QUESTION TWO $(2)$

$($a$)$ Write down a mathematical relationship for the following pairs of fluid properties:

$($i$)$ Mass density $()$ and specific weight $()$; and

$($ii$)$ Specific volume $(V_s)$ and mass density $()$

$($b$)$What is a channel of best section?

$($c$)$ Derive an equation for the hydraulic radius of a rectangular channel of best section.

$($d$)$The specific volume of a gas is $0\mathrm{.}90\frac{m^3}{k}g$ and $30m^3$ of oil weighs $98\mathrm{.}81KN.$ Calculate:

$($i$)$ The specific weights of the gas;

$($ii$)$ The specific weight of oil; and

$($iii$)$ The mass density of the gas.