Two liquid storage systems are shown in figure. Each tank is 4 feet in diameter. For System 1, the valve acts as a linear resistance with the flow?head relation q = 8.33 h, where q is in gallium and ii is in feet. For System II, variations in liquid level h do not affect exit flow rate q. Suppose that each system is initially at steady state with h = 6ft and q₁ = 50 gal/min and that at time = 0 the inlet flow rate suddenly changes from 50 to 70 gal/mm. For each system, determine the following information:

(a) The transfer function H?(s)|Q|(s) where the primes denote deviation variables.

(b) The transient response h(s).

(c) The new steady-state levels.

(d) If each tank is 8 ft tall, which tank overflows first? when?

9i System II System I