ES330 Section 2
Exam#1
Name:
You will have 1.5 hours to complete the exam. Please show all work and list any
assumptions you are making. You must draw a control volume, free body diagram, and
coordinate system if required by the problem to receive credit for your work.
Problem #1 (40 points)
Wind power is becoming more and more common as energy needs grow. The wind
entering and leaving the turbine can be described by the streamlines that bound all of the
mass flowing into the blades as shown below.
Turbine
blades
V
1
A
1
V
2
A
2
bounding
streamlines
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ES330 Section 2
Exam#1
Name:
Starting with the following equation:
∫
∫
•
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+
+
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+
+
∂
∂
=
+
cs
cv
net
net
dA
n
V
gz
V
P
u
V
d
gz
V
P
u
t
W
Q
ˆ
2
2
2
2
v
(
(
&
&
ρ
ρ
ρ
ρ
(a)
Derive an expression for the amount of power that is available from the wind if
the wind speed approaching a turbine is V
wind
, the area of the blades is A
b
, the exit
area A
2
, and there are no losses. A
1
≈
A
b
, V
1
=V
wind
. (10 points)
(b)
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 Spring '08
 Bohl
 Wind turbine, Windmill

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