Flow Through A Venturi Meter 1a2p3b

Kuwait University College of Engineering & Petroleum Mechanical Engineering Department

Lab B1 ME-437/01

Experiment A3

Flow through a Venturi Meter

By Omar Saleem 205111466 Group: A

Supervised by Dr. Nawaf Aljuwahel Eng. Ammar Bahman

Objectives •

To determine the venturi meter coefficient of discharge and to study the dependence of this discharge coefficient on the flow Reynolds number.

•

To compare the ideal pressure distribution along a venturi meter with the measured one.

Data: For table 1: V 0.03 0.03 Va = a = = = 4.91722 × 10 − 4 m 3 / s t avg . 60 + 62.56 + 60.47 61.01 3 D* = D 3 = 0.016 m V= 30 lit   π 2g C = D *2   4 4 1 − ( D * / D ) 

1/ 2

= 9.6226 × 10 -4

1/ 2 1/ 2 Vth = C ( h2 − h3 ) = (9.6226 × 10 −4 ) × ( 0.27 − 0.028 ) = 4.73369 × 10 -4 m 3 / s

π  u 3 = Vth  D32  = 2.35435 m / s 4  For table 2: D* = D 3 = 0.016 m D 2 = 0.026 m

For table 3:

ν =1.004 × 10 −6 m 2 / s T = 20 oC

Tables: Table 1: Measurements of pressure distribution at maximum flow rate.

Piezometer

Di

hi

4

Tube. No.

mm

mm water

A=2 B C D=3 E F G H J K L

26 23.2 18.4 16 16.8 18.47 20.16 21.84 23.53 25.24 26

270 259 165 28 44 126 171 202 219 235 240

Sample calculation for 2nd row of table 1 : Ideal : 4

4

4

4

 D*   D*  0.016   0.016   =    −   −  = - 0.0828  0.026   0.0259   D   Di  Measured:

Pressure coefficient Measured Ideal  D*   *   −D   D   Di      0 -0.0828 -0.4283 -0.8566 -0.6793 -0.4197 -0.2533 -0.1446 -0.0704 -0.0181 0

4

(hi − h2 )  u2   3  2g    0 -0.0389 -0.3716 -0.8566 -0.8000 -0.5097 -0.3504 -0.2407 -0.1805 -0.1239 -0.1062

( hi − h2 ) u     2g  2 3

=

0.259 - 0.270 = −0.0389 2.354 2 2 × 9.81

Table 2: Measurements at various flow rates.

Run

 V

t

No.

L

s

1 2 3 4 5 6 7 8

30 30 25 25 20 20 15 15

61.01 65.82 58.87 63.59 57.84 64.44 53.68 63.35

h2

Piezometric head h3

h4

mm 270 279 285 285 289 291 296 299

mm 28 61 101 133 164 196 222 249

mm 240 248 257 261 267 272 283 290

Table 3: Calculations at various flow rates.

( h 2 − h 3 )1/ 2

 V th

1/2

3

Run

 V a

No.

3

m /s

1

0.000492

37519.46

0.492

0.000473

1.0388

0.001

0.8760

2

0.000456

35610.42

0.467

0.000449

1.0145

0.000976

0.8578

3

0.000425

32715.82

0.429

0.000413

1.0288

0.00099

0.8478

4

0.000393

29735.19

0.390

0.000375

1.0479

0.001008

0.8421

5

0.000346

26965.21

0.354

0.00034

1.0164

0.000978

0.8240

6

0.00031

39777.12

0.522

0.000502

1.0465

0.001007

0.8000

7

0.000279

20747.45

0.272

0.000262

1.0675

0.001027

0.8243

u D Re = 3 3 ν

m

Cd

Cm

R

m /s

8

0.000237

17054.3

0.224

Sample calculation for 2nd row of table 3:

V Va = = 0.000456 m 3 / s t

Re =

u 3 D3

ν

= 35610.42

( h2 − h3 ) 1 / 2 = 0.467

1/ 2 Vth = C ( h2 − h3 ) = 0.000449

Cd =

Va = 1.0145 Vth

C m = C d × C = 0.000976

0.000215

1.1004

0.001059

0.8200

R=

h4 − h3 = 0.8578 h2 − h3

Figures 0

measured ideal

Pressure distributions

-100

-50

-0.1 0

50

100

150

-0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 position of piezometer tubes

Figure 1: Pressure coefficient for ideal and measured versus distance from inlet to contraction section.

0.0005 0.00045 0.0004 0.00035 Series1

V

0.0003 0.00025 0.0002 0.00015 0.0001 0.00005 0 0.000

0.100

0.200

0.300

0.400

0.500

0.600

(h3-h2)^2

Figure 2: Relationship between the flow rate and (h2-h3)2. 1.2000 1.0000

discharge coefficient meter coefficient

Cd&Cm

0.8000 0.6000 0.4000 0.2000 0.0000 0

10000

20000

30000

40000

Re

Figure 3: Relationship between the meter and discharge coefficient with the Reynolds number

1.0000 0.9000 0.8000 0.7000 Series1

R

0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 0

5000

10000

15000

20000

25000

30000

35000

40000

Re

Figure 4: Relationship between the recovery ratio and the Reynolds number.

Discussion The ideal and measured pressure distribution of the flow through the venturi meter is shown in fig.1. It can be seen, that the pressure is minimum at the throat section, this is due to the increase in velocity as the diameter decreases across the length of the tube. So therefore, the diameter of the tube is inversely proportional to the velocity, while proportional to the pressure of the fluid flowing through the tube. It is noticed that the curve for the measured pressure does not return to zero as the ideal one this is due to losses during the flow.

The value of Coefficient of discharge is greater than one in our results, since the coefficient of discharge represents the ratio of actual flow rate to the measure flow rate. Therefore a

value higher than one means that the actual flow rate is greater than the ideal one which is not possible. This results is most likely due to errors in the apparatus used. Also ,From Fig.3 it is seen that the venturi meter coefficient (Cm) and the discharge coefficient values oscillate between 0.001 to 0.001059 , 1.0145 to 1.1004 respectively. The Relation ship between the Recovery ratio and Reynolds number is shown in fig.4 notice the recovery ratio represents the difference between the actual and ideal pressure ratio distributions and is always below 1 as seen in fig.4.

The reasons for errors can be as follows: •

The water level was fluctuating in the manometers because of the vibration in the equipment while readings were being recorded.

•

If the water level reading is not taken from a proper view level, it will result in parallax error.

•

The recorded time readings will have some inaccuracy because of time delay caused by human reaction time. (i.e. not stopping the watch at exact time)

•

The flow rates will be effected by the friction in the inner walls of the Venturi meter.

Conclusion It can be concluded from the results of the experiment that, Venturi meter can be used to determine the coefficient of discharge for a given fluid. Also, Venturi meter can

display the trend of pressure distribution, as the fluid es through a tube with variable inner diameter. Also, the pressure distribution can be measured in many different locations inside the tubes. In the throat section the velocity is maximum and pressure distribution is minimum.