Problem 4.28
[Difficulty: 1]
Given:
Data on filling of a sink
Find:
Time to half fill; rate at which level drops
Solution:
This is an unsteady problem if we choose the CS as the entire sink
Basic equation
t
M
CV
∂
∂
CS
ρ
V
→
⋅
A
→
⋅
(
)
∑
+
0
=
Assumptions:
1) Incompressible flow
Given data:
m
rate
4 gpm
⋅
=
L
2 ft
⋅
=
w
18 in
⋅
=
d
12 in
⋅
=
Q
4 gpm
⋅
=
Q
drain
1 gpm
⋅
=
Hence
t
M
CV
∂
∂
CS
ρ
V
→
⋅
A
→
⋅
(
)
∑
−
=
Inflow
Outflow
−
=
(1)
To half fill:
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 Fall '07
 Lear
 Fluid Mechanics, Speed of sound, Trigraph, Vlevel, L⋅ w⋅

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