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

1. Apr 1, 2012

### ryancalif

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