#  [m ] 2 r ```#HW3 Wind Energy 風能

1. A solid steel shaft has a radius of 0.1 m and a length of 0.8 m. Find the area
moment of inertia J and the mass moment of iertia I. if the volume density of steel
is 7800 kg/m3.
.
J
 ro 4
2
[m 4 ] , I  J  a [kg m 2 ]
The mass moment of inertia is found from the area moment of inertia by
multiplying by the area density ρa in kg/m2 . The area density is measured across
the area perpendicular to the axis of rotation.
2. If an expression for the real wind power is
Pw 
 Au 3
2
1.7 pAu 3
=
[W]
T
In this equation, p is the pressure in kPa and T is the temperature in kelvin. As
shown in figure, u is 10 m/s and R is 20 m.
(1) Find the Pw based on the climate of 1 atm and 30 oC.
(2) Find the difference between real Pw and ideal Pw. (need to look up the density of
air at 30 oC)
R
u
1 atm 下，30&deg;C 時，空氣密度為多少 kg/m3？（空氣平均分子量為 28.8，3 分）
30&deg;C 下 1 mole 的空氣體積 = (24.45 x 10-3 m3)= 0.02486 m3
30&deg;C 下 1 mole 的空氣質量 = 28.8 g = 28.8 x 10-3 kg
pa = 28.8 x 10-3/0.02486 = 1.158 kg/m3
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mmHg
700
710
720

15℃
20℃

25℃
30℃
1.13
1.14
1.16
1.09
1.10
1.12
1.07
1.09
1.10
1.14
1.15
1.17
1.19
1.20
1.12
1.13
1.15
1.16
1.18
1.11
1.12
1.14
730
1.18
1.16
740
1.19
1.17
750
1.21
1.19
760
1.23
1.21
770
1.24
1.22

```