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I hope this is right place to post this question (this is not a homework question).

I wanted to find out in what time a tank under low pressure (gas/air) is filled by the atmospheric pressure through a restriction.

(Tankpressure in relation of time or Flowrate through the restriction in relation of time.)

The flowrate is: V'(t)=delta_p(t)*C1 (Assuming a round restriction (pipe) and laminar flow C1=pi*r

^{^4}/(8*viscosity*l))

delta_p(t)= po-ptank+C2/V(t)

(po=atmospheric_pressure, ptank=Intial_tank_pressure, V(t)=is the Volume of air which entered the tank through the restriction C2=n*R*T; p*V=n*R*T (actually the temperature T would also be a variable but for now I would assume it to be constant))

Therefore: V'(t)=C1*(po-ptank+C2/V(t))

(since po and ptank are constants they can be written as C3=po-ptank).

And I end up with this differential equation:

**V'(t)-C1*C2/V(t)-C1*C3=0**

Can anybody think of an analytical solution for this equation (I haven't dealt with differential equations for 15 years) or think of an alternative way to solve this problem?

If I were to plot the flowrate through the restriction, I would expect a curve that would look something like this: V'(t) = V'o*e

^{-t*C}(Which is why I believe there should be an analytical solution.)