Problem 4.209
[Difficulty: 3]
z
x
d
V
2
c
e
CV
(
a
)
CV
(
b
)
z
max
Given:
Data on fire boat hose system
Find:
Volume flow rate of nozzle; Maximum water height; Force on boat
Solution:
Basic equation: First Law of Thermodynamics for a CV
Assumptions:
1) Neglect losses 2) No work 3) Neglect KE at 1 4) Uniform properties at exit 5) Incompressible 6) p
atm
at 1 and 2
Hence for CV (a)
W
s
−
V
2
2
2
g z
2
⋅
+
⎛
⎜
⎜
⎝
⎞
⎠
m
exit
⋅
=
m
exit
ρ
V
2
⋅
A
2
⋅
=
where m
exit
is mass flow rate (Note:
Software cannot render a dot!)
Hence, for V
2
(to get the flow rate) we need to solve
1
2
V
2
2
⋅
g z
2
⋅
+
⎛
⎜
⎝
⎞
⎠
ρ
⋅
V
2
⋅
A
2
⋅
W
s
−
=
which is a cubic for V
2
!
To solve this we could ignore the gravity term, solve for velocity, and then check that the gravity term is in fact
minor.
Alternatively we could manually iterate, or use a calculator or Excel, to solve.
The answer is
V
2
114
ft
s
⋅
=
Hence the flow rate is
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 Fall '07
 Lear
 Dynamics, Fluid Dynamics, Fluid Mechanics, Mass flow rate, Zmax, mexit

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