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Problem 4.72
[Difficulty: 4]
Given:
Gate held in place by water jet
Find:
Required jet speed for various water depths
Solution:
Basic equation: Momentum flux in x direction for the wall
Note: We use this equation ONLY for the jet impacting the wall.
For the hydrostatic force and location we use computing equations
F
R
p
c
A
⋅
=
y'
y
c
I
xx
Ay
c
⋅
+
=
Assumptions:
1) Steady flow
2) Incompressible flow 3) Uniform flow
Hence
R
x
V
ρ
⋅
V
−
A
jet
⋅
()
⋅
=
ρ
−
V
2
⋅
π
D
2
⋅
4
⋅
=
This force is the force generated by the wall on the jet; the force of the jet hitting the wall is then
F
jet
R
x
−
=
ρ
V
2
⋅
π
D
2
⋅
4
⋅
=
where D is the jet diameter
For the hydrostatic force
F
R
p
c
A
⋅
=
ρ
g
⋅
h
2
⋅
h
⋅
w
⋅
=
1
2
ρ
⋅
g
⋅
w
⋅
h
2
⋅
=
y'
y
c
I
xx
c
⋅
+
=
h
2
wh
3
⋅
12
⋅
h
2
⋅
+
=
2
3
h
⋅
=
where h is the water depth and w is the gate width
For the gate, we can take moments about the hinge to obtain
F
jet
−
h
jet
⋅
F
R
hy
'
−
⋅
+
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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, Gate

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