Q$6.$ U$-$tube manometer for pressure differences

$($a$)$ Determine the equation for $p_A-p_B$ in terms of the specific weight of the flowing fluid,

${}_1,$ the specific weight of the gage fluid, ${}_2,$ and the various heights indicated in the

figure as shown.

$($b$)$ For ${}_1=9\mathrm{.}8k\frac{N}{m^3},{}_2=15\mathrm{.}6k\frac{N}{m^3},h_1=1m,h_2=0\mathrm{.}5m,$ what is the value of the

pressure drop, $p_A-p_B?$