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)**

**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**

_{ }**2h _{s}=0.275**

**
h _{s}=0.1375 meter.**

** **

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