4) The tank shown has a bottom area A. A pressure source \hat{p}_s = p_s(t) + p_a is connected through a linear
valve resistance, R?, to the bottom of the tank. Another linear valve resistance, R?, allows the fluid to
exit the tank.
(a) Assume R? = R? = R, and develop a model of h, where \hat{h} = h(t). What is the time constant of the
model?
(b) Right before both valves open simultaneously to allow fluid in and out of the tank, the height of the
fluid in the tank is h?. If p?(t) = P_u s(t), determine the total response of the system for when both valves
are open and fluid flows in and out of the tank, i.e., h(t). (20 points)