Problem 4.21
[Difficulty: 3]
Given:
Data on flow into and out of tank
Find:
Time at which exit pump is switched on; time at which drain is opened; flow rate into drain
Solution:
Basic equation
t
M
CV
∂
∂
CS
ρ
V
→
⋅
A
→
⋅
()
∑
+
0
=
Assumptions:
1) Uniform flow
2) Incompressible flow
After inlet pump is on
t
M
CV
∂
∂
CS
ρ
V
→
⋅
A
→
⋅
∑
+
t
M
tank
∂
∂
ρ
V
in
⋅
A
in
⋅
−
=
0
=
t
M
tank
∂
∂
ρ
A
tank
⋅
dh
dt
⋅
=
ρ
V
in
⋅
A
in
⋅
=
dh
dt
V
in
A
in
A
tank
⋅
=
V
in
D
in
D
tank
⎛
⎜
⎝
⎞
⎠
2
⋅
=
where h is the level of water in the tank
Hence the time to reach h
exit
= 0.7 m is
t
exit
h
exit
dh
dt
=
h
exit
V
in
D
tank
D
in
⎛
⎜
⎝
⎞
⎠
2
⋅
=
t
exit
0.7 m
⋅
1
5
×
s
m
⋅
3m
⋅
0.1 m
⋅
⎛
⎝
⎞
⎠
2
×
=
t
exit
126 s
=
After exit pump is on
t
M
CV
∂
∂
CS
ρ
V
→
⋅
A
→
⋅
∑
+
t
M
tank
∂
∂
ρ
V
in
⋅
A
in
⋅
−
ρ
V
exit
⋅
A
exit
⋅
+
=
0
=
A
tank
dh
dt
⋅
V
in
A
in
⋅
V
exit
A
exit
⋅
−
=
dh
dt
V
in
A
in
A
tank
⋅
V
exit
A
exit
A
tank
⋅
−
=
V
in
D
in
D
tank
⎛
⎜
⎝
⎞
⎠
2
⋅
V
exit
D
exit
D
tank
⎛
⎜
⎝
⎞
⎠
2
⋅
−
=
Hence the time to reach h
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 Fall '07
 Lear
 Fluid Dynamics, Fluid Mechanics, Trigraph, Incompressible Flow, Tdrain, Texit, Vin⋅

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