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Problem 4.48
[Difficulty: 3]
Given:
Data on draining of a tank
Find:
Depth at various times; Plot of depth versus time
Solution:
0
=
⋅
+
∂
∂
∫
∫
CS
CV
A
d
V
V
d
t
r
r
ρ
Basic equation
Assumptions:
1) Uniform flow
2) Incompressible flow
3) Neglect air density
Treating the tank as the CV the basic equation becomes
t
0
y
y
ρ
A
tank
⋅
⌠
⎮
⌡
d
∂
∂
ρ
V
⋅
A
opening
⋅
+
0
=
or
ρ
π
4
⋅
D
2
⋅
dy
dt
⋅
ρ
π
4
⋅
d
2
⋅
V
⋅
+
0
=
Using
V2
g
⋅
y
⋅
=
and simplifying
dy
dt
d
D
⎛
⎝
⎞
⎠
2
−
2g
⋅
⋅
y
1
2
⋅
=
Separating variables
dy
y
1
2
d
D
⎛
⎝
⎞
⎠
2
⋅
⋅
dt
⋅
=
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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

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