Problem *4.114
[Difficulty: 3]
CS
c
d
Given:
Water jet striking disk
Find:
Expression for speed of jet as function of height; Height for stationary disk
Solution:
Basic equations: Bernoulli; Momentum flux in z direction
p
ρ
V
2
2
+
gz
⋅
+
constant
=
Assumptions:
1) Steady flow
2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow
The Bernoulli equation becomes
V
0
2
2
g0
⋅
+
V
2
2
gh
⋅
+
=
V
2
V
0
2
2g
⋅
h
⋅
−
=
VV
0
2
⋅
h
⋅
−
=
Hence
M
−
g
⋅
w
1
ρ
−
w
1
⋅
A
1
⋅
()
⋅
=
ρ
−
V
2
⋅
A
⋅
=
But from continuity
ρ
V
0
⋅
A
0
⋅
ρ
V
⋅
A
⋅
=
so
VA
⋅
V
0
A
0
⋅
=
Hence we get
Mg
⋅
ρ
V
⋅
V
⋅
A
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 Fall '07
 Lear
 Fluid Dynamics, Fluid Mechanics, Flux, Expression, Incompressible Flow, 4.28 m

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