Question 2 A tank with a volume is supplied with compressed air at a rate that i

Question

Question 2 A tank with a volume is supplied with compressed air at a rate that is a complicated function of the tank pressure, rim i P). At the same time pressurised air is withdrawn from the tank at a mass flow rate that depends on the exit line flow resistance, R a(P P) where a and b are constants, Pis the instantaneous tank pressure, and Pe is the instantaneous usable pressure. Let Crepresent the mass storage capacity of the tank. Provide: a. A sketch of the problem. b. A sketch of the analogous flow network using a capacitor symbol to indicate tank mass storage. c. Set up a model for simulating the gas pressure, Pversus time t.Assume the perfect gas law, PV mGT, where G is the universal gas constant holds

Explanation / Answer

a.Volune of the tank=V

Tank pressure,mi=f(p)

Resistance R=a(P-Pe)^b

Storage capacity of tank=C

b.Analogous flow network using capacitor symbol is given as,

The general equation is V(mi)(input)=R(output)

The capacitor symbol is given as,-ll-

The capacitor charges and discharges the electric current through it and the capacitor consists of two parallel plates separated by a dielectric medium in between.

Similarly the pressurized air is sent in and taken out simultaneously which can be conpared to electric charging and discharging in a capacitor.

c.When simulation model is performed,pressure is plotted with respect to time and we infer that the pressure increases with time and from the equation we infer that the pressure decreases with increase in volume.

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