Problem $5$

A channel of right triangular cross section, which is $25$ m long and $1$ m deep, is used for the storage of water. The water and the surrounding air are both at a temperature of $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the relative humidity of the air is $\backslash (50\backslash \%\backslash ).$

$($a$)$ If the air moves at a velocity of $\backslash (5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ along the length of the channel, determine the rate of water loss due to evaporation at the surface.

$($b$)$ For the condition in part $($a$),$ obtain an expression for the rate at which the water depth would decrease with time due to evaporation. How long would it take for all water to evaporate?