# Chapter7: Wind Energy¶

## Ex7.1:Pg-216¶

In [1]:
# given data
import math
rho=1.226 # air density in kG/m^3
alpha =0.14
H=10.0 # height at which wind speed is given in m
uH=12.0 # speed in m/s
z=100.0 # tower height in m
D=80.0 # diameter  in m
effigen=0.85 # efficiency og generator

A=math.pi*(D**2)/4 # area in m^3
u0=uH*(z/H)**alpha # velocity at 100 m in m/s
u1=0.8*u0 # exit velocity in m/s
Po=(A*rho*u0**3)/2 # Total Power in Wind
# Part 1
print "Total Power in Wind is ",round(Po/1000000,2),"MW"

# Part 2
a=(u0-u1)/u0 # interference factor
Cp=4*a*(1-a)**2 # Power Coefficient
PT=Cp*Po/1000000 # power to turbine in MW

print "The power extracted by turbine is ",round(PT,2),"MW"

# Part 3
Pelec=effigen*PT # electrical power generated in MW

print "The Electrical power generated is ",round(Pelec,2),"MW"

# Part 4
FA=4*a*(1-a)*(A*rho*u0**2)/2 # axial thrust in N

print "The axial thrust is ",round(FA,2),"N"

# Part 5

Fmax=(A*rho*u0**2)/2 # maximum thrust in N
print "Maximum axial thrust is ",round(Fmax,2),"N"

Total Power in Wind is  14.0 MW
The power extracted by turbine is  7.17 MW
The Electrical power generated is  6.09 MW
The axial thrust is  541094.1 N
Maximum axial thrust is  845459.53 N


## Ex7.2:Pg-216¶

In [30]:
# given data
import math
u0=20.0 # wind speed in m/s
T=273+27.0 # temp in kelvin
P=1.01325e5 # pressure in Pa
R=287.0 # gas constant
r=80/2.0 # radius of rotor in m
w=2*math.pi*40/60.0 # rotor speed in rad/s
A=math.pi*r**2 # area of rotor in m^2

# soln:
rho=P/(R*T) # density in Kg/m^3
a=1/3.0 # condition for maximum output
Cpmax=4*a*(1-a)**2 # Power Coefficient
Lambda=r*w/u0 #tip speed ratio

Po=(A*rho*u0**3)/2000000 # Total Power in Wind in W

Tm=Po*r/u0 # Torque in N

Ctmax=Cpmax/Lambda # torque coefficient

Tshmax=Tm*Ctmax # torque at shaft

print "The torque at shaft for maximum output is ",round(Tshmax,2),"N"

The torque at shaft for maximum output is  3.35 N


## Ex7.3:Pg-217¶

In [31]:
# Given Data
# given data
import math
u0=15.0 # wind speed in m/s
R=80/2.0 # radius of rotor in m

For optimum energy the rotor speed should be 15.0 rpm