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
