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Developing Fluid Concepts and the Fluid/Electric Circuit Analogy
William Schwalm, Mizuho Schwalm and Dean Smith, University of North Dakota-Grand Forks
The concept of flow rate is unfamiliar to most introductory students. They have
difficulty differentiating between the amount of fluid, for instance, and the rate of
flow. Often pressure difference is also a new concept. These are among the
difficulties one faces in trying to use the fluid analogy for electric circuits. Some
texts use a mechanical model of fluid flowing down hill to circumvent the problem
of pressure, but this is not so helpful vis-à-vis Ohm’s law as it does not provide as
good a model of resistance. A fluid model using air pressure difference is used in
CASTLE*. However the incompressibility of water has advantages. To establish
fluid flow concepts for later use in understanding circuits, we propose context rich
laboratory activities on pressure difference and direct measurement of liquid flow
rate. To go along with a simple fluid apparatus was built.
*Capacitor-Aided System for Teaching and Learning Electricity
Hydraulic Analogy for Electric Circuits
Design and Setup
Problem Solving Lab
OBJECTIVE
In this laboratory unit, including the pre-lab study, students should gain experience that
would enable them to do the following.
A coupling is inserted between two six inch long
standard copper water pipes. The diameter of the
copper pipe is 0.5 inch. In order to filter the flow,
about 3/4 regular cotton ball and one layer of fine
mesh are placed at the end of one of the pipes next to
the middle coupler. To hold the mesh and cotton, a
hollow nylon cylinder (inner diameter approximately
0.3”) is also inserted. The range of the pressure
gauges is 0-60 PSI.
1. Define pressure P and explain what an (approximately) incompressible is, giving also
an example of one.

2. Describe what a fluid flow is, and what the fluid velocity v means at a given time and
a given point in space.
3.Explain what it means for a flow to be irrotational or incompressible.
4.Explain what the equation of continuity means, physically, and where it comes from,
particularly how it simplifies in the case of an incompressible fluid
5. Define viscosity.
6. Describe how the rate of flow through a porous filter should depend on pressure
difference.
Question: When water flows through a filter in a pipe, the rate of flow
could depend on several factors. In particular, what is the functional
form of the relation between rate of flow I and the pressure difference
between the two ends of the filter?
Electric current flowing in a circuit is like water flowing (in complete circuits or
“round-trips”) through pipes. The rate of flow of water is analogous to the
electric current, and the pressure difference between points in the plumbing is
like the voltage difference in the electric circuit.
electric
1.
2.
3.
4.
5.
6.
7.
8.
PREDICTION QUESTIONS
hydraulic
current in Amps
voltage (potential) in Volts
wires forming electric circuit
voltage source (battery, generator)
electrical resistor flow
volt meter measures potential
ammeter measures current
Electric field
1. rate of flow (gallons/second)
2. pressure difference
3. pipes forming hydraulic circuit
4. a circulating pump
5. a filter offering resistance **to
6. pressure gauge measures pressure
7. flow meter measures rate of flow
8. minus pressure gradient
* This should be a filter, not a constriction as some authors suggest because
constriction causes non linear flow.
Rate of Flow Meter
Filter
FILTER
pump
Resistor
Battery
V
Pressure difference meter
A
1. How do you expect the rate of flow I to depend on pressure difference?
2. How sure are you about this? Why?
3. What do you expect to be the most difficult aspect of this exploration?
METHOD QUESTIONS
The water flow tends to be non linear due to the
turbulence. So one must stay away from the turbulent
region and stay in the linear range. Adding a right
amount of the filter material and selecting the right
diameter of the pipe are crucial. A sample run shown
below indicates the flow is almost linear.
1. For the case of water, how is mass related to fluid volume?
2. Considering the apparatus pictured here, if you had a stop watch, a large container and
a triple beam balance, how could you use these to determine the rate of flow I of water
out of the end of a pipe?
3. You will use pressure gauges at each end of the filter to measure pressure. Since the
pressure in the pipes in the building fluctuates quite a bit during the measurements, can
you think of a way to come up with some typical values for your measurements? What
kind of measurement procedure can you think of that might help cope with this?
4. A related problem is to try to see how you might estimate the amount of error in your
pressure, volume and time measurements. How might you estimate this using your
measurements and how can you use this in reporting the accuracy of your results?
5. What kind of a graph would you want to make to best indicate what kind of relationship
there is between the pressure difference P Upstream—P downstream and the rate of
flow through the filter? How could you use this graph to define a resistance of the filter
to the water flow?
Acknowledgements
We are grateful to UND Physics machinist Rob Czapiewski for contributing
many good ideas and correcting errors to get optimal design of the
apparatus.
P1 − P 2 = ∆ P = I k
The project is funded in part by NSF DUE-0510570
American Association of Physics Teachers Summer Meeting 2006