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Problem 4.165
[Difficulty: 3]
y
x
CS
at speed
U
V
e
Y
X
Given:
Data on rocket weapon
Find:
Expression for speed of weapon; minimum fraction of mass that must be fuel
Solution:
Basic equation: Momentum flux in x direction
Assumptions:
1) No resistance
2) p
e
= p
atm
3) Uniform flow 4) Use relative velocities 5) Constant mass flow rate
From continuity
dM
dt
m
rate
=
constant
=
so
MM
0
m
rate
t
⋅
−
=
(Note: Software cannot render a dot!)
Hence from momentum
a
rfx
−
M
⋅
dU
dt
−
M
0
m
rate
t
⋅
−
()
⋅
=
u
e
ρ
e
V
e
⋅
A
e
⋅
⋅
=
V
e
−
m
rate
⋅
=
Separating variables
dU
V
e
m
rate
⋅
M
0
m
rate
t
⋅
−
dt
⋅
=
Integrating from U = U
0
at t = 0 to U = U at t = t
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.
 Fall '07
 Lear
 Fluid Mechanics, Flux

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