Problem 9 97

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Problem 9.97 [Difficulty: 2]
Given: Windmills are to be made from surplus 55 gallon oil drums
D 24 in H 29 in
Find: Which configuration would be better, why, and by how much
Solution:
Basic
equations:
FD CD
1
2
 ρ V
2
 A (Drag)
Assumptions: (1) Standard air
(2) Neglect friction in the pivot
(3) Neglect interference between the flow over the two halves
For the first configuration:
ΣM
D
2
Fu
D
2
Fd
D
2
Fu Fd  Where Fu is the force on the half "catching" the wind and Fd is the
force on the half "spilling" the wind.
ΣM
D
2
CDu
1
2
 ρ V
2
 A CDd
1
2
 ρ V
2
 A




D
2
CDu CDd 
1
2
ρ V
2
 A




For the second configuration:
ΣM
H
2
Fu
H
2
Fd
H
2
Fu Fd 
ΣM
H
2
CDu
1
2
 ρ V
2
 A CDd
1
2
 ρ V
2
 A




H
2
CDu CDd 
1
2
ρ V
2
 A




Since H > D, the second
configuration will be superior.
The improvement will be:
H D
D
20.8 %