# Chapter6-Wind Energy¶

## Example 6.2.1-pg244¶

In [5]:
##Ex.6.2.1.
import math
##For air,the value of gas constant
R=0.287 ##unit=kj/kg K
##T=15. in degreecalcius
T=15.+273.;##in kalvin
RT=0.287*10**3*288.;
P=1.01325*10**5;##unit=Pa;at 1 atm
Vi=15.;##unit=m/s
gc=1.;
D=120.;##turbine diameter;unit=m
N=40./60.;
##Air density
p=(P/RT);
print'%s %.2f %s'%("Air density p=",p," kg/M^3");
##1] Total_power= Ptotal=p*A*Vi^3/2*gc
##power density =Ptotal/A=p*Vi^3/2*gc
power_density=(1./(2.*gc))*(p*Vi**3.);
##2] Maximum_power_density=Pmax/A=8*p*Vi^3/27*gc
Maximum_power_density=(8./(27.*gc))*(p*Vi**3);
print'%s %.2f %s %.2f %s '%("\n power density =Ptotal/A= ",power_density," W/m^2"and " \n Maximum power density=Pmax/A= ",Maximum_power_density," W/m^2");
##3]Assuming n=35%
n=0.35;
##let P/A=x
x=n*(power_density);
print'%s %.2f %s'%("\n P/A=",x," W/m^2");
##4]Total power P= power density * Area
Total_power_P=724.*(math.pi/4.)*(D**2) ##Total power P= power density*(%pi/4)*D^2
print'%s %.2f %s %.2f %s'%("\n Total_power_P=",Total_power_P," watt"and "=",Total_power_P*10**-3," kW")
##5]Torgue at maximum efficiency
Tmax=(2./(27.*gc))*((1.226*D*Vi*Vi*Vi)/N);##Tmax=(2/(27*gc))*((p*D*Vi*Vi*Vi)/N);
print'%s %.2f %s'%("\n Torgue at maximum efficiency=",Tmax," Newton")
##and maximum axial thurst
Fxmax=(3.14/(9.*gc))*1.226*D**2.*Vi**2.;##Fxmax=(%pi/(9*gc))*p*D^2*Vi^2;
print'%s %.2f %s'%("\n maximum axial thurst=",Fxmax," Newton");

Air density p= 1.23  kg/M^3

power density =Ptotal/A=  2068.65
Maximum power density=Pmax/A=  1225.86  W/m^2

P/A= 724.03  W/m^2

Total_power_P= 8188247.09 = 8188.25  kW

Torgue at maximum efficiency= 55170.00  Newton

maximum axial thurst= 1385870.40  Newton