Question

5. (10 points) Consider the liquid-level system shown. At steady state, the inflow rate is Q: the outflow rates are Q1 and Q, respectively; the flow rate from tank 1 to tank 2 is Q12, and the heads of tanks 1 and 2 are H and H2, respectively. If the inflow rate is changed from Q to Q+q, determine the transfer function Hz(8)/Q(s). Assume the deviations 4,91,92,912, h, and hy are all small. 6th Jan Hathe +7 т/ н+А, JE>,+8. Rz Ri - Qatar Riz

Answer 1

Solutions Consider the liquid level system out oflow rated Equation. female - Fore ldre (0-2,-2) су RIQ tanks of flow rate is, Then, we get > C to required in head dhe = .912-4 dt * from accordang by use of Toplace transformation Equation Substitution. Similarly we get, C25 H(s) = Quiz (s) – Qz (s) Hy (s) Ry Q15) - from ☺ and (2), are equation is. CeSH263) = 989-C to

RU Biz (8) = ceas Hy be) - 0,65) = Riga 0,4+ Hoe (s) 06) = { Photo cca kasut) my w 4, B,C) = Rie (CZ. RR +) +P2 x H. 4 0 R, Rq from Substitution, 3 and @ Equation 29,6=003) -0,45), GIRIS'x Hols) - Reloppest!) +Rex Heb . Rq RIRR 5 (G Risto) (@, (5)) - pus) - Can Past") X H_G) * The transformation function is liquid level System, o H₂ (s) - R R2 Q(s) R12 (48,5+) (2 RS+1) + R2 (C, RS +1) +R, - (RS) = H2 (5) = - Rj Rz Rus) RI Rq R 12 C1 C₂ S2 + (R, R2 4+ R1 R₂ C2 +10 O [ +GR;R12 & solution . R12+R+R2 out flow rate change, Hence proved the