Answer:
[tex]D=0.1160m[/tex]
Explanation:
From the question we are told that:
Output Power [tex]P=1.2kw[/tex]
Density [tex]\rho=1.29kg/m^3[/tex]
Wind speed [tex]V=17.5mph=>7.8m/s[/tex]
Efficiency [tex]\gamma=60\%=>0.60[/tex]
Let Betz Limit
[tex]C_p=\frac{16}{27}[/tex]
Generally the equation for Turbine Efficiency is mathematically given by
[tex]\gamma=\frac{P}{P'}[/tex]
Where
P'=input power
[tex]P' = In\ power[/tex]
[tex]P'=1/2*C_p*\rho u^3*A[/tex]
[tex]P'=1/2*C_p*\rho u^3*\frac{\pi}{4}*D^2[/tex]
Therefore the blade diameter for a two-blade propeller type rotor is
[tex]\gamma=\frac{P*2*27*4}{16*\rho u^3*\pi*D^2}[/tex]
[tex]D^2=\frac{P*2*27*4}{16*\rho u^3*\pi*\gamma}[/tex]
[tex]D^2=\frac{1.2*2*27*4}{16*1.29*7.91^3*\pi*0.60}[/tex]
[tex]D^2=0.0135[/tex]
[tex]D=\sqrt{0.0135}[/tex]
[tex]D=0.1160m[/tex]
