Problem 10.106 [Difficulty: 3]
CS
U
X
Y
x
y
V
FD
Given: Data on jet-propelled aircraft
Find: Propulsive efficiency
Solution:
Basic equation: (4.26)
(4.56)
Assumption: 1) Atmospheric pressure on CS 2) Horizontal 3) Steady w.r.t. the CV 4) Use velocities relative to CV
The x-momentum is then FD
u1mrate
u2mrate
U()m
rate
V()m
rate
or FDmrate VU() where mrate 50 kg
s
is the mass flow rate
The useful work is then FDUmrate VU()U
The energy equation simplifies to WU2
2
mrate
V2
2
mrate
mrate
2V2U2
Hence η
mrate VU()U
mrate
2V2U2
2V U()U
V2U2
2
1V
U
With U 225 m
s
and η45%VU
2
η1
V 775 m
s
