(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a first-order differential equation problem involving a changing fluid density and changing tank pressure.

Tank contents: Nitrogen

Tank pressure: 390 psig

Temperature of compressed nitrogen: 0 C

Atmospheric volume = infinity

Atmospheric pressure = 14.7 psi

Atmospheric temperature = 0 C

2. Relevant equations

Use the following two equations

1. Bernoulli's compressible fluid equation (neglecting gravitational potential): (v^2)/2+(γ/γ-1)*(p/ρ) = constant

2. Mass flow rate for an ideal compressible gas:

3. The attempt at a solution

I am trying to set up a DE in order to solve for the time to evacuate the tank from 390 psig to atmospheric pressure. Pretty standard conservation of mass problem... I thought about treating it similarly to a volume flow rate tank drain problem (i.e. A*(dh/dt) = -a*2gh), however, the mass flow rate in this case involves compressible fluid, where exit velocity and density vary with time.

Any ideas would be very helpful! Thanks

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# Homework Help: Find time to evacuate compressed air tank (conceptual verification)

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