Mechanics of Fluids SI Edition 5th Edition by Potter – Test Bank
Solutions for Section 9.1 – 9.4
1. In which one of the following flows must compressibility be considered?
(D) Flow around the wing of a commercial aircraft in its approach to an airport
Speeds must be in excess of 100 m/s (360 kph or 240 mph) before compressibility
must be considered in flow around an object. Commercial aircraft take off at speeds
less than 40 m/s, considerably below M = 0.3. Only (D) qualifies.
2. An aircraft flies at an altitude of 20,000 m. With what speed would it fly if M = 1?
(C) 295 m/s
M 1 295 m/s
1 4 287 217 . . .
V V V V
c kRT == = ∴
3. A traffic flow on a freeway is very dense and it is proposed that possibly a fluid flow could
simulate the flow. If it was decided to study the feasibility of the proposal, which flow would
be a possibility?
(C) M >1
Consider a primary characteristic of an incompressible flow or a subsonic flow: as
the area decreases, the velocity increases. For a supersonic flow, as the area
decreases the velocity decreases, as demanded by Eq. 9.3.10. We all know that when
a traffic flow encounters a decrease in the number of lanes, the traffic slows down, it
does not speed up. So, it would require a compressible flow model with M > 1.
4. A farmer is using a tank of 20°C nitrogen pressurized to 540 kPa absolute. It exits the tank out
a hose. The hose snaps and the farmer is hit with the expanding nitrogen. Air is primarily
nitrogen so assuming it is air, the temperature of the exiting nitrogen is nearest:
The pressure ratio between the exit and the tank is 0 /e p p = 100/540 = 0.185. From the
isentropic flow Table D.1 we find, at M = 1.76, that
0 6175 181 K or 92 C or 134 F
293 . T T
= = = −° − °
Such a low temperature would require that the farmer be treated for ‘burns.” The
temperature of the nitrogen in the tank is hardly a factor since it would undoubtedly
be in the range of 10°C < T < 35°C.
5. A bomb blast sends a shock wave through the 20°C atmosphere. At a certain location, the
shock wave is travelling at M = 3. The induced velocity behind the wave is nearest:
(A) 760 m/s
At M = 3 the normal-shock flow Table D.2 gives M 0 4752 2 = . and 2 T = × 293 2 679 .
= 785 K. Hence,
22 2 V M kRT = = ×× = 0 4752 1 4 287 785 267 m/s . .
This is the velocity behind a stationary shock wave. Superpose the velocity
1 V = ×× = 3 1 4 287 293 1029 m/s . and find
V = −= 1029 267 762 m/s
Such high induced velocities obviously cause severe damage.