A storage tank has a Diameter of 6 m and a height of 3 m. The output volumetric

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 ?

Explanation / Answer

1)   FIN-Fout=AD(h)/Dt    where FIN is input flow rate; Fout 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 FIN = Fout   ,    at stedy stateFIN = 275L/min=0.275 meter/min; Fout   = 2 hs

        2hs=0.275

        hs=0.1375 meter.

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