A centrifugal pump with a $20-$inch diameter impeller, a rotational speed of its impeller of $1,300$ revolutions per minute and a power of $12\mathrm{.}21$ horsepower, It pumps a water flow rate of $4\mathrm{.}00$ cubic feet per minute. Consider that this system of water distribution, the existing pump will be replaced with a new unit, geometrically similar and manufactured by the same manufacturer, which will operate with the same rotation speed of its impeller, but with a required power of $37\mathrm{.}24$ horsepower of strength. Determine the required impeller diameter $($inches$)$ of the new pump