37. According to the problem, the volume of the horizontal cylindrical tank is given by:
(
2
2
sin
2
L R
R
=
π
−
α−
α
)
V
L
(1)
where
α
is a function of time.
If we try to calculate the value of h (high) with this definition of variables, we have:
cos(
)
2
R
h
R
α
=
+
⋅
(2)
Then:
•
h = 0 when
α
= 360
o
•
h = R or H/2 when
α
= 180
o
•
h = 2R or H when
α
= 0
o
To calculate the variation of the
α
with time:
dV
Q
dt
ρ
ρ
⋅
=
⋅
(3)
Now, plugging 3 into 1:
(
)
2
2
sin
2
d
L R
L R
Q
dt
π
α
α
−
−
=
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 Winter '10
 B.G.Higgins
 According to Jim, 2 2 L, dt Plugging equation

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