Question $1(33$ points$)$

A university intends to install a wind tunnel in a student laboratory. The wind tunnel will have three cylindrical sections. The design requirements are below.

The volumetric flowrate of air through the tunnel will be $\backslash (15\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$

Section $1$ will have a diameter of $1\mathrm{.}5$ meters.

Section $2$ will have a diameter of $1\mathrm{.}0$ meters.

Section $3$ will have a diameter that permits an air velocity of $\backslash (75\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$

Given the above information answer the following questions:

a$.$ Calculate the air velocity in section $1.$

b$.$ Calculate the air velocity in section $2.$

c$.$ Calculate the diameter of section $3.$