CE 2200 Homework Assignment08
(DUE Thursday November 8, 2007)
1.
Problem7.13:
An approximate equation for the velocity distribution in a
rectangular channel with turbulent flow is
n
d
y
V
V
⎟
⎠
⎞
⎜
⎝
⎛
=
max
where
V
max
is the velocity at the surface,
y
is the distance from the floor of the
channel,
d
is the depth of flow, and
n
is an exponent that varies from about 1/6 to
1/8 depending on the Reynolds number. Derive a formula for the kineticenergy
correction factor
α
as a function of
n
. What is the value of
α
for
n
= 1/7?
2.
Problem7.21:
An engineer is making an estimate for a home owner. This owner
has a small stream (
Q
= 1.4 cfs,
T
= 40
o
F) that is located at an elevation
H
= 34
ft above the owner's residence. The owner is proposing to dam the stream,
diverting the flow through a pipe (penstock). This flow will spin a hydraulic
turbine, which in turn will drive a generator to produce electrical power. Estimate
the maximum power in kilowatts that can be generated if there is no head loss and
both the turbine and generator are 100% efficient. Also, estimate the power if the
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 Spring '09
 DENG
 Fluid Dynamics, Orders of magnitude, head loss, Colin MacIntyre

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