Q $1$:$($a$)$ Show that inside a swimming pool, the pressure of water is directly proportional to depth and depends on the density of water.

$($b$)$ Show the pressure distribution on the vertical, horizontal and inclined $(45$ inclination$)$ surfaces of the pool. The depth of water in the pool is $5$ meters. $($Sp$.$ Weight of water $=9\mathrm{.}81$kN$//$m$^(1))$

Q$2$:$($a$)$ In figure $1,$ find the height $"$ h $"$ in terms of oil of specific gravity, S$=4.$ What is the absolute pressure of air in the tank?

$($b$)$ In figure $1,$ if the oil is replaced by water $($ S$=1),$ what would be the rise of mercury in the right column of the manometer.