$2^{nd}$ semester $2023-2024(1445)$

$4.$ The two tanks in the figure below are connected through a mercury manometer. What is the relation between $z$ and $h?$

$5.$ An open U$-$tube manometer $($see the figure below$)$ is being used to measure the absolute pressure $P_a$ in a vessel containing air. The pressure $P_b$ is atmospheric pressure, which is $754mmHg.$ The liquid in the manometer is water having a density of $1000k\frac{g}{m^3}.$ Assume that the density ${}_b$ is $1\mathrm{.}3k\frac{g}{m^3}$ and that the distance $Z$ is very small. The reading $R$ is $0\mathrm{.}415m.$ Calculate $P_a$ in:

a$.$ psia

b$.$ kPa.