Design of Experiment --- Flow Measurement with Orifice Plate Meter
Controlling the flow in piping systems is a significant issue in the fluid systems and chemical
process industries. Obviously, in order to control the flow in a pipe, the flow must be measured.
This experiment will introduce you to three devices that are used to measure flow. One, the
rotameter, is a simple mechanical device that is designed to be read by an operator. It is rugged,
relatively inexpensive, and easily installed. The second, the orifice plate, can be set up to be read
locally or remotely using pressure transducers. Both are designed for flows that do not contain
significant amounts of solid material. The third, the magnetic flow meter, is a more sophisticated
device than either the rotameter or the orifice plate. It requires that the flowing material be
electrically conductive, but can measure flows with suspended material. Brief descriptions of the
three devices are on the attached pages, along with the simplified directions and questions.
Orifice Plate Experiment
The purpose of this portion of the experiment is to design and calibrate an orifice plate so it may
be used to measure flow.
Sufficiently far ( about 10 pipe diameters ) from an any obstruction, turbulent flow in a pipe is
reasonably stable in that the velocity at any point in the flow cross section is the same as all other
points, on average. Thus, at line 1 in Figure 1 below, the velocity is almost constant across the
pipe cross section. In order to pass through the restricted opening at line 2 (the orifice), the flow
must converge and accelerate in order to pass through the restriction. The flow forms a jet as it
exits the orifice and the cross section of the jet continues to decrease for some small distance
downstream*. Eventually, the flow diverges and within a few pipe diameters of the orifice the
flow is again constant across the pipe cross section. The pressure exerted by the fluid is related
to its velocity and it can be shown (and you will do so in MENG203), that the flow rate through
the orifice is given by:
Q  C  A2 
2  P
A2
  (1  22 )
A1
(1)
Where
Q is the volumetric flow rate
A1 is the cross sectional area of the pipe
A2 is the cross sectional area of the orifice
P is the pressure drop (P1 - P2)
C is coefficient of discharge
 is the fluid density
The coefficient of discharge is dependent on the ratio A2/A1 and somewhat dependent upon the
Reynolds Number. The Reynolds Number is used to characterize the flow of fluids and its
definition should be remembered. The definition is:
Re 
Du  

(2)
where
D = pipe diameter
u = fluid velocity
 = fluid density
 = fluid viscosity
Fortunately, this dependence on Re is relatively weak and for our purposes, we can treat C as a
constant.
For a particular installation, A1 and A2 are constants, so many of the terms in equation (1) can be
collected and (1) rewritten as:
QK
2  P
(3)

In this experiment, vary the flow rate through the orifice plate by slowly closing the valve on the
discharge side of the flow system setup. Measure the flow at any given valve position by using
an appropriate container and stop watch. Record the pressure difference (P) at the same time as
the flow is being measured.
A plot of Q vs
P will result in a calibration curve for the orifice plate. Is this a straight line?
Equation (1) is dimensionally consistent and "C" is dimensionless.
Convert everything to
consistent units and determine the value and units of "K".
In this experiment, the pressure difference is displayed by two different methods and you can
develop calibrations curves for any one method. Method one uses the manometer, while method
two uses the electronic display from the differential pressure transducer. (Note – this signal could
be taken to a computer for display via a LabView vi.)
For the manometer, the pressure drop is directly proportional to the difference in height between
the liquid heights in the two legs of the manometer. The differential pressure transducer displays
a value that is proportional to the pressure difference. Is this displayed value a voltage or a
current? Is the resulting calibration curve linear?
Since the fluid is water, the following properties are approximately true:
Density: 999 kg/m3
Viscosity: 1.002 x 10-3 Pa s
DIAMETER
GROUP 1
GROUP 2
GROUP 3
GROUP 4
[cm]
D1
10
8
9
12
D2
1
1
0.8
1
*
The point of the minimum jet diameter is called the vena contracta and ideally it is at this point
that the down stream pressure measurement is made. In practice, however, the downstream
pressure measurement is made in the flange near the orifice. Since the diameter of the vena
contracta is a function of the orifice diameter, we can bundle all the variation into one
coefficient (C in equation 1) and use the orifice diameter. Thus the value of C in equation 1 is a
function of Re and A2/A1.
1
2
P1
P2
Figure 1: Orifice Plate Schematic
Note: Each student will perform the design according to the list given by the lecturer. If
you produce prototype of the orifice meter you will get extra 10 points bonus mark.