This preview shows pages 1–2. Sign up to view the full content.
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
r
R
⎛
⎝
⎞
⎠
2
−
⎡
⎢
⎣
⎤
⎥
⎦
⋅
−
=
The angular velocity
ω
is related to the frequency of rotation through:
ω
2
π
⋅
f
⋅
=
ω
2
π
⋅
2
×
rad
s
⋅
12.57
rad
s
⋅
=
=
Now since h
1
is the z value which corresponds to r = 0:
h
1
h
o
ω
R
⋅
2
4g
⋅
−
=
Substituting known values:
h
1
0.3 m
⋅
1
4
12.57
rad
s
⋅
0.25
×
m
⋅
⎛
⎝
⎞
⎠
2
×
s
2
9.81 m
⋅
×
−
=
h
1
0.05 m
=
The solution is independent of
ρ
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '07
 Lear
 Statics, Fluid Mechanics

Click to edit the document details