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ME3251 Flow of Compressible Fluids
Dr. T. J. Barber
Spring 2013
Problem Set 1
Problem 1
Calculate the speed of sound at 288 K for the following gases:
1. Hydrogen, H2
2. Helium, He
3. Nitrogen, N2
Under what conditions will the speed of sound in H2 and He be equal?
Problem 2
A supersonic aircraft flies horizontally at 1500 m altitude with a constant velocity of 750
m/s. The aircraft passes directly over a stationary ground observer. How much time
elapses after it has passed over the observer before the latter hears the aircraft? Assume
that the airplane creates a small disturbance that may be treated as a sound wave.
Problem 3
A baseball, which has a mass of 145 grams and a diameter of 3.66 cm, when dropped
from a very tall building reaches high speeds. If the building is tall enough the speed will
be controlled by the drag, as the baseball will reach terminal speed. At this state
W = FD
where
W (weight)
= mg,
g (acceleration of gravity) = 9.81 m/s2,
FD (drag force)
= CDρairAV2/2,
CD (drag coefficient)
= 0.5 and
A (projected area of sphere) = πR2.
Find the terminal speed of the baseball and determine the corresponding Mach number if
the ambient air temperature is 23°C and the ambient air pressure is 101 kPa.