Problem *3.114
[Difficulty: 3]
Given:
Cylindrical container rotating as in Example 3.10
R
0.25 m
⋅
=
h
o
0.3 m
⋅
=
f2
H
z
⋅
=
Find:
(a) height of free surface at the entrance
(b) if solution depends on
ρ
Solution:
We will apply the hydrostatics equations to this system.
Governing Equations:
(Hydrostatic equation)
Assumptions:
(1) Incompressible fluid
(2) Atmospheric pressure acts everywhere
In order to obtain the solution we need an expression for the shape of the free surface in terms of
ω
, r, and h
o
. The required
expression was derived in Example 3.10. The equation is:
zh
o
ω
R
⋅
()
2
2g
⋅
1
2
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 Fall '07
 Lear
 Statics, Fluid Mechanics

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