Consider the liquid level system shown in the figure Assume

Consider the liquid level system shown in the figure. Assume the outflow rate Q (m^3/s) through the outflow value is related to the liquid level H by Q = 0.01 squareroot H Assume also that, when the inflow rate Q_i and outflow rate Q are at 0.015 m^3/s, the liquid level stays at constant H_o. The capacitance C of the tank is 2m^2. Find the steady state value of the liquid level system H_o. Develop the governing equations for the liquid level system and linearize the governing equations obtained from (a) at the steady state point H = H_o. Derive the transfer function H(s)/Q_i(s).

Solution

Q = 0.1*sqrt(H)

given, Q = Q_i = 0.015, A = 2 m^2

therefore, H_o = (0.015/0.1)^2 = 0.0225 m

Qi - Q = dH*A

Q_i = 2*(H - H₀) + 0.1*sqrt(H)