Question

Considering the following liquid-level qo where the liquid is laminar flow and .0-steady-state flow rate (m'/s) . H-steady-state head (m) rate from the steady-state value (m/s) qi-small deviation of inflow . qo-small deviation ofoutflow rate from the steady-state value (m/s) h - small deviation of head from its steady-state value (m) . R-the resistance of the laminar flow in the output flow pipe · C-the capacitance of the tank Derive the differential equation model of the liquid-level-system with input as the inflow deviation qi-cos(at) and output as the liquid level deviation h. Also find the output response with respect to the following input assuming initial value h(0) 1

Answer 1

CONTROL VALVE Area of cross section OF-tank-A Hth. LOAD VALVE 改+90 Applying Volume Floro rate balance in-Rout(A0)container (a1%)-(Q+9): (aa) container dt dt Assuming Laminar Flono in fluid system:-, co-h r here R→ Resistance - at at For constant cross sectional Area of container capacitane CA dt dも 9 dt dh 3h cos 2t d t Auxilary Equation for above Differential equatio

:Complementary function For Particular Integrol FD) D+3 Using ecosbx e-3t e" (acasbxt bsinbx 2tb2 C3)2+22 6t 13 Complete SolutionCF+P T 13 Initial condition ho) 1 13 13 13 16 este(2sin2t -3 cos2t) 12 13 tHence hlt) is the output response