In the process shown below, two liquid streams with mass flowrates $w_1$ and

$w_2(k\frac{g}{s})$ and a density of $(\frac{kg}{m^3}),$ enter the cylindrical tank with a cross$-$

sectional area, $A.$ The outgoing stream mass flowrate is given in term of the

liquid level in the tank by $w=k\sqrt[\phantom{2}]{h},$ where $k$ is a constant.

Develop the process and disturbance transfer functions relating the manipulated

variable $(w_1)$ and the disturbance $(w_2)$ to the controlled variable $(h).$ Write

down the expressions for the system time constant and the process$/$load steady$-$

state gain.

Show that the unit of the time constant is in sec$.$

Sketch the P&ID and the block diagram for the level control loop, assuming

that the level transducer and the controller are analog electronic units with an

output $4-20$ mA and the control valve is pneumatically actuated.