QUESTION $1[50$ MARKS$]$

The pressure difference between an oil pipe and water pipe is measured by a double$-$fluid manometer, as shown in Figure $1.$

$($a$)$ For the given manometer fluid heights and specific gravities, calculate the pressure difference.

$($b$)$ Sketch the pressure distribution in the manometer fluids for each manometer arms.

$($c$)$ Provide engineering assumptions and engineering model for solving $($a$)$ and $($b$)$