The figure shows a simple level-control system in which a closed relay opens the valve and an open relay closes the valve. Input flow is not controlled. The level sensor has a transfer function of V h...

The figure shows a simple level-control system in which a closed relay opens the valve and an open relay closes the valve. Input flow is not controlled. The level sensor has a transfer function of  V_h=0.8h+0.4. The system uses 12 V supply. The relay closes at 6.4 V and opens again at 4.7 V.

a-Find the value of amplifier gain, K, required to open the valve when the level reaches 1.5 m.
b. At what level does the valve close?
c. Suppose Q₁=5 m³/min  , Q2=2 m³ ⁄min and  Q_out
=9 m³/min (when open). What is the period of the level oscillation?