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 observatio

n

Mass ofbucket

with water(kg)

Mass ofwater(kg)

Time(s)

Manometer Reading

Leftcolumn

(cm)

Rightcolumn

(cm)

Difference(cm)

1 4.80 4.35 16 26.6 35.3 8.72 5.75 5.3 16.2 24.9 36.8 11.93 6.40 5.95 16 23.3 38.6 15.34 6.60 6.15 15.5 21.2 41.4 20.25 6.90 6.45 16.3 18.5 44.4 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, ρw = 996.22 kg/m3

Density of Carbon Tetra Chloride, ρCCl4 = 1575.79 kg/m3

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 flowrateKg/s

Volumetric flow rate Q

m3/sec

Area of the orifice

m2

Velocity at orifice u0

m/sec

ReynoldsNumber

NRe

1 0.271875 0.000273

5.07E-04

0.538277 16315.962 0.32716 0.000328 0.647735 19633.793 0.371875 0.000373 0.736264 22317.234 0.396774 0.000398 0.785562 23811.55 0.395706 0.000397 0.783446 23747.36

4

Table 3: Table for Calculation of Orifice Coefficient

Manometer Reading Change in

pressure

head H

(m)

Root of

change in

pressure

head

√ΔH

Orifice

Coefficiet

C0Left

column

(cm)

Right

column

(cm)

Difference

of Pressure

(cm)

Difference

of Pressure

(m)

26.6 35.3 8.7 0.087 0.0506140.22497

5 0.510564

24.9 36.8 11.9 0.119 0.0692310.26311

7 0.525325

23.3 38.6 15.3 0.153 0.0890110.29834

7 0.526613

21.2 41.4 20.2 0.202 0.1175170.34280

8 0.488999

18.5 44.4 25.9 0.259 0.1506780.38817

3 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 =

πD02

4 =

π×(0 . 0254 )2

4 m2 = 5.067×10-4 m2

Weight of bucket = 0.450 kg

Weight of water & bucket = 6.60 kg

5

Weight of water, m = ( 6.60 - 0.450 ) kg = 6.15 kg

Time of collection of water, t =15.5 s

Mass flow rate of water, m=m

t=6 . 15 kg

15 .5 s=0. 396774

kg/s

Density of water at 28o C, ρw = 996.22 kg/m3

Volumetric flow rate of water, Q= m

ρW=0 . 396774 kg/s

996 .22kg/m3=3. 98×10−4

m3/s

Velocity at orifice, Vo =

QAo

=3 . 98×10−4m3 /s5. 067×10-4m2

=0 . 785562 m/s

Dynamic Viscosity of water w =0.0008348Ns/m2 (at 28.50 C)

Reynolds number, Re =

Do vo ρwμw

=0 .0254×0.786×996 .228 . 348×10−4

=23811. 5

Difference in manometer reading, R = (41.4 - 21.2) cm =20.2 = 0.202m

Density of Carbon Tetra Chloride, ρCCl4 = 1575.79 kg/m3

Change in pressure head,

H =

R ( ρCCl4− ρw)

ρw=

0 . 202×(1575. 79−996 .22 )996 . 22

=0.117517m

∴H = 0.117517 m0.5 =0.342808 m0.5

Acceleration of gravity, g = 9.81 m/s2

Orifice co-efficient,

6

C0=Q√1−(

DoD

)4

Ao √2 gΔH=

3. 98×10−4×√1−( 0 .02540 . 0525

)4

5 . 067×10−4 √2×9 .81×0 . 117517=0 . 488999

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 observatio

n

ReynoldsNumber

NRe

Change in pressure head

H(m)

Root of change in pressure head

√ΔH

Orifice Coefficiet C0

1 16315.96 0.050614 0.224975 0.5105642 19633.79 0.069231 0.263117 0.5253253 22317.23 0.089011 0.298347 0.5266134 23811.5 0.117517 0.342808 0.4889995 23747.36 0.150678 0.388173 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

8

re-tested prior to its use as a mass flow rate sensor using a larger bucket to measure the

mass flow rate.

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 √∆ . e) Plot of CΗ 0 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. √ΔH are rectangular parabola.

0.00026 0.00028 0.0003 0.00032 0.00034 0.00036 0.00038 0.0004 0.000420

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

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

volumetric flow rate,Q [m3/s]

Chan

ge in

pre

ssu

re h

ead

, ∆H

[m

]

9

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

0.00026 0.00028 0.0003 0.00032 0.00034 0.00036 0.00038 0.0004 0.000420

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

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

volumetric flow rate,Q [m3/s]

Sqrt

of p

ress

ure

head

, ∆H

[m0.

5]

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

rate.

10

0.04 0.06 0.08 0.1 0.12 0.14 0.160

0.1

0.2

0.3

0.4

0.5

0.6

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

Change in pressure head, ∆H [m]

Ori

fice

Coe

ffic

ien

t,C0

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

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.40

0.1

0.2

0.3

0.4

0.5

0.6

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

Sqrt of pressure head, ∆H [m0.5]

Ori

fice

Coe

ffic

iet,

C0

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

Coefficient, C0

11

15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 250000

0.1

0.2

0.3

0.4

0.5

0.6

Plot of Reynolds Number,Re Vs Orifice Coefficiet,C0

Reynolds Number,Re

Ori

fice

Coe

ffic

iet,

C0

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

12