CHEG 281
Experiment 2 --- Flow Measurement
Controlling the flow in piping systems is a significant issue in the 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.
Below are some basic experimental guidelines that are common to all three sub-experiments.
1. Trace the piping in the flow loop so you understand the basic process of getting flow from
the feed tank to the receiving tank .
2. Ensure that the water level in the receiving tank is above the pump that recycles the water in
the receiving tank to the feed tank. Use the hose and tap to fill as necessary
3. Ensure that the feed tank is about 60% full of water. Use the recycle pump to pump from the
receiving tank to the feed tank. Before activating the recycle pump, have the lab instructor
verify that you have the valves in the correct position.
4. Refill the receiving tank to about 50% full.
5. Ensure that the water will only flow from the feed pump through the desired flow measuring
device. Follow the piping and open and close the necessary valves to allow the water to
flow from the feed pump, through the measuring device, and back to the receiving tank.
6. Close the final (discharge) valve just prior to the discharge into the receiving tank.
7. Have the lab instructor verify that your valving is correct for the measuring device you want
to use.
8. Turn on the feed pump
9. Slowly open the discharge valve until you obtain a desired reading. Slowly change the
discharge valve opening to obtain different flow rates.
10. When the receiving tank is about 50 - 60% full, activate the recycle pump.
11. Monitor the level in the receiving tank and turn off the recycle pump if the receiving tank
level approaches the level of the top of the recycle pump.
12. When you are ready to leave the lab, have the lab instructor verify that you have left the flow
loop in the proper condition.
Experiment 2 -- Flow Measurement
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CHEG 281
Rotameter Experiment
The purpose of this portion of the experiment is to develop a calibration curve for a rotameter so
that it may be used to measure flow in a pipe.
The rotameter is a very commonly used flow measuring device, especially in low pressure
systems. It is used for both liquid and gas flows. As shown in Figure 1 below, this simple
device is just a tapered tube with a metal bob on a central shaft. (The bob can actually be any
material that does not react with the fluid being measured and the central shaft is not really
necessary, but serves to keep the bob aligned in the tube.) As the fluid flows in the annular space
between the bob and the tube, a drag force is generated that tends to pull the bob along. The
force of gravity tends to resist this drag force. The drag force is proportional to the square of the
velocity, whereas the gravitational force is proportional to the mass of the bob. If the drag force
is greater than the gravitational force, the bob rises. As the bob rises, the annular space gets
bigger and the velocity, and hence the drag force, drops. At some point, the drag force and
gravitational force balance and the bob remains fairly steady. (If there is no balance point, the
bob either sits at the bottom of the tube or slams against the top of the tube --- neither condition
is very useful for measuring flow!)
As you will show in CHEG 3110, the flow rate through a rotameter is given by:
u
2  g  Vb  b   f
(
)
C  Ab
f
(1)
Q  A*u
(2)
A  f ( y)
(3)
where
u = flow velocity
Vb = volume of the bob
b = density of the bob
f = density of the fluid
Ab = frontal area of the bob
A = area of the annulus between the bob and tube wall
y = distance from the bottom of the meter
f(y) = the function that defines the tube taper
g = gravitational acceleration
C = a drag coefficient
Q = volumetric flow rate
The annular cross section (A) at any distance above the base is a function of the design of the
meter. The proper choice of the bob diameter and the tube taper can make the functional term
nearly linear such that the formula reduces to:
Experiment 2 -- Flow Measurement
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CHEG 281
Q  Cm  y 
b   f
f
(4)
where Cm now contains the constants and the drag coefficient from equations (1) - (3).
While Cm could be evaluated for each meter, it is much more convenient to develop a calibration
curve for a particular application. That will be the exercise in this portion of the lab.
Vary the flow rate through the rotameter by slowly opening the valve on the discharge line.
Measure the flow with an appropriate container and a stop watch. Build a calibration curve for
the flow meter. In equation (4), note that the flow is dependent on the density of the fluid and
the bob, both of which change as the temperature changes. Therefore, you will need to record
the fluid temperature for each of your observations. Take between five and ten different flows
and rotameter positions for the calibration curve.
Some questions:
What calculations and assumptions would you have to make to build a calibration curve that
would apply over a fairly large fluid temperature range?
Estimate the meter coefficient (Cm in equation 4) from your data.
Bob
Flow
Rotameter Schematic
Figure 1
Experiment 2 -- Flow Measurement
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CHEG 281
Orifice Plate Experiment
The purpose of this portion of the experiment is to calibrate an orifice plate so it may be used to
measure flow.
Sufficiently far (about 5 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 2 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
downstream1. 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 CHEG 3110), that the flow rate
through the orifice is given by:
Q  C  A2 
2  p
A2
  (1  22 )
A1
(5)
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  

where
D = pipe diameter
u = fluid velocity
 = fluid density
 = fluid viscosity
Experiment 2 -- Flow Measurement
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CHEG 281
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 (5) can be
collected and (5) rewritten as:
QK
2  p

(6)
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 (5) 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 are to
develop calibrations curves for both methods. 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: 62.4 lbm/ft3
Viscosity: 0.01 centipoise
A1 = 1.049 inches
A2 = 0.777 inches
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 5) and use the orifice diameter. Thus the value of C in equation 5 is a
function of Re and A2/A1.
Experiment 2 -- Flow Measurement
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CHEG 281
1
2
P1
P2
Orifice Plate Schematic
Figure 2
Magnetic Flow Meter Experiment
The magnetic flow meter is a relatively sophisticated device (compared to the rotameter or
orifice plate). The flowing, conductive particles (ions or true particles) induce an electric
potential which is measured by the flow meter electronics. Flow meters are sized for a
maximum flow and the induced potential is essentially compared to the maximum permitted
potential. In this way, the flow through the meter is related to the maximum measurable flow.
The flow meter display can display the flow directly (in appropriate units) or as a percentage of
the maximum measurable flow. The flow meter in this experiment displays the flow as a percent
of the maximum.
Your goal in this experiment is to determine:
a) what is the maximum measurable flow rate?
b) build a LabView vi to take the signal from the flow meter and display the volumetric
flow rate on a meter of some form. Be sure to include the flow units on the meter
display.
Experiment 2 -- Flow Measurement
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