For the figure shown here;

$($a$)$ Develop an equation for the pressure at $B(p_B)$ for the original case as shown.

Neatly reproduce the sketch.

$($b$)$ Develop an equation to determine the new differential manometer reading when the pressure at $A$ is increased to $p_{A1}.$ Neatly sketch the applicable case relative to the original case.

$($c$)$ Develop an equation to determine the new differential manometer reading when the pressure at A is decreased to $p_{A2}.$ Neatly sketch the applicable case relative to the original case.

$($d$)$ Calculate the differential readings of $($b$)$ and $($c$)$ above, if pipe A contains gasoline