Question

Consider the liquid level system shown in Figure 1. At steady state, the inflow rate and outflow rate are both Ở and the flow rate between the tanks is zero. The heads at tank 1 and tank 2 are both H. At t = 0, the inflow rate is changed from 0 to + , where is the small change in the inflow rate. The resulting changes in the heads (h/ and h2) and flow rates are assumed to be small. The capacitances of Tank 1 and Tank 2 are C, and C2 respectively. The resistance between the tanks are R, and that of the outflow valve is R2. Find transfer function of Hz(s)/Q(s). eta Tank 2 Tank 1 H+h H+h2 +92 R R2 Figure 1 Liquid level system

Answer 1

Considering a liquid - Jevel system shown below FM Q+q Tanks 1 pok Tank 2 thi +92 R2 01 का from Tanks: adh -aidt; a arche adhe-91 het AQSh che +0 From Tank 9 Cedha = (-91-92) at tq.dt 9,- home 92 - head Cedha ha ha +9 de RE Semana PIR2 G dhe de + (PitR2) hz - Rilpaq Applying laplace Transform on both sides

(ABGS+ Ri+B) 09- AB94) GO)hrs) 965 PiR2 PIBGS+ Pithe

ANSWER : h₂(s)/Q(s) = R₁R₂ / (R₁R₂C₂S + R₁ +R₂)

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