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Problem 4.177
[Difficulty: 3]
Given:
Data on "jet pack" rocket
Find:
Initial exhaust mass flow rate; mass flow rate at end; maximum time of flight
Solution:
Basic equation: Momentum flux in y direction
Assumptions:
1) Jet pack just hovers
2) Steady flow
3) Uniform flow 4) Use relative velocities
Given data
V
e
3000
m
s
⋅
=
M
0
200 kg
⋅
=
M
fuel
100 kg
⋅
=
g
moon
0.17 g
⋅
=
g
moon
1.67
m
s
2
=
At all instants, the momentum becomes
M
−
g
moon
⋅
v
1
−
m
rate
⋅
=
V
e
−
m
rate
⋅
=
or
m
rate
Mg
moon
⋅
V
e
=
Hence, initially
m
rateinit
M
0
g
moon
⋅
V
e
=
m
rateinit
0.111
kg
s
=
Finally, when all the fuel is just used up, the mass is
M
f
M
0
M
fuel
−
=
M
f
100 kg
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 Fall '07
 Lear
 Fluid Mechanics, Flux

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