Calibration of Venturi and Orifice Meters

HIRIZZA JUNKO M. YAMAMOTO

Department of Chemical Engineering, College of Engineering and Architecture, Cebu Institute of Technology – University

N. Bacalso Ave. Cebu City, 6000 Philippines

This experiment aims to be calibrate both the venture apparatus and the orifice apparatus. The

coefficient of discharge of a sharp orifice is obtained and Reynolds number is calculated. It is

then plotted in a graph. The coefficient of discharge of a venturi is also obtained and plotted

against the corresponding calculated Reynolds number. The pressure drop is also plotted

against the water flow rate. In order to calibrate flow meters specifically the venturi and

orifice flow meters, a known volume of fluid is used to pass to measure the rate of flow of the

fluid through the pipe. Venturi meters consist of a vena contracta-shaped, short length pipe

which fits into a normal pipe line. Orifice meters, on the other hand, consists of a thin plate

with a hole and is placed at the middle of the pipe and behaves similarly to a venturi meter.

1. Introduction

An orifice meter is a thin plate with a hole in the middle that is placed in a

pipe through which the fluid flows. It increases the velocity of the fluid as it flows

through it, which decreases the pressure. It is a conduit and a restriction to create a

pressure drop. An hour glass is a form of orifice. [1] For orifice meter, as NRe

increases, C should decrease since friction increase and a greater head loss results.

(a) (b)

Figure 1. (a)Orifice Meter Device, (b)Orifice Meter Diagram

A nozzle, venturi or thin sharp edged orifice can be used as the flow

restriction. In order to use any of these devices for measurement it is necessary to

empirically calibrate them. That is, pass a known volume through the meter and note

the reading in order to provide a standard for measuring other quantities. Due to the

ease of duplicating and the simple construction, the thin sharp edged orifice has been

adopted as a standard and extensive calibration work has been done so that it is

widely accepted as a standard means of measuring fluids. Provided the standard

mechanics of construction are followed no further calibration is required. The

minimum cross sectional area of the jet is known as the “vena contracta.”

A venturi meter uses a narrowing throat in the pipe that expands back to the

original pipe diameter. It creates an increase in the velocity of the fluid, which also

results in a pressure drop across that section of the pipe. It is more efficient and

accurate than the orifice meter. The long expansion section (diffuser) enables an

enhanced pressure recovery compared with that of an orifice plate, which is useful in

some metering applications. As NRe increases in fluid flow, C should increase since

friction effects decrease and flow rate approaches the theoretical. [2]

Figure 2.  Venturi Meter Diagram

The hydrostatic equation is applicable to all types of flowmeters (venturi and orifice)

(Equation 1). By Bernoulli’s equation, the cause of the pressure drop is determined to be the

increase of velocity of the pipe flow (Equation 2). By aggregating the hydrostatic, Bernoulli’s

and continuity equations, the theoretical flow rate passing through the venturi meter can be

calculated. Bernoulli’s equation is an energy balance equation and is given as:

P1/ρ + V1 2/2 + gz1= P2/ρ + V2 2/2 + gz2 (Equation 1)

WhereP1 is the pressure of the fluid flow as it enters the meter,ρ is the density of the flowing fluid,V1 is the upstream velocity of the flow,G is gravitational acceleration,z1 is the height of the fluid as it enters the meter,P2 is the pressure of the fluid at the throat of the meter,V2 is the velocity of the flow at the throat andz2 is the height of the fluid at the throat of the meter.

Considering a horizontal application, gravitational potential energy is neglected

because there is no change in height of the fluid and Bernoulli’s equation can be rewritten as:

P1/ρ + V1 2/2 = P2/ρ + V2 2/2 (Equation 2)

Bernoulli’s equation can then be rearranged to solve the energy balance in terms of the

velocities of the flow at state 1 and state 2.

ΔP/ρ = V2 2/2– V1 2/2 (Equation 3)

Where:

ΔP is the pressure difference P1– P2

Because the pressure drop, ΔP, and the velocities V1 and V2 cannot be measured directly, the

hydrostatic equation (Equation 4) and the continuity equation (Equation 5) are employed. The

Δh variable of the hydrostatic equation is the difference in height of the air over water

manometer due to pressure and is measured directly.

ΔP = ρgΔh (Equation 4)

Qth= V1A1= V2A2 (Equation 5)

Equation 5 is rearranged to solve for V1 and is written as follows:

V1= V2A2/A1= V2(D22/D12) (Equation 6)

Where:

D2 is the diameter of the throat of the venturi meter and D1 is the diameter of the upstream

region of the meter. Still, the velocity at state 2 is unknown and can be solved for by

rearranging the continuity equation to be substituted into Equation 3.

V22= (Qth/A2)2 (Equation 7)

where

Qth is the theoretical flow rate

Substituting Equation 4 in for ΔP and Equation 6 in for V1, the Bernoulli equation (Equation

3) becomes:

gΔh = [V22/2 - V2(D22/D12)] (Equation 8)

Tidying up Equation 8 yields the following:

2gΔh = V22 [1 - (D22/D12)] (Equation 9)

Substituting Equation 7 into Equation 9 yields the following:

2gΔh = Qth2/A22 [1 - (D22/D12)](Equation 10)

Rearranging to solve for the theoretical flow rate

Qth yields the following:

Qth= A2(2gΔh)1-D22D12=A22(P1-P2)ρ1- (D2D1 )4 (Equation 11)

The Reynolds number of the pipe flow can be calculated using the following equation:

Re = V2D2 / ν = V2D2ρ/µ (Equation 12)

where ν is the kinematic viscosity of the fluid.

The coefficient of discharge, Cv (for venturi) and Co (for orifice), can be calculated using the

following equation

C = Qact/ Qth (Equation 13)

Where: Qth is the theoretical flow rate and Qact is the indicated flow rate of the testing

apparatus. [2]

2. Materials and Methods

2.1 Apparatus

2.1.1 Hydraulic Bench Apparatus

2.1.2 Orifice Meter

2.1.3 Venturi Meter

2.2 Materials

2.2.1 Stopwatch

2.2.2 Manometer

2.2.3 Water

2.2.4 Vernier Caliper

2.2.5 One 1-L graduated cylinder

Sketch:

2.3 Methods

All materials and apparatus were checked and prepared before the experiment

started. All materials and apparatus were also cleaned appropriately.

For the calibration of venture meter/ orifice meter apparatus, the venturi or orifice

meter apparatus was set up. The pump was started and the main regulating flow valve

was opened to fix the water flow rate. The tubes from the venture or orifice pressure

tapping points to the manometer (mouth or inlet tap point and throat tap point) were

connected. It was ensured that there is no trapped air in the connecting lines. Ample

time was allowed to stabilize the flow before readings were taken.

The upstream and downstream of the manometer were read and recorded. The

diameter of the cylindrical cross-section of the tapping points of the venture or orifice

apparatus was recorded. The theoretical volumetric flow rate was computed. For any

reading of the manometer, the volume discharged was collected at the outlet and the

time to collect the volume discharged at the outlet was measured using a graduated

cylinder. The volume collected and the time was recorded. The actual volumetric flow

rate from the volume collected divided by the time obtained was computed. Several

trials were taken by adjusting the main flow regulating valve. All the data were

recorded and the coefficient of discharge of the Venturi and Orifice apparatus and

their Reynolds Number were computed respectively.

3. Results

Table 1. Orifice Meter Data

ORIFICE METER

TRIAL

MANOMETER READINGRm (cm)

∆P Qtheo (m3/s)

VOLUMETRIC FLOW

RATE, Qactual (m3/s)

C NreUPSTREAM

DOWNSTREAM

1 34 cm 30 cm 4 3911.20583

4.57393E-05 0.00012 2.623563

31

6694.05841

2 59 cm 53.4 cm 5.6 5475.68817

5.41195E-05 0.000146 2.697734

09

8144.43773

3 49.3 cm 47.5 cm 1.8 1760.04262

3.06829E-05 0.00012 3.910977

27

6694.05841

4 68.8 cm 67.9 cm 0.9 880.021312

2.16961E-05 0.000152 7.005878

99

8479.14065

5 28.8 cm 25.4 cm 3.4 3324.52496

4.21696E-05 0.00018 4.268480

92

10041.0876

6 77.3 cm 70.9 cm 6.4 6257.92933

5.78562E-05 0.000146 2.523499

17

8144.43773

7 20.9 cm 18.3 cm 2.6 2542.28379

3.68762E-05 0.00014 3.796484

75

7809.73481

8 68.8 cm 61.3 cm 7.5 7333.51094

6.26311E-05 0.00034 5.428609

27

18966.4988

9 32.8 cm 28.7 cm 4.1 4008.98598

4.63075E-05 0.00012 2.591371

13

6694.05841

10 81.3 cm 74.3 cm 7 6844.61021

6.05074E-05 0.00015 2.479034

31

8367.57301

Graph 1: Reynolds number of the fluid vs C in a venturi flowmeter

Graph 2: Pressure drop vs Qactual in an orifice flow meter

Table 2. Venturi Meter Data

VENTURI METER

TRIAL

MANOMETER READINGRm (cm)

∆P Qtheo (m3/s)

VOLUMETRIC FLOW

RATE, Qactual (m3/s)

C NreUPSTREAM

DOWNSTREAM

1 52.5 cm 45.5 cm 7 6844.61021

6.0507E-05 0.00014 2.313765

36

7809.73481

2 71.5 cm 64.5 cm 7 6844.61021

6.0507E-05 0.00015 2.479034

31

8367.573011

3 45.5 cm 43 cm 2.5 2444.50365

3.616E-05 0.000136 3.761050

82

7586.59953

4 44 cm 42.5 cm 1.5 1466.70219

2.8009E-05 0.000126 4.498473

99

7028.761329

Graph 3: Reynolds number of the fluid vs C in a venturi flow meter

Graph 2: Pressure drop vs Qactual in a venturi flow meter

4. Discussion

Orifice plate is a plate with an orifice that restricts the flow, thereby causing a

pressure drop which is related to the volumetric flow based on Bernoulli’s equation.

Orifice plates causes high energy losses and high pressure loss to the flow being

measured. Venturi meter, on the other hand, is also based on Bernoulli’s principle just

like the orifice plate. But instead of sudden constriction caused by an orifice, venture

meter uses a relatively gradual constriction much like a reducer to cause the pressure

drop by increasing fluid velocity. The volumetric flow is proportional to the square

root of this pressure drop and venture meter can be calibrated accordingly.

For the orifice meter, if viscosity is higher, Reynolds number is lower and a

higher flow rate for the same pressure difference in front of and after the orifice leads

to a higher coefficient of discharge. The discharge coefficient in a venture meter

varies noticeably at low values of the Reynolds number.

The probable sources of error in the result are the bubbles that may have

appeared in the hose. Another is in reading the measurements and some human errors.

5. Conclusion

The aim of this experiment is to be able to calibrate the orifice and venturi

flow meters by letting a known volume of water pass through and reading the pressure

changes from a manometer. The data gathered in the venturi is more accurate as seen

in the graph which shows how the data fits in the regression line.

When Reynolds number is decreased, the coefficient discharge of a venturi

flow meter increases. The increase in the pressure drop vs volumetric flow rate in an

orifice is greater than in the venturi flow meter. Pressure losses in an orifice, though,

is approximately twice than that of a venturi.

Appendix

Sample Calculation for both Orifice and Venturi Meters;

Diameter of the pipe = 25 mm = 0.025 m

Throat Diameter = 12.5 mm = 0.0125 m

At 25 degrees Celsius: density of water = 997.08 kgm3

*The equations apply for venturi and orifice meters.

Cross sectional area of thethroat diameter ( A2 )= π (D)2

4=π (0.0125m)2

4=0.0005m3

∆ h = upstream - downstream =34-30 = 0.4 mmH2O = 0.0004 mmH2O

∆ P∈manometer=∆hgρ=0.0004m(9.8066ms2 )(997.08 kg

m3 )=3.9112Pa

Volumecollected=0.0006m3

Qactual=0.0006m3

5 s=1.2 x10−4m3

s

Qtheo .=A2 √ (2 )(P1−P2)ρ

(1−D2

D1

4

)=0.0005m3 √ (2 )(3.9112Pa)

997.08kg /m3

¿¿ ¿

C=QactualQtheo .

=2.62 v=Qactual

A2=

1.2 x10−4 m3

s0.0005m3 =0.24 m

s

N ℜ=D2 vρμ

=(0.025m )(0.24 m

s )(997.08 kgm3 )

0.0008937 kgm . s

=6694.05841

References:

[1] C.J. Geankoplis, et. al. Principles of Transport Processes and Separation Processes,

Pearson Education Inc., New Jersey, 2003.

[2] W.L. McCabe, et. al. Unit Operations of Chemical Engineering, 5th ed, McGraw-Hill

Inc., Singapore, 1993.

Other Sources:

http://www.enggcyclopedia.com/2011/07/pressure-drop-based-flow-measurement-devices/.

Retrieved January 2017