Examine the figure below, where water flows through an orifice. The manometer fluid has a specific gravity of $13\mathrm{.}6.$ The density of water can be taken as $1000k\frac{g}{m^3}.$

a$)$ Derive the pressure difference between points A and $B(P_A-P_B)$

b$)$ Calculate the difference in height of the two columns of manometer fluid $(H)$