Fluid Mechanics Problem:

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Homework Statement




6. A tank filled with air of initial density ρo=1.2 kg/m3 and initial pressure Po=100 kPa is to be evacuated by a vacuum pump. The tank volume is 1 m3 and the pump evacuates 0.0013 m3 of air per second regardless of the pressure. The process is isothermal and for an ideal gas such as air, this means that P/ρ = Po/ρo = constant. Derive an equation that shows how the pressure inside the tank, P, changes with time, t and then use it to calculate the time needed to reduce the tank pressure to 1 kPa.



Homework Equations



m1+m2-m3-m4= dM/dt

Mass Flow Rate = Rho x V x A
Mass inside control volume = Rho(Volume)

The Attempt at a Solution



The answer is (t = 3,542 s) but I am unsure of the method to get there.
 

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