(a)[3]
Work out the SI base units of power.
(b)
Fig. 1.1 shows a turbine that generates electrical power using the wind. The power $P$ available from the wind is given by $P = C L^2 \rho v^3$, where $L$ is the length of each turbine blade, $\rho$ is the air density, $v$ is the wind speed, and $C$ is a constant.
(b(i))[3]
Show that $C$ is unitless.
(b(ii))[3]
The blade length $L$ of the turbine is $25.0\,\text{m}$ and the air density $\rho$ is $1.30$ in SI units. The constant $C$ is $0.931$. The turbine efficiency is $55\%$ and the electrical power output $P$ is $3.50 \times 10^5\,\text{W}$. Calculate the wind speed.
(b(iii))[2]
Give two reasons why the turbine’s electrical power output is smaller than the power available from the wind.