Answer:
Explanation:
Given Data
The diameter of the wind mills is d = 40m
Velocity of the air is V = 6
m
/
s
Required power output is: P
₀
=
2100
k
W
Expression to calculate the exergy of the air is
E
=
V
²
/ 2
Substitute the value in above expression
E
=
(
6
m
/
s
)
²
/ 2
E
=
18
m
²
/
s
² x (1kJ/kg / 1000m²/s²)
E
=
0.018
k
J
/
k
g
Expression to calculate the density of the air is
P
v
=m
R
T
m
/v
=
P /RT
⋯
⋯(
I
)
Here
m is the mass of the air,
v is the volume of the air,
P is the atmospheric pressure,
T is the standard temperature at the atmospheric pressure and
R is the gas constant
As the density is
ρ
=
m
/V
Substitute the value in expression (I)
ρ
=
101 kP
a
/(
0.287
k
J
/
k
g
⋅
K
)
(
298
K
)
ρ
=
1.180
k
g
/
m
²
Expression to calculate the mass flow rate is
m
=
ρ
A
V
⋯
⋯
(
I
I
)
Here A is the area of the windmill
Expression to calculate the A is
A
=
π
/4 d
²
Substitute the value in above expression
A
=
π
/4
(
40
m
²)
A
=
1256.63
m
²
Substitute the value in expression (II)
m
=
(
1.180
k
g
/
m
³)
(
1256.63
m
²)
(
6
m
/
s
)
m
=
8896.94 k
g
/
s
Expression to calculate the maximum power available to the windmill is
P
w
=
m
(
V
²
/2
)
Substitute the value in above expression
P
w
=
8896.94 k
g
/
s
(
(6m/s)²/2
)
P
w
=
160144.92
W ×
(
1
W
/1000
k
W
)
P
w
=
160.144
k
W
Expression to calculate the number of windmills required is
n
=
P
o
/P
w
Substitute the value in above expression
n=2100kw/160.144kw
n=13.11
