Updated 10/28/04
Flowmeter Comparison: Theory
The goal of this experiment is to evaluate the operation of three different
basic types of flowmeters through measured results and comparisons with
theoretical calculations based on the Bernoulli equation. The three
flowmeters are the Venturi meter, the orifice plate, and the variable area
meter. The second part of the lab examines in depth the coefficient of
discharge that accounts for frictional losses through a small orifice plate.
Summary of Theory
The Bernoulli equation for incompressible flow is
2
2
V1
P
V
P
 1  Z1  2  2  Z 2
2g
g
2g
g
(1)
In addition, a mass balance of the system shows that the volume flowrate is related to
the cross sectional area and flow velocity by
Q  A1 V1  A2 V2
(2)
where
V1, V2 = Flow velocity at points 1 and 2 respectively (m/sec, ft/sec, etc.)
P1, P2 = Static pressure at points 1 and 2 respectively (mm H20, psi, N/m2, Pa,
etc.)
Z1, Z2 = Heights of points 1 and 2 respectively relative to a common datum
level (inch, meter, etc.)

= Density of the fluid (mass/volume)
g
= Acceleration due to gravity
Q
= Volume flowrate (l/s, l/min, gallon/min, etc.)
A1, A2 = Cross sectional areas at points 1 and 2 respectively (m2, cm2, ft2, in2,
etc.)
-1-
Updated 10/28/04
Because the Venturi meter and the orifice plate are oriented in a horizontal position, the
influence of the heights in Bernoulli’s equation is negligible, (i.e. Z1 – Z2 = 0). By
combining equations (1) and (2) the basic Bernoulli equation then reduces to
Q  Cd A2
2 ( P1  P2 )
  A 2 
 1   2  
  A1  
.
(3)
The new equation takes into account drag forces by adding a factor Cd called the
coefficient of discharge (units are dimensionless). This coefficient depends on the pipe
geometry and is different for both the Venturi meter and the orifice plate. Values for Cd
in these two conditions are given in the technical data section.
Technical Data
Venturi Meter
Upstream pipe diameter =
31.75 ±0.25 mm
Throat diameter
=
Upstream taper =
21 inclusive
Downstream taper
=
Coefficient of discharge, Cd
15 ± 0.25 mm
14 inclusive
=
0.98
Orifice Plate:
Upstream pipe diameter
= 31.75± 0.25 mm
Throat diameter
= 20 ± 0.25 mm
Coefficient of discharge, Cd
= 0.63
Questions
1. From the pressure readings obtained for the Venturi meter and the orifice plate,
calculate the volume flowrate using Bernoulli’s equation with the relevant Cd factor.
What is the measurement uncertainty?
2. Compare your calculated flow values from both the orifice plate and Venturi meter
as well as the reading on the variable area meter with the volumetric “true” flowrate
-2-
Updated 10/28/04
determined using the Hydraulics Bench facility. Present in terms of % difference. Are
any systematic errors prevalent?
3. Plot the timed collection “true” flowrate vs. measured pressure drop (P = P1 – P2)
for the Venturi meter. Add in the theoretical equation curve to the graph (from
equation 3). Do not fit the data. Repeat for the orifice plate. Be sure to include error
bars in your experimental values.
4. Compare the losses in each of the meters in relation to the volume flowrate. (Note
that the loss in the Venturi meter and the orifice plate may be related to the velocity
head, V2/2g.). What trends do you observe?
5. In this experiment you altered the static pressure of the system using the hand
pump. What impact, if any, will the static pressure have on your measurements?
6. What is the effect of orientation on the three flowmeters? Suppose you later
discovered that the Hydraulics Bench was not horizontal as originally assumed,
rather it was tilted at a 10 angle. What effect would this have on your flow
measurements?
7. Based on the data you collected as well as your newfound experience with
flowmeters, name the advantages and disadvantages for each of the four different
means for measuring volumetric flowrate (Venturi meter, orifice plate, variable area
meter, and timed volume collection).
References
1. Instruction Manual for Hydraulics Bench and Accessories, F1-00. Armfield Limited.
Issue 18, April 1996.
2. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, John Wiley & Sons,
Inc. New York, 1960, pp. 224 – 226.
-3-