Question

The power, P, produced by a wind turbine is given by:

P = ( ½) C𝜌Av³

where 𝜌 is the density of air [ML^-3 ], A is the cross-sectional area [L² ] of the blade and v is the velocity of air. Determine in MLT the dimensions of:

i. v³

ii. P

iii. C

Answer 1

i)

$v^3=(LT^{-1})^3=L^3T^{-3}$

II)

$P=ML^2T^{-3}$

III)

$C=\frac{ML^2T^{-3}}{ML^{-3}\cdot L^3T^{-3}L^2}=1$