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1
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Problem.
Lake
A round lake of diameter
d
is fed by a river and drained by seepage. The normal flow rate of the
river is
Q
in
= 40 m
3
/
min
and is equal to the rate of seepage. Thus, the water level in the lake is
constant. Should the lake level rise, the water from the lake flows through a triangular notch in a
retaining wall and into a flood plain. Normally the water level matches the bottom of the triangular
notch.
Water level in lake is normally at the
bottom of the triangular notch in the dam.
View of dam from flood plain
Suddenly the flow rate of the river increases to 1.5 times the normal rate. The extra water flows
out through the triangular notch at a rate determined by the height of the lake above the bottom of
the notch. The rate of flow through the notch is given by the following equation:
Q
notch
=
αh
5
/
2
m
3
/
min
,
where
h
is the height of the lake surface above the bottom of the notch
, and
α
is a constant.
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 Fall '07
 BERMAN
 Fluid Dynamics, Calculus, 1 m, 4 m, 1m, Qin, Qnotch

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