The design month values for sizing a wind pumping system are as follows:

$$ Total pumped head $=18$ m

$$ Volumetric flow rate $=0\mathrm{.}0015$ m$3$s$-1$

$$ Average monthly wind speed $=5\mathrm{.}9$ m s$-1$

$$ Estimated mean windpump efficiency $=16\%$

Calculate the diameter of the rotor of the windpump $($in m$,$ to $2$ d$.$p$.)$ needed to meet the design month values.

$\{$In this location, the density of air is $1\mathrm{.}23$ kgm$-3$ the density of water is $1000$ kgm$-3$ and gravitational acceleration is $9\mathrm{.}81$ ms$-2\}$