Let so consider liquid of
thickens de at height $x$
below the surface
$P = pgx$
$\int p _{ mt }= P _{ Total }=\int_0^{ H } pgx ( dx )$
$p _{ mt }= pg \frac{ x ^2}{2} I _0^{ H }$
$p _{ mt }=\frac{ pgH ^2}{2}$
$p _{ avg }=\frac{ p _{ mt }}{ H }=\frac{ pgH }{2}$


