Question

(b) In a paint mixing plant, two tanks supply fluids to a mixing cistern. The height, h, of the fluid in the cistern is dependent upon the difference between the input mass flow rate, q, and the output flow rate, qe A nonlinear differential equation describing this dependency is given by Ae dh (2) V2gh + A dt pA where A cross-sectional area of the cistern, Ae due to gravity, and p = cross-sectional area of the exit pipe, g = acceleration liquid density Linearize Eq. (2) for the equilibrium point (ho, ^o)

Answer 1

Solution : Given Data A non-linear differential equation describing this dependency is given by cht he Vagh - I equation- Here: A = cross-sectional area of the cistern, Ae=Cross -- sectional area of the exit pipe g = Accleration due to gravity P = Liquid density From equation - jedoch = -( 7296) + nec - ( Tag ) uh uh uh The output flow rate is the de = Paelz = (PAe Vzg ) With For solving above equation we can consider these constraints: ki= pedag ķ2 = 1 / 1 kg a PA etag - Above constraints are applying in the above equations ha. Kyph + kag equation- - We a k3th = > equation - So the functional form of the equations a A

equillibrium point fChiq) = h = Kight kaq and h(h,g) = %=k3th Then, the relation ship between (ero, hol is % = -K 1 The 1% = 12g Aetho