Example

A U$-$tube manometer $($Fig$.$ below$)$ measures the pressure difference between two points A and $B$ in a liquid of specific weight ${}_1.$ The U$-$tube contains mercury of specific weight ${}_2,$ Calculate the difference in pressure if $a=1\mathrm{.}5m,b=0\mathrm{.}75m$ and $h=0\mathrm{.}5m,$ if the liquid at A and B is water and the specific gravity of mercury is $13\mathrm{.}6.$