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)
Where
P1 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 and
z2 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
TRIA
L
MANOMETER READING
Rm
(c
m)
∆P
Qtheo
(m3/s)
VOLUMET
RIC FLOW
RATE,
Qactual
(m3/s)
C NreUPSTREA
M
DOWNSTRE
AM
1 34 cm 30 cm 4
3911.205
83
4.57393
E-05
0.00012
2.623563
31
6694.058
41
2 59 cm 53.4 cm 5.6
5475.688
17
5.41195
E-05
0.000146
2.697734
09
8144.437
73
3 49.3 cm 47.5 cm 1.8
1760.042
62
3.06829
E-05
0.00012
3.910977
27
6694.058
41
4 68.8 cm 67.9 cm 0.9
880.0213
12
2.16961
E-05
0.000152
7.005878
99
8479.140
65
5 28.8 cm 25.4 cm 3.4
3324.524
96
4.21696
E-05
0.00018
4.268480
92
10041.08
76
6 77.3 cm 70.9 cm 6.4
6257.929
33
5.78562
E-05
0.000146
2.523499
17
8144.437
73
7 20.9 cm 18.3 cm 2.6
2542.283
79
3.68762
E-05
0.00014
3.796484
75
7809.734
81
8 68.8 cm 61.3 cm 7.5
7333.510
94
6.26311
E-05
0.00034
5.428609
27
18966.49
88
9 32.8 cm 28.7 cm 4.1
4008.985
98
4.63075
E-05
0.00012
2.591371
13
6694.058
41
10 81.3 cm 74.3 cm 7
6844.610
21
6.05074
E-05
0.00015
2.479034
31
8367.573
01

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
TRIA
L
MANOMETER READING
Rm
(c
m)
∆P
Qtheo
(m3/s)
VOLUMET
RIC FLOW
RATE,
Qactual
(m3/s)
C NreUPSTREA
M
DOWNSTRE
AM
1 52.5 cm 45.5 cm 7
6844.610
21
6.0507
E-05
0.00014
2.313765
36
7809.7348
1
2 71.5 cm 64.5 cm 7
6844.610
21
6.0507
E-05
0.00015
2.479034
31
8367.5730
11
3 45.5 cm 43 cm 2.5
2444.503
65
3.616E
-05
0.000136
3.761050
82
7586.5995
3
4 44 cm 42.5 cm 1.5
1466.702
19
2.8009
E-05
0.000126
4.498473
99
7028.7613
29
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
𝑘𝑔
𝑚3
*The equations apply for venturi and orifice meters.
𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑟𝑜𝑎𝑡 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 ( 𝐴2) =
𝜋(𝐷)2
4
=
𝜋(0.0125 𝑚)2
4
= 0.0005 𝑚3
∆ℎ = upstream - downstream =34-30 = 0.4 mmH2O = 0.0004 mmH2O
∆𝑃 𝑖𝑛 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟 = ∆ℎ𝑔𝜌 = 0.0004 𝑚 (9.8066
𝑚
𝑠2
) (997.08
𝑘𝑔
𝑚3
) = 3.9112 𝑃𝑎
𝑉𝑜𝑙𝑢𝑚𝑒 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑒𝑑 = 0.0006 𝑚3
𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 =
0.0006 𝑚3
5 𝑠
= 1.2𝑥10−4 𝑚3
𝑠
𝑄𝑡ℎ𝑒𝑜. = A2√
(2)(P1−P2)
ρ
(1−
D2
D1
4
)
= 0.0005 𝑚3 √
(2)(3.9112 Pa)
997.08 kg/m3
(1−(
0.025 m
0.0125 m
)4)
= 4.57x10−5 𝑚3
𝑠
𝐶 =
𝑄 𝑎𝑐𝑡𝑢𝑎𝑙
𝑄𝑡ℎ𝑒𝑜.
= 2.62 𝑣 =
𝑄 𝑎𝑐𝑡𝑢𝑎𝑙
A2
=
1.2𝑥10−4 𝑚3
𝑠
0.0005 𝑚3 = 0.24
𝑚
𝑠
𝑁 𝑅𝑒 =
𝐷2 𝑣𝜌
𝜇
=
(0.025 𝑚)(0.24
𝑚
𝑠
)(997.08
𝑘𝑔
𝑚3)
0.0008937
𝑘𝑔
𝑚. 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