$5\mathrm{.}22.$ The performance requirements for an air mover are stated as flow

rate, $Q=60\frac{m^3}{m}in$; total pressure rise, $p_T=500Pa.$ Ambient air

density, $=1\mathrm{.}175k\frac{g}{m^3}.$ The machine is constrained not to exceed

the $90$ dB sound power level.

a$.$ Determine a suitable speed and diameter for the fan and estimate

the total efficiency.

b$.$ Correct the total efficiency for the effects of Reynolds number,

a running clearance of $2\mathrm{.}5$ Ideal, and the influence of a belt$-$

drive system $($assume a drive efficiency of $95\%).$