A liquid-level system is formed of a tank of capacitance Cl communicating with a pipe segment equipped with a valve of resistance Rl, as sketched in Figure 5.15. a. Derive a mathematical model for...

A liquid-level system is formed of a tank of capacitance Cl communicating with a pipe segment equipped with a valve of resistance Rl, as sketched in Figure 5.15.

a. Derive a mathematical model for this system by connecting the output (either the flow rate qo or the head h) to the input flow rate qi. Assume that the pressure at the input and output ports is zero.

b. For a unit ramp input, find the solution qo(t) and plot it against time considering that Rl,p = 5 # 104 N-s/m5 and Cl,p = 2 # 10-6 m5 /N. The slope of the ramp input is Q = 10-4 m3 /s.