Question

A storage tank has a Diameter of 6 m and a height of 3 m. The output volumetric flow from this tank is given by fout(t)=2h(t) where h(t) is the height of the liquid in the tank. At a particular time the tank is at steady state with an input flow of 275 L/min .

1) develope the mathematical model describing this process.Define all variables and give initial conditions where appropriate. Clearly state all assumptions that you used to develope this model .

2) what is the steady-state liquid height of liquid in the tank ?

Answer 1

1)   F_IN-F_out=AD(h)/Dt    where F_{IN is input flow rate;} F_{out is output flow rate ;} A is cross sectional area of tank

h is height of water in tank at any time.

assumptions: 1. density is constant or incompressible flow. 2. intially there is no water in tank.

             so intial condition is that at t=0, h=0

2)    at steady state D(h)/Dt=0

       so F_{IN =} F_{out   ,    at stedy state}F_{IN = 275L/min=0.275 meter/min;} F_out   = 2 h_s

        2h_s=0.275

        h_s=0.1375 meter.