Question $1$

$($a$)$ An open tank contains $5\mathrm{.}7m$ of water covered with $2\mathrm{.}8m$ of kerosene $({}_k=820\frac{kg}{m^3}).$

Find the pressure at the interface and at the bottom of the tank.

$5$ Marks

$($b$)$ A rigid steel container of $2\mathrm{.}464$ litres volume is half filled with water at $1500$kPa.

Calculate the Bulk Modulus of water, if volume of water in the container is reduced to

$1\mathrm{.}231$ litres under a pressure of $3000$kPa.

$5$ Marks

$($c$)$ Water flows through a nozzle at a rate of $60k\frac{g}{s}.$ The inlet and outlet diameters of the

nozzle are $220mm$ and $80mm,$ respectively. Compute the average velocities at inlet

and outlet sections.

$5$ Marks

$($d$)$ Water flows in a $20mm$ diameter $PVC$ pipe of $1\mathrm{.}2km$ length between points A and $B.$

At point $A,$ the elevation of the pipe is $32m$ and the pressure is $275$kPa. At point $B,$

the elevation of the pipe is $30m$ and the pressure is $280$kPa. If the total headloss is

measured as $5m,$ compute the flow through the pipe.

$5$ Marks

$($e$)$ An orifice meter fitted to a pipe of $500mm$ diameter has an orifice diameter of $200$

$mm.$ Find the quantity of water flowing through the pipe if headloss $($h$)$ across the

orifice is $200mm$ of water. Take $C_d=0\mathrm{.}75$ and $Q=C_{d}A\sqrt[\phantom{2}]{\frac{2gh}{m^2-1}},$ where $\text{'}m\text{'}$ is the ratio of

pipe and orifice diameters.

$5$ Marks