Assume a sirocco$-$type fan with the performance as shown in the figure below. This blower operates at a fixed speed of $1,381$ RPM$,$ with an airflow rate $($Q$)$ of $6\mathrm{.}2$ CMM at the operating point, where the static pressure is $21\mathrm{.}6$ mmAq. Assume that this operating point is the point of maximum efficiency. Also, the fan diameter is $160$ mm$,$ and the inlet casing clearance is assumed to be $1$ mm$.$ Answer the following questions:

$($A$)$ Calculate the expected efficiency $(\backslash$eta t$)$ based on the specific speed and specific diameter.

$($B$)$ If the same specific speed is maintained to keep the operating point constant, determine the change in maximum efficiency $(\backslash$eta t$)$ as the fan diameter varies from $100$ mm to $200$ mm$.$ Also, indicate the required fan speed for each diameter $($assuming that the static pressure at the operating point remains constant despite changes in diameter$).$

$($C$)$ Under the conditions of $($B$),$ compare the performance curves for each diameter.