Q$.31$ A fan operating at $N=1800rpm$ and a volume flow rate of $4\mathrm{.}5\frac{m^3}{s}$ develops a head of $15$ cm $,$ measured on a U$-$tube manometer filled with water. For a geometrically similar fan that will produce the same head at the same efficiency, but at a speed of $N=1200rpm,$ the flow rate will be

$($a$)10\mathrm{.}12\frac{m^3}{s}$

$($b$)6\mathrm{.}75\frac{m^3}{s}$

$($c$)15\mathrm{.}18\frac{m^3}{s}$

$($d$)8\mathrm{.}27\frac{m^3}{s}$