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Summery Orifice meters are most commonly used for continuous measurement of fluid flow in pipes. It uses Bernoulli's principle according to which the velocity increases when pressure decreases and vice versa. For this experiment velocity of the fluid (water) was found to be the within the range of 0.538277 m/sec to 0.783446 m/sec and the pressure drop of water was within 0.050614 m to 0.150678 m. We used these values to find orifice coefficient and Reynolds number for different flow rates. The orifice coefficient was within the range of 0.43 to 0.526 and the Reynolds number was within 16315.96 to 23811.5. These values were graphically represented from which the orifice meter can be calibrated.

1

Experimental Set up

Fig-1: Orifice meter

2

Observed data

Nominal pipe dia. = 2 inch Schedule No = 40 Orifice Diameter = 1 inch Mass of the empty bucket = 0.450 kg Temperature of the room = 29.5 0C Temperature of the water = 28.5 0C

Table.1: Table on water flow rate and readings of manometer. No. of observation

1 2 3 4 5

Mass of bucket with water (kg) 4.80 5.75 6.40 6.60 6.90

Mass of water (kg)

Time (s)

4.35 5.3 5.95 6.15 6.45

16 16.2 16 15.5 16.3

Manometer Reading Left column (cm) 26.6 24.9 23.3 21.2 18.5

Right column (cm) 35.3 36.8 38.6 41.4 44.4

Difference (cm) 8.7 11.9 15.3 20.2 25.9

3

Calculated data

All physical constants data provided here are taken from Franzini and Finnemore, Fluid Mechanics, 10th edition .729-737page and

Inside diameter, D = 2.067 inch = 0.0525 m Area of the orifice, Ao = 5.067×10-4 m2 Density of Water, w = 996.22 kg/m3 Density of Carbon Tetra Chloride, CCl = 1575.79 kg/m3 4

Viscosity of water at 28.5 0C=0.0008348Ns/m2

Table 2: Table for Calculation volumetric flow rate, average velocity and Reynold’s number. No. of observati on

Mass flow rate Kg/s

Volumetric flow rate Q m3/sec

1 2 3 4 5

0.271875 0.32716 0.371875 0.396774 0.395706

0.000273 0.000328 0.000373 0.000398 0.000397

Area of the orifice m2

Velocity at orifice u0 m/sec

Reynolds Number NRe

5.07E-04

0.538277 0.647735 0.736264 0.785562 0.783446

16315.96 19633.79 22317.23 23811.5 23747.36

4

Table 3: Table for Calculation of Orifice Coefficient Manometer Reading

Change in

Root of

Orifice

pressure

change in

Coefficiet C0

Left

Right

Difference

Difference

head H

pressure

column

column

of Pressure

of Pressure

(m)

head

(cm)

(cm)

(cm)

(m)

26.6 24.9 23.3 21.2 18.5

35.3 36.8 38.6 41.4 44.4

8.7 11.9 15.3 20.2 25.9

0.087 0.119 0.153 0.202 0.259

H 0.050614 0.069231 0.089011 0.117517 0.150678

0.224975 0.263117 0.298347 0.342808 0.388173

0.510564 0.525325 0.526613 0.488999 0.430688

Sample Calculation

Sample Calculation for observation 4 Nominal pipe diameter = 2 inch Schedule No = 40 Inside diameter, D = 2.067 inch = 0.0525 m Orifice diameter, Do = 1 inch = 0.0254 m Area of the orifice, Ao =

D0 2 4

=

(0.0254 ) 2 4

m2 = 5.067×10-4 m2

Weight of bucket = 0.450 kg Weight of water & bucket = 6.60 kg Weight of water, m = ( 6.60 - 0.450 ) kg = 6.15 kg Time of collection of water, t =15.5 s

5

Mass flow rate of water, m

m 6.15 kg 0.396774 kg/s t 15.5 s

Density of water at 28o C, w = 996.22 kg/m3 Volumetric flow rate of water, Q

Velocity at orifice, Vo =

m

W

0.396774 kg/s 3.98 10 4 m3/s 996 .22 kg/m 3

Q 3.98 10 4 m 3 / s 0.785562m/s Ao 5.067 10-4 m 2

Dynamic Viscosity of water w =0.0008348Ns/m2 (at 28.50 C) Reynolds number, Re =

Do vo w

w

0.0254 0.786 996 .22 23811 .5 8.348 10 4

Difference in manometer reading, R = (41.4 - 21.2) cm =20.2 = 0.202m Density of Carbon Tetra Chloride, CCl 4 = 1575.79 kg/m3 Change in pressure head, H =

R( CCl 4 w )

w

0.202 (1575.79 996.22) 0.117517m 996.22

H = 0.117517 m0.5 =0.342808 m0.5

Acceleration of gravity, g = 9.81 m/s2

Orifice co-efficient,

Do 4 0.0254 4 3.98 10 4 1 ( ) ) 0.0525 D 0.488999 2 gH 5.067 10 4 2 9.81 0.117517

Q 1 ( C0

Ao

6

Results The results of our experiment are summarized in Table-4. Table-4: Summary of the Results for Velocity, Pressure Drop and Orifice Co-efficient. No. of observation

1 2 3 4 5

Reynolds Number NRe 16315.96 19633.79 22317.23 23811.5 23747.36

Change in pressure head H (m) 0.050614 0.069231 0.089011 0.117517 0.150678

Root of change in pressure head

Orifice Coefficiet C0

H 0.224975 0.263117 0.298347 0.342808 0.388173

0.510564 0.525325 0.526613 0.488999 0.430688

From The table we know that the determined orifice coefficient was 0.43 to 0.526.

7

Discussion

The largest contribution to the uncertainty in the measured coefficient is due to the time measurement. At the higher mass flow rates, the bucket filled much too quickly causing large temporal uncertainty. The simplest solution to this problem would be to use a larger vessel to capture the water. This would increase the filling time and reduce the uncertainty in the temporal measurement. If the orifice plate is to be used at higher flow rates than those presented here, it would be necessary to recalibrate and expand the Reynolds number range. Expanding the Reynolds number range would benefit from a larger bucket as well. The main disadvantage of this meter is the greater frictional loss it causes as compared with the other devices and hence causes large power consumption. While water passing through the orifice, it increase the velocity head at the expense of the pressure head. But when it again expands at downstream all of the pressure loss is not recovered because of friction and turbulence in the stream. It is recommended that the project be repeated with a square edge orifice with flange taps that are designed and located according to ASME standards. We also recommend a sufficient length of pipe upstream of the orifice to insure fully developed flow prior to the orifice. Within the limits of the experimental uncertainty and the Reynolds number range investigated, the results obtained for the discharge coefficient through an orifice plate agree with the empirical relation. Unfortunately, the large uncertainty in the experimental data significantly reduces the reliability and utility of the data. The orifice plate should be re-tested prior to its use as a mass flow rate sensor using a larger bucket to measure the mass flow rate.

8

Graphs Five graphs are plotted according to our results. a)plot of ∆H Vs Q; b) plot of √∆H Vs Q; c) plot of C0 Vs ∆H, d) plot of C0 Vs √∆Η. e) Plot of C0 Vs NRe From figure-2, the relation between change in pressure head and volumetric flow rate is parabola asymmetric about Y axis. From figure-3, a linear relationship between root of change in pressure head and volumetric flow rate is found. In figure-4 and figure-5, the relation between Co Vs. H and Co vs.

H are rectangular parabola.

Plot of change in pressure head,∆H Vs volumetric flow rate,Q 0.16

Change in pressure head, ∆H [m]

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.00005

0.0001

0.00015

0.0002

0.00025

volumetric flow rate,Q

0.0003

0.00035

0.0004

0.00045

[m3/s]

Figure-2: The relation between change in pressure head and volumetric flow-rate

9

Plot of Sqrt of change in pressure head,√∆H Vs volumetric flowrate,Q 0.45

0.4

Sqrt of pressure head, ∆H [m0.5]

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

volumetric flow rate,Q [m3/s]

Figure-3: The relation between sqrt of change in pressure head and volumetric flowrate.

10

Change in Orifice Coefficiet, C0 Vs pressure head, ∆H [m] 0.6

Orifice Coefficient,C0

0.5 0.4 0.3 0.2 0.1 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Change in pressure head, ∆H [m]

Figure-4: The relation between change in pressure head and Orifice Coefficient, C0

Plot of Orifice Coefficiet C0 Vs Sqrt of change in pressure head,√∆H 0.6

Orifice Coefficiet,C0

0.5 0.4 0.3 0.2 0.1 0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Sqrt of pressure head, ∆H [m0.5]

Figure-5: The relation between sqrt of change in pressure head and Orifice Coefficient, C0

11

Plot of Reynolds Number,Re Vs Orifice Coefficiet,C0 0.6

Orifice Coefficiet,C0

0.5 0.4 0.3 0.2 0.1 0 0

5000

10000

15000

20000

25000

30000

Reynolds Number,Re

Figure-6: The relation between Reynolds number, Re and Orifice Coefficient, C0

12

1

Experimental Set up

Fig-1: Orifice meter

2

Observed data

Nominal pipe dia. = 2 inch Schedule No = 40 Orifice Diameter = 1 inch Mass of the empty bucket = 0.450 kg Temperature of the room = 29.5 0C Temperature of the water = 28.5 0C

Table.1: Table on water flow rate and readings of manometer. No. of observation

1 2 3 4 5

Mass of bucket with water (kg) 4.80 5.75 6.40 6.60 6.90

Mass of water (kg)

Time (s)

4.35 5.3 5.95 6.15 6.45

16 16.2 16 15.5 16.3

Manometer Reading Left column (cm) 26.6 24.9 23.3 21.2 18.5

Right column (cm) 35.3 36.8 38.6 41.4 44.4

Difference (cm) 8.7 11.9 15.3 20.2 25.9

3

Calculated data

All physical constants data provided here are taken from Franzini and Finnemore, Fluid Mechanics, 10th edition .729-737page and

Inside diameter, D = 2.067 inch = 0.0525 m Area of the orifice, Ao = 5.067×10-4 m2 Density of Water, w = 996.22 kg/m3 Density of Carbon Tetra Chloride, CCl = 1575.79 kg/m3 4

Viscosity of water at 28.5 0C=0.0008348Ns/m2

Table 2: Table for Calculation volumetric flow rate, average velocity and Reynold’s number. No. of observati on

Mass flow rate Kg/s

Volumetric flow rate Q m3/sec

1 2 3 4 5

0.271875 0.32716 0.371875 0.396774 0.395706

0.000273 0.000328 0.000373 0.000398 0.000397

Area of the orifice m2

Velocity at orifice u0 m/sec

Reynolds Number NRe

5.07E-04

0.538277 0.647735 0.736264 0.785562 0.783446

16315.96 19633.79 22317.23 23811.5 23747.36

4

Table 3: Table for Calculation of Orifice Coefficient Manometer Reading

Change in

Root of

Orifice

pressure

change in

Coefficiet C0

Left

Right

Difference

Difference

head H

pressure

column

column

of Pressure

of Pressure

(m)

head

(cm)

(cm)

(cm)

(m)

26.6 24.9 23.3 21.2 18.5

35.3 36.8 38.6 41.4 44.4

8.7 11.9 15.3 20.2 25.9

0.087 0.119 0.153 0.202 0.259

H 0.050614 0.069231 0.089011 0.117517 0.150678

0.224975 0.263117 0.298347 0.342808 0.388173

0.510564 0.525325 0.526613 0.488999 0.430688

Sample Calculation

Sample Calculation for observation 4 Nominal pipe diameter = 2 inch Schedule No = 40 Inside diameter, D = 2.067 inch = 0.0525 m Orifice diameter, Do = 1 inch = 0.0254 m Area of the orifice, Ao =

D0 2 4

=

(0.0254 ) 2 4

m2 = 5.067×10-4 m2

Weight of bucket = 0.450 kg Weight of water & bucket = 6.60 kg Weight of water, m = ( 6.60 - 0.450 ) kg = 6.15 kg Time of collection of water, t =15.5 s

5

Mass flow rate of water, m

m 6.15 kg 0.396774 kg/s t 15.5 s

Density of water at 28o C, w = 996.22 kg/m3 Volumetric flow rate of water, Q

Velocity at orifice, Vo =

m

W

0.396774 kg/s 3.98 10 4 m3/s 996 .22 kg/m 3

Q 3.98 10 4 m 3 / s 0.785562m/s Ao 5.067 10-4 m 2

Dynamic Viscosity of water w =0.0008348Ns/m2 (at 28.50 C) Reynolds number, Re =

Do vo w

w

0.0254 0.786 996 .22 23811 .5 8.348 10 4

Difference in manometer reading, R = (41.4 - 21.2) cm =20.2 = 0.202m Density of Carbon Tetra Chloride, CCl 4 = 1575.79 kg/m3 Change in pressure head, H =

R( CCl 4 w )

w

0.202 (1575.79 996.22) 0.117517m 996.22

H = 0.117517 m0.5 =0.342808 m0.5

Acceleration of gravity, g = 9.81 m/s2

Orifice co-efficient,

Do 4 0.0254 4 3.98 10 4 1 ( ) ) 0.0525 D 0.488999 2 gH 5.067 10 4 2 9.81 0.117517

Q 1 ( C0

Ao

6

Results The results of our experiment are summarized in Table-4. Table-4: Summary of the Results for Velocity, Pressure Drop and Orifice Co-efficient. No. of observation

1 2 3 4 5

Reynolds Number NRe 16315.96 19633.79 22317.23 23811.5 23747.36

Change in pressure head H (m) 0.050614 0.069231 0.089011 0.117517 0.150678

Root of change in pressure head

Orifice Coefficiet C0

H 0.224975 0.263117 0.298347 0.342808 0.388173

0.510564 0.525325 0.526613 0.488999 0.430688

From The table we know that the determined orifice coefficient was 0.43 to 0.526.

7

Discussion

The largest contribution to the uncertainty in the measured coefficient is due to the time measurement. At the higher mass flow rates, the bucket filled much too quickly causing large temporal uncertainty. The simplest solution to this problem would be to use a larger vessel to capture the water. This would increase the filling time and reduce the uncertainty in the temporal measurement. If the orifice plate is to be used at higher flow rates than those presented here, it would be necessary to recalibrate and expand the Reynolds number range. Expanding the Reynolds number range would benefit from a larger bucket as well. The main disadvantage of this meter is the greater frictional loss it causes as compared with the other devices and hence causes large power consumption. While water passing through the orifice, it increase the velocity head at the expense of the pressure head. But when it again expands at downstream all of the pressure loss is not recovered because of friction and turbulence in the stream. It is recommended that the project be repeated with a square edge orifice with flange taps that are designed and located according to ASME standards. We also recommend a sufficient length of pipe upstream of the orifice to insure fully developed flow prior to the orifice. Within the limits of the experimental uncertainty and the Reynolds number range investigated, the results obtained for the discharge coefficient through an orifice plate agree with the empirical relation. Unfortunately, the large uncertainty in the experimental data significantly reduces the reliability and utility of the data. The orifice plate should be re-tested prior to its use as a mass flow rate sensor using a larger bucket to measure the mass flow rate.

8

Graphs Five graphs are plotted according to our results. a)plot of ∆H Vs Q; b) plot of √∆H Vs Q; c) plot of C0 Vs ∆H, d) plot of C0 Vs √∆Η. e) Plot of C0 Vs NRe From figure-2, the relation between change in pressure head and volumetric flow rate is parabola asymmetric about Y axis. From figure-3, a linear relationship between root of change in pressure head and volumetric flow rate is found. In figure-4 and figure-5, the relation between Co Vs. H and Co vs.

H are rectangular parabola.

Plot of change in pressure head,∆H Vs volumetric flow rate,Q 0.16

Change in pressure head, ∆H [m]

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.00005

0.0001

0.00015

0.0002

0.00025

volumetric flow rate,Q

0.0003

0.00035

0.0004

0.00045

[m3/s]

Figure-2: The relation between change in pressure head and volumetric flow-rate

9

Plot of Sqrt of change in pressure head,√∆H Vs volumetric flowrate,Q 0.45

0.4

Sqrt of pressure head, ∆H [m0.5]

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

0.0004

0.00045

volumetric flow rate,Q [m3/s]

Figure-3: The relation between sqrt of change in pressure head and volumetric flowrate.

10

Change in Orifice Coefficiet, C0 Vs pressure head, ∆H [m] 0.6

Orifice Coefficient,C0

0.5 0.4 0.3 0.2 0.1 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Change in pressure head, ∆H [m]

Figure-4: The relation between change in pressure head and Orifice Coefficient, C0

Plot of Orifice Coefficiet C0 Vs Sqrt of change in pressure head,√∆H 0.6

Orifice Coefficiet,C0

0.5 0.4 0.3 0.2 0.1 0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Sqrt of pressure head, ∆H [m0.5]

Figure-5: The relation between sqrt of change in pressure head and Orifice Coefficient, C0

11

Plot of Reynolds Number,Re Vs Orifice Coefficiet,C0 0.6

Orifice Coefficiet,C0

0.5 0.4 0.3 0.2 0.1 0 0

5000

10000

15000

20000

25000

30000

Reynolds Number,Re

Figure-6: The relation between Reynolds number, Re and Orifice Coefficient, C0

12