1
3.12 The pipe flow in Fig. P.3.12 fills a cylindrical tank as shown. At
time t = 0, the water depth in the tank is 30cm. Estimate the time required
to fill the remainder of the tank.
Solution:
Z
d
0=
ρdV − ρQ1 + ρQ2
dt CV
Z
πd2
πd2
d
+ ρV2
=
ρdV − ρV1
dt CV
4
4
where
d
dt
Z
CV
πD2 dh
ρdV = ρ
4 dt
V (t) = h(t)
πD2
4
Therefore,
ρπD2 dh
πd2
0=
+ρ
(V2 − V1 )
4
dt
4
2
dh
d
∴
=
(V2 − V1 ) = 0.0153
dt
D
dh
0.7
dt =
=
= 46s
0.0153 0.0153
2
Alternate solution approach: Assume steady flow, one inlet and two
exits with uniform flow.
0 = −Q1 + Q2 + Q3
V3
Q3 = Q1 − Q2 =
dt
πD2
dh 4
V3
dt =
= πD2
= 46s
Q1 − Q2
(V
−
V
)
1
2
4