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ME 152 B Final Exam
Student name (if not using a separate sheet):
Please read these instructions carefully
This is an open-book exam: you may use course notes and textbook. You may not discuss it with other
students.
You must write the following statement on your exam, and sign underneath it: “I confirm that the work I
submit is my own and my own only, and that I did not use resources beside course notes and the
textbook.” If this statement is not written and signed, you will get a score of zero.
If you will print the exam or use a tablet, you may use the spaces provided to develop your answers.
You may also use a separate sheet of paper to develop your answers. If doing so, please scan your
solutions and upload them to Gauchospace by the posted time.
If you need to ask a question, please email the instructor.
1
Multiple choice
Note: you do not need to justify your answers to the multiple-choice questions on this page.
Select one answer per question.
1. The Buckingham-Pi theorem states that a problem with n independent variables and r different
dimensions can be reduced to a problem with ...
(a) r − n dimensions;
(b) r − n dimensionless numbers (or Pi-groups);
(c) n− r dimensions;
(d) n− r dimensionless numbers (or Pi-groups).
2. When the flow in a pipe is laminar, the velocity is ...
(a) Maximum at the wall;
(b) Minimum at the center of the pipe;
(c) A linear function of the distance to the center of the pipe;
(d) A parabolic function of the distance to the center of the pipe.
3. The momentum integral equation for a boundary layer...
(a) assumes irrotational flow everywhere;
(b) can be applied only to laminar flow;
(c) applies equally to laminar and turbulent flow;
(d) can be applied to time-varying flows.
4. Which of these assumptions is not required to derive the Euler turbomachinery equation for a cen-
trifugal pump:
(a) Incompressible and steady flow;
(b) Uniform flow at inlet and outlet;
(c) No swirl at the inlet;
(d) Neglecting torques not associated with shaft.
5. The ‘best efficiency point’ (BEP) corresponds to the point...
(a) Where the flow rate is maximum;
(b) Where the efficiency is maximum for any impeller diameter;
(c) Where the pressure head is maximum;
(d) Where the efficiency is maximum for a given impeller diameter.
6. The speed of sound in an ideal gas is...
(a) faster than in a solid;
(b) only dependent on the density of the gas;
(c) only dependent on the temperature of the gas;
(d) the same for all gases.
7. The flow process through a shock wave...
(a) is adiabatic and is reversible;
(b) is adiabatic and is irreversible;
(c) is not adiabatic and is reversible;
(d) is not adiabatic and is irreversible.
2
8. A small aerosol particle of diameter d and density ρp = 2, 500 kg/m
3 falls in air (density ρair =
1.2 kg/m3, and dynamic viscosity µair = 1.8×10−5 Pa · s). For small Reynolds numbers, Re 1, the
terminal settling speed of the particle V depends only on d, µair, the density difference (ρp − ρair)
and the gravitational acceleration g.
(a) List all the relevant variables and the dimensions associated with this problem. Using the
Buckingham Pi theorem, determine how many dimensionless groups govern this problem.
(b) Form the dimensionless groups.
It is often difficult to visualize the settling of small aerosol particles of diameter d = 10µm.
Therefore, a model system is built in the lab using water as a fluid (density ρw = 1, 000 kg/m