ME2134-2

ME2134-2

FLOW & ENERGY LOSS

VENTURI METER & ORIFICE PLATE METER (WS2-02-46)

SEMESTER 3 2015/2016

NOTE TO STUDENTS: Students are requested to find out in advance the exact location and directions to the lab. Latecomers who are more than 15 minutes late will not be permitted to perform the experiments.

NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF MECHANICAL ENGINEERING

CONTENTS Page TABLE OF CONTENTS

i

LIST OF SYMBOLS

ii and iii

INTRODUCTION

1

DESCRIPTION OF EQUIPMENT

1

THEORY OF OPERATION

2

PROCEDURE

7

A BRIEF NOTE ON FLOW MEASUREMENTS

9

REFERENCES

10

Figure 1

Schematic diagram of flow measuring apparatus

Table 1

Raw Data Sheet

11

Table 2

Processed Data Sheet 1

12

Table 3

Processed Data Sheet 2

13

SUMMARY OF EQUATIONS

2

14

i

i

LIST OF SYMBOLS A

Cross-sectional area of flow (subscripts 1-9 denote the location)

AO

Orifice plate opening area

C

Overall coefficient of orifice plate meter

Cc

Coefficient of area contraction due to vena contracta in orifice plate meter

Cd

Discharge coefficient

D

Diameter of pipe

g

Gravitational acceleration = 9.81 m/s2

h

*

P P* Piezometric head = . (subscripts 1-9 denote the location) +Z= ρg ρg

∆HO

Head loss in orifice plate meter

∆HV

Head loss in venturi-meter

K

Loss factor (subscripts V and O denote the venturi meter and orifice plate meter respectively)

Re

Reynolds Number =

P

Pressure (subscripts 1-9 denote the location)

P*

Piezometric pressure = P + ρgZ

QA

Actual volumetric flow rate

QT

Theoretical volumetric flow rate

Q'T

Quasi-theoretical volumetric flow rate in orifice plate meter

V

Average velocity = Q/A (subscripts 1-9 denote the location)

v

Local velocity

Z

Potential head (subscripts 1-9 denote the location)

VD

ν

ii

Greek Symbols: ρ

Density of fluid

g

Specific weight of fluid = ρg

α

Kinetic energy correction factor given by α =

µ

Dynamic viscosity

ν

Kinematic viscosity =

µ ρ

ii

1 v 3 dA 3 ∫ AV A

INTRODUCTION There are many measurements which need to be taken in fluid flow experiments. The setup in this experiment features some typical flow devices: (a) venturi meter, (b) orifice plate meter, (c) rotameter, (d) diffuser and (e) a 90° elbow, but measurements will only focus on two of these.

Objectives This experiment is prepared for students taking ME2134 - Fluid Mechanics I with the following objectives: a)

To become familiar with some flow measuring devices, such as the venturi meter and orifice plate meter.

b)

To determine the energy losses and pressure drops or losses for the venturi meter and orifice plate meter.

c)

To determine the coefficient of discharge for the venturi meter and orifice plate meter.

Scope This manual contains a detailed description of the equipment, theory of operation and the procedure for conducting the experiment in a systematic manner.

DESCRIPTION OF EQUIPMENT A schematic diagram of the flow measuring apparatus is shown in Figure 1. The experiment is conducted using water, which is an incompressible fluid. Water enters the equipment through a perspex Venturi meter having pressure tappings at inlet (1), throat (2) and exit (3). After a change in cross-section through a diffuser and another pressure measuring station (4), the flow continues down a settling length and through an orifice plate meter having pressure tappings at (5) and (6). After a further settling length and a 90o Elbow with pressure tappings at (7) and (8), the flow enters the rotameter which consists of a transparent tapered tube having a float which takes up an equilibrium position. The position of the float, estimated from the scale on the wall of the rotameter, provides an indication of the flow rate. The pressure drop across the rotameter can be derived from the pressure readings at (8) and (9). The water flowing past the rotameter returns to the reservoir after flowing through a control valve and the weighing tank. All the pressure tappings are connected to a bank of vertically inverted water-air manometers which give the piezometric pressure head. Note that the piezometric pressure head is the same as the pressure head if the elevation head Z is zero.

1

Figure 1

Schematic diagram of flow measuring apparatus. 1-9 denote locations connected to manometers.

THEORY OF OPERATION As fluid flows through the Venturi meter, the orifice meter, the rotameter, the diffuser and the 90° elbow, the continuity equation (which is a restatement of the principle of conservation of mass) for a steady incompressible fluid flow between any two general locations x and y is given by Vx ⋅ A x = Vy ⋅ A y = Q ,

(volumetric flow rate)

(I)

where A is the cross sectional area and V is the average velocity, which is related to the local velocity v by V=

1 Q vdA = . ∫ AA A

As fluid flows through the flow measuring devices, the energy equation for steady incompressible fluid flow between any two general points x and y can be written as

2

Py Vy2 Px V2 + α x x + Z x − ΔH = + αy + Zy , γ 2g γ 2g where

(II)

∆H

V2 , = Loss of energy, or head loss, generally expressed as ∆H = K 2g where K is the loss factor

g

= Specific weight of fluid = ρg

α

= Kinetic energy correction factor =

1 v 3dA , AV 3 ∫A

A is the cross sectional area considered, v is the local velocity and V is the average velocity. Note that for turbulent flow through pipes with circular cross sections, α = 1.06 ~ 1. If viscous effects and other energy losses are neglected, the energy equation (II) becomes identical to the Bernoulli’s equation: Py Vy2 Px Vx2 + + Zx = + + Zy . γ 2g γ 2g

(III)

Equations (I) and (II) are the two fundamental equations which will be applied repeatedly to yield expressions for the head loss corresponding to the various flow measuring devices. (i)

Venturi Meter Assuming negligible energy losses between locations 1 and 2, Bernoulli’s equation (III) can be written as P1 V12 P2 V22 + = + γ 2g γ 2g

(Z1 = Z2 = 0)

and the continuity equation (I) for steady incompressible flow is given by: V1 ⋅ A 1 = V2 ⋅ A 2 = Q

(volumetric flow rate)

The terms P1/g and P2/g are the pressure heads at locations 1 and 2, respectively. P1/g and P2/g can be, respectively, represented by piezometric heads h1* and h2* , which are the heights of the liquid column in the manometric tubes 1 and 2, since the elevation head Z is zero. The above equations can be simplified to yield an expression for the theoretical flow rate of the form:

3

1

 2g(h 1* −h *2 )  2 Q T = A1   . 2  (A1 /A 2 ) −1

(a.1)

The actual discharge QA is determined from weighing tank measurements, and is less than the theoretical discharge QT due to losses. The coefficient of discharge Cd is defined as: Cd = Q A QT .

(a.2)

Head Loss for Venturi Meter The loss of energy in terms of head loss ∆H V can be found by applying the energy equation (I) between pressure tappings at locations 1 and 3. Applying the energy equation (I) between 1 and 3: P3 V32 P1 V12 + + Z1 = + + Z 3 + ΔH V . γ 2g γ 2g The head loss associated with the Venturi meter is thus given by ∴

ΔH V =

P1 P3 − = h 1* − h *3 , γ γ

since V1 = V3 due to continuity and Z1 = Z2 = Z3 = 0. Hence, ∆H V =h 1* −h *3 . Also, since ΔH V = K V KV =

(a.3)

V22 , therefore: 2g

ΔH V , (V22 /2g)

(a.4)

where KV is the loss factor for the Venturi meter. (ii)

Orifice Plate Meter The semi-theoretical volumetric flow rate through the orifice plate meter can be expressed as 1

 2g(h *5 −h *6 )  2 , Q'T = A O  2  − 1 (A /A ) O 5  

(b.1)

where AO is the orifice opening area, h6* is the piezometric head at the vena contracta (location 6), and A5 and h5* are the cross-sectional area and piezometric head at location 5 before the orifice plate meter.

4

The actual discharge QA for the orifice plate meter can be expressed as Q A = C Q 'T ,

(b.2)

where C is similar to the discharge coefficient. The actual discharge QA is determined from weighing tank measurements, and is less than QT’ due to losses. The term QT’ does not exactly represent the theoretical discharge since h *6 is slightly different from the piezometric head at the orifice i.e. h *6 ≠ h *O . The piezometric head at the orifice cannot be measured directly. Hence, C is not exactly the same as the normally defined discharge coefficient Cd. In fact,  1−(A O /A 5 ) 2  C = Cd  2 2  1−C d (A O /A 5 ) 

1

2

,

(b.3)

however the difference between C and Cd for high values of Cd and low values of AO/A5 is small. This may be verified in the present experiment.

Head Loss for Orifice Meter Applying the energy equation (II) between locations 5 and 6, the head loss in the orifice plate meter is given by ∆H O =

V52 − V62 P5 − P6 + 2g g

since

Z 5 =Z 6 = 0 .

For steady flow, according to the continuity equation (I), the volumetric flow rate. Q A = V5 ⋅ A 5 = V6 ⋅ A 6 = V6 ⋅ C C A O = VO ⋅ A O . Hence, Q 2A  1 1  * * ΔH O =  2 − 2 2 +h5 − h6 2g  A 5 C c A O     C2A2   1 1  O  (h *5 − h *6 )  2 − 2 2  + h *5 − h *6 = 1 − ( A O ) 2   A5 CCA 0    A5     1  A  2    −  O   2  A 5   C  = (h *5 − h *6 ) 1 − C 2  c   2     A   O   1 −     A 5    

(

5

)

Assuming the coefficient of area contraction Cc = 1, since the contraction of area due to the vena contracta is small,

(

)

)(

∴

ΔH O = h *5 − h *6 1 − C 2 .

Also,

∆H O = K O

(b.4)

VO2 , 2g

where KO is the loss factor for the orifice plate meter. Thus,

KO =

∆H O . (VO2 / 2g)

(b.5)

A summary of the relevant equations for analysing the experimental results is provided on the last page of this manual.

6

PROCEDURE Experiment 1.

Close the delivery valve and open the exit valve after the rotameter fully.

2.

Start the pump and control the flow rate through the apparatus by opening the delivery valve slowly.

3.

Bleed the air entrapped in the apparatus completely before taking any measurement.

4.

Pressurise the vertical inverted water manometer by means of a bicycle pump to obtain a suitable reference pressure so that the variations of piezometric heads are within the manometer range. The magnitude of this reference pressure need not be known since it will be cancelled out when computing the difference between the piezometric heads.

5.

Determine the maximum and minimum flow rate in terms of maximum and minimum rotameter and manometer readings. A total of 6 readings will be taken in this range (steps 6-8).

6.

Allow sufficient time for the flow to stabilise before taking the manometer readings.

7.

Record the time required for both 5 kg and 10 kg of water to be collected in the weighing tank.

8.

Repeat steps 6 and 7 for another five different flow rates.

9.

Close the delivery valve and then switch off the pump at the end of the experiment.

10.

Measure the temperature of the water and use interpolation to calculate its kinematic viscosity ν. T (oC)

ν (m2 s-1)

20

1.004 x 10-6

30

0.801 x 10-6

Computation 1. From the experimental data recorded in Table 1, calculate the flow rates and head losses required in Table 2 according to the equations given in THEORY OF OPERATION (in particular, see the SUMMARY OF EQUATIONS on the last page) and enter the processed data in Table 2. 7

1a. For the venturi meter, calculate QA at various QT [using Equation (a.1)], and then determine Cd using see Equation (a.2). 1b. For the orifice plate meter, calculate QA at various Q'T [using Equation (b.1)], and then determine C using Equation (b.2). 1c. Tabulate ∆Hv and ∆Ho at various QA in Table 2 to compare the pressure losses between venturi and orifice plate meter. 2. Calculate the Reynolds number and loss factors in Table 3. Recall that the Reynolds number Re is given by Re = VD/ν, where ν is the kinematic viscosity. The Reynolds number should be computed based on the average velocity and diameter at the local cross section. 3. Plot the loss factors KV and KO against their corresponding Reynolds number Re. 4. Provide sample calculations for one set of readings.

Discussion 1. Comment on the relative advantages and disadvantages of venturi meter and orifice plate meter as flow measuring devices, based on your experimental observation of their comparative simplicity and accuracy. 2. Comment on the head losses associated with both flow devices studied in this experiment, emphasising the relationship between the mechanism of loss generation and its magnitude. Where do you think the greatest head loss would occur, and why? 3. Explain with the aid of simple sketches what is the vena contractor of an orifice meter? How is this area contraction considered in computing the actual discharge from the head loss (compare equation (a.2) for venturi meter with equations (b.2) and (b.3) for orifice)?

8

A BRIEF NOTE ON FLOW MEASUREMENTS Fluid flow measurements involve measurement of pressure, velocity, discharge, density, viscosity and many other properties, and may be accomplished in a number of ways. These are basically either direct or indirect methods using gravimetric, volumetric, electronic, electromagnetic, optical and other new techniques. There are a number of parameters which govern fluid flow. One important parameter is the quantity of flow or discharge. The flow is generally expressed in terms of volumetric rate of flow for incompressible fluids and mass rate of flow for compressible fluids. Direct methods of discharge measurement involve determining the weight of fluid passing through a section in a given time interval. Indirect methods of discharge measurement require determination of head, pressure differential, or computing the discharge. The most precise ones are the gravimetric or volumetric measurements in which the weight or volume is measured directly by a weighing scale or by a calibrated tank for a time interval measured by a stopwatch. Velocity measurements can be achieved, for example, by a simple Pitot-static tube or Prandtl tube, current meter, hot wire anemometer, laser Doppler anemometer, etc. The flow of gas can be measured using a gas flow meter. Electromagnetic flow devices and laser Doppler devices are utilised for flow measurement in conduits. For the case of free surface flows in open channels, weirs and notches are utilised for the measurement of flow. Flow can also be measured using positive displacement meter like disc meter or wobble meter employed in domestic water distribution systems. A number of flowmeters like orifice meters, Venturi meters, etc. are standardised according to the test codes given by the British Standards Institution, for example. The following references might be useful for a better understanding of flow measurements.

9

REFERENCES British Standards Institution: BS 1042. Dally J.W., Riley W.F. and McConnell K.G., “Instrumentation for Engineering Measurements”, John Wiley & Sons, 2nd Edition, 1993. Elrod Jr H.G. and Rouse R.R., “An Investigation of Electromagnetic Flowmeters”, Trans. ASME Vol. 74, 589, May 1952. Goldstein R.J., “Fluid Mechanics Measurements”, Taylor & Francis, 2nd Edition, 1996. Holman J.P., “Experimental Methods for Engineers”, McGraw Hill, 6th Edition, 2001. Phan-Thien, N., Lecture notes for ME2134: Fluid Mechanics I. Massey B.S., “Mechanics of Fluids”, Taylor & Francis, 8th Edition, 2006. Sabersky R.H., Acosta A.J., Haupymann E.G. and Gates E.M., “Fluid Flow”, Upper Saddle River, NJ: Prentice Hall, 4th Edition, 1998. Streeter V.L., Wylie E.D. and Bedford K.W., “Fluid Mechanics”, McGraw Hill, 9th Edition, 1997. Ward-Smith A.J., “Internal fluid Flow, The Fluid Dynamics of Flow in Pipes and Ducts”, Oxford, 1980. Yuan S.W., “Foundations of Fluid Mechanics”, Prentice Hall, SI Unit Edition, 1970, pp. 157 - 166.

10

Table 1: Raw Data Sheet Diameters (mm)

Trial No.

Manometer Reading (mm) at Location 1 2 3 5 6

D1 = D3 =

Rotameter Reading (mm)

Weight (kg) 5.0

1 D2 =

10.0

D5 = D6 =

5.0 2

Do =

10.0 5.0

Areas (mm2)

3 10.0

A3 =

5.0 4

A2 =

10.0

A5 = A6 =

5.0 5

Ao =

10.0 5.0 6 10.0

Temperature of water = Kinematic Viscosity of water ν =

11

Time (s)

Table 2: Processed Data Sheet 1 (See SUMMARY OF EQUATIONS on last page)

Trial No.

Rotameter Reading (mm)

QA (mm3/s)

QT Venturi (mm3/s) [Eqn. a.1]

1 2 3 4 5 6

12

Q'

T

Orifice (mm3/s) [Eqn. b.1]

Venturi Loss ∆HV (mm) [Eqn. a.3]

Orifice Loss ∆HO (mm) [Eqn. b.4]

Table 3:

Processed data sheet 2 (See SUMMARY OF EQUATIONS on last page) Estimation of loss factors

Trial No

Actual flow QA

Velocity V2 [Eq f.1]

Venturi meter Reynolds No. Re2 [Eq f.6]

Orifice plate Reynolds Velocity No. VO ReO [Eq f.2] [Eq f.7]

Loss Factor KV [Eq a.4]

1 2 3 4 5 6

13

Loss Factor KO [Eq b.5]

Remarks

SUMMARY OF EQUATIONS Computation of energy loss or head loss between any two stations x and y: 2  * Vx2   * Vy   ,  − h y + ∆H xy =  h x +   2g 2g     Q Q where Vx = A and Vy = A . Ax Ay a.

Venturi Meter (between 1 and 3): Q V2 = A A2

b.

∆H ΔH V = h − h (a.3) ⇒ K V = 2 V (a.4), where (V2 / 2 g ) Orifice Meter (between 5 and 6):

∆H (b.4) ⇒ K O = 2 O (b.5), where (VO / 2g)

Q VO = A AO

* 1

(

)(

∆H O = h − h 1 − C * 5

* 6

* 3

2

)

1

(f.1)

 2g(h 1* −h *2 )  Q T =A 1   2  (A1 /A 2 ) −1

(f.2)

 2g(h *5 −h *6 )  2 (b.1) Q'T =A O  2  1−(A O /A 5 ) 

2

(a.1)

1

 1−(A O /A 5 ) 2  C=Cd  2 2  1−C d (A O /A 5 )  c.

C d = Q A Q T (a.2)

1

Q A =CQ'T (b.2)

2

(b.3)

Rotameter (between 8 and 9): ∆H R = h *8 − h *9 (c.2) ⇒ K R =

∆H R (c.3), where (V82 / 2 g )

V8 =

QA A8

(f.3)

d.

Diffuser (between 3 and 4): ΔH Q Q 2A  1 1  * *  2 − 2  (d.1) ⇒ K D = 2 D (d.2), where V3 = A (f.4) ΔH D = (h 3 − h 4 ) + A3 2g  A 3 A 4  (V3 /2g) e. 90° Elbow (between 7 and 8): ∆H Q Q 2A  1 1  * *  2 − 2  (e.1) ⇒ K E = 2 E (e.2), where V7 = A (f.5) ∆H E = (h 7 − h 8 ) +  A7 2g  A 7 A 8  (V7 / 2 g ) Reynolds Number: V D VD VD VD Re O = O O (f.7); Re 8 = 8 8 (f.8); Re 3 = 3 3 (f.9); Re 2 = 2 2 (f.6);

ν

ν

ν

ν

14

Re 7 =

V7 D 7

ν

(f.10)