Is My Air Flow Rate Equation for a Train Braking System Accurate?

[iscariotrail]

I can't seem to find an equation that fits the situation I am facing. Either that, or I just don't believe the answer the current equations are providing.

I am trying to develop the size for an air compressor to fill up a train braking sytem. I have equations for most of the system, but I can not find a relationship for the flow rate of the air through the entry point as the system fills with air.

The train pipe is 8,000 feet long, 1.25" Schedule 80 steel. It is initially at 0 psig, while the connection point is 90 psig. Considered isothermal, I've been using the equation:

P₁² - P₂² = [ M²RT / gA² ] * [fL / D + 2 Ln (P₁/P₂) ]

Solving for the equation, I'm coming up with:

M = 0.1673 LB/s
Q = 17.1 CFM
v = 32.1 ft/s

The flow rate just seems too low, and that's why I question the equation I'm using. When the 90 psig is connected to the 0 psig, air should be rushing in (I'm thinking between 150 & 200 CFM), right?

Any thoughts or suggestions? Would be much appreciated.

 

[edgepflow]

Initially with an 80 psig air supply pressure, the flow is probably limited by the speed of sound (i.e choked flow). So determine the speed of sound in the pipe and multiply by the cross sectional area.

Eventually, as the back pressure increases, you will exit choked flow. There are several formulas for testing for choked flow, but an ininital check is that the back pressure is less than 50% of inlet pressure.

After you exit choked flow, just use basic fluid mechanics: DP = f (Leq/d) rho vel^2 but time step it to account for increase in back pressure and changes in air density.