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MAE420 Applied Fluid Mechanics
Homework #5 (6 problems)
Due: 10:00pm on May 25, 2015.
-----------------------------------------------------------------------------------------------1. Derive Eq. 9.40 (the relationship among dV, dA, and dp) of the text book from Eqs. 9.38 and
9.39.
2. Derive Eq. 9.50 (Rankine-Hugoniot relation) from Eqs. 9.49a to 9.49c.
3. Given the pitot stagnation temperature and pressure and the static pressure measurements in
the figure below estimate the air velocity V, assuming (a) incompressible flow and (b)
compressible flow (k = 1.4).
4. A force F = 1100 N pushes a piston of diameter 12 cm through an insulated cylinder
containing air at 20℃, as in the figure below. The exit diameter is 3 mm, and pa = 1 atm.
Estimate (a) Ve, (b) Vp, (c) ṁe.
Hint: Stagnation pressure inside the larger cylinder = F/A + pa, and stagnation temperature
inside the larger cylinder is 20℃. The smaller cylinder is chocked, and Ve is equal to velocity
at Ma=1 (think why the smaller cylinder is chocked).
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MAE420 Applied Fluid Mechanics
Homework #5 (6 problems)
Due: 10:00pm on May 25, 2015.
-----------------------------------------------------------------------------------------------5. Air flows from a tank through a nozzle into the standard atmosphere, as in the figure below.
A normal shock stands in the exit of the nozzle, as shown. Estimate (a) the (stagnation) pressure
in the tank and (b) the mass flow.
Hint: In the tank, thermodynamic properties are all stagnation properties because velocity is
zero. After the shock wave, pressure is 1 atm.
6. Air flows through a converging-diverging nozzle between two large reservoirs, as shown in
the figure below. A mercury manometer between the throat and the downstream reservoir reads
h = 15 cm. Estimate the downstream reservoir pressure. Is there a normal shock in the flow? If
so, does it stand in the exit plane or farther upstream of the exit plane?
Hint: In the reservoirs, all properties are stagnation properties. If the normal shock occurs, the
throat should be chocked (Ma=1 at the throat).
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