, the velocity profile at any section is non-uniform. The kinetic energy per unit mass at any section is then greater than and Bernoulli's equation incorrectly assesses this term. The fluid mechanics entailed in all but the very simplest internal flow problems is too complex to permit the head loss (H to be obtained by other than experiment means. Since a contraction of stream boundaries can be shown (with incompressible fluids) to increase flow uniformity and a divergence correspondingly decreases it, (H is typically negligibly small between the ends of a contracting duct but is normally significant when the duct walls diverge.

Principle of Rotameter

The cause of the pressure difference is the head loss associated with the high velocity of water around the float periphery. Since this head loss is constant then the peripheral velocity is constant. To maintain a constant velocity with varying discharge rate, the cross-sectional area through which this high velocity occurs must vary. This variation of cross-sectional area will arise as the float moves up and down the tapered rotameter tube.

From Fig. 4, if the float radius is Rf and the local bore of the rotameter tube is 2Rt then,

= Cross sectional area

= Discharge / Constant peripheral velocity

Now ( = l(, where l is the distance from datum to the cross section at which the local bore is Rt and ( is the semi-angle of tube taper. Hence l is proportional to discharge. An approximately linear calibration characteristic would be anticipated for the rotameter.

Figure 4. Principle of the rotameter.

4. EXPERIMENTAL PROCEDURE

a) Close the apparatus valve fully then open it by 1/3 open with the air purge closed.

b) Switch on the bench and slowly open its valve until the water starts to flow, allow the apparatus to fill with water then continue to open the bench valve until it is fully open.

c) Close the apparatus valve fully.

d) Couple the hand pump to the purge valve and pump down until all the manometers read approximately 280 mm.

e) Dislodge entrained air from the manometers by gentle tapping with the fingers.

f) Check that the water levels are constant. A steady rise in levels will be seen if the purge valve is leaking.

g) Open the apparatus valve until the rotameter shows a reading of about 10 mm. When a steady flow is maintained measure the flow with the Hydraulic Bench as outlined in Fig. 2.h) During this period, record the readings of the manometers in a table of the form of Fig. 5.

i) Repeat this procedure for a number of equidistant values of rotameter readings up to a maximum of approximately 220 mm.

5. RESULTS AND CALCULATIONS

1) Calculations of Discharge

The venturi meter, the orifice meter and the rotameter are all dependent upon Bernoullis equation for their principal of operation.

a) Venturi meterSince is negligibly small between the ends of a contracting duct, the z terms, can be omitted from Eq. (1) between stations (A) and (B).

From continuity,

(2)

The discharge, (m3/s)

(3)

Taking the density of water as 1000 kg/m3, the mass flow rate will be

(kg/s)

(4)Figure 5. Form of results table.Manometric levels (mm)Rota-

meter

(cm)Water

mass m (kg)Time

t (s) (k/s)H/inlet kinetic head

Test No.ABCDEFGHIVenturi

(4)Orifice

(8)Rota-meter

Calibration curveWeigh tank

m/tVenturi*

(10)/(11)Orifice

(12)/(13)Rota-meter

(15)/(16)Diffuser

(18)/(19)Elbow

(21)/(22)

* Numbers between brackets refer to the equation numbers

b) Orifice MeterFrom Fig. 6 between tapping (E) and (F), in Eq. (1) is by no means negligible. Rewriting the equation with the appropriate symbols

(5)

i.e. the effect of the head loss is to make the difference in manometric height (hE-hF) less than it would otherwise be.

An alternative expression is

(6)where the coefficient of discharge, K, is given by previous experience in BS1042 (1943) for the particular geometry of the orifice meter. For the apparatus provided K is given as 0.601.

The expression for the discharge of the orifice meter can be obtained in exactly the same way as for venturi meter,

The discharge,

(7)Again the density of water is 1000 kg/m3, the mass flow rate will be

(kg/s)

(8)

Figure 6. Construction of the orifice meter.

c) RotameterThe mass flow rate is plotted as a function of rotameter scale reading as shown in Fig. 7. An approximate linear calibration characteristic would be anticipated.

Figure 7. Typical rotameter calibration curve.2) Calculations of Head LossBy reference to Eq. (1) the dimensionless head loss associated with each meter can be evaluated.

a) Venturi meterApplying the equation between pressure tappings (A) and (C), the head loss is expressed as;

(9)

i.e.

(10)This can be made dimensionless by dividing it by the inlet kinetic head,

Thus

(11)b) Orifice MeterApplying Eq. (1) between (E) and (F) by substituting kinetic and hydrostatic heads would give an elevated value to the head loss for the meter. This is because at an obstruction such as an orifice plate, there is a small increase in pressure on the pipe wall due to part of the impact pressure on the plate being conveyed to the pipe wall. BS1042 (Section 1.1.1981) gives an approximate expression for finding the head loss and generally this can be taken as 0.83 times the measured head difference.

Therefore

(mm)

(12)The orifice plate diameter is approximately twice the venturi inlet diameter, therefore the orifice inlet kinetic head is approximately 1/16 that of the venturi. Thus

(13)

The dimensionless head loss can be calculated by dividing it by the inlet kinetic head of orifice meter which is based on the venturi's inlet kinetic head.

c) RotameterFor this meter, application of Eq. (1) gives

(14)Then as shown in Fig. 8:

(15)

Figure 8. Rotameter head loss.Since the connecting tube has a 26 mm bore the inlet kinetic head is as it is with the venturi meter.

Thus

(16)

d) Wide-Angled DiffuserThe inlet to the diffuser may be considered to be at (C) and the outlet at (D).

Applying Eq. (1),

(17)

(18)

Since the area ratio, inlet to outlet, of the diffuser is 1:4, the outlet kinetic head is onesixteenth of the venturi's inlet kinetic head.

Thus

(19)

e) Right-Angled BendThe inlet to the bend is at (G) where the pipe bore is 51 mm and outlet is at (H) where the bore is 26 mm. Applying Eq. (1);

(20)

(21)

The outlet kinetic head is now approximately sixteen times the venturi's inlet kinetic head.

Thus

(22)

6. DISCUSSION OF RESULTS

Comment on the fluid discharge, head loss of various methods of measuring fluid flow rate.

REFERENCES:1. Massey, B.S. (1989). Mechanics of Fluids. 6th Ed, Chapman & Hall.

2. White F.M. (1994). Fluid Mechanics. 3rd Ed., McGraw-Hill.

3. Van Dyke M. (1982). An Album of Fluid Motion. Parabolic Press.

4. Coulson, J.M.; and Richardson, J.F. Chemical Engineering, Volume 1., 6th Ed., Butterworth-Heinemann.Last updated on 8/2009 by Dr. Abdulkareem Sh. Mahdi

Last updated on 9/2009 by Dr. Abdulkareem Sh. Mahdi

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