How to calculate gas flow rate through a system?

[Gurj]

The pressure at the start of a 180km stainless steel natural gas pipeline is 4MPa and at the end is 2MPa. if the diameter is 0.4m, what will be the gas flow rate through the system?
(ignore losses other than friction, ρ= 40 kg/m^3, μ= 11x10^-6 Pa)

Could anybody please point me in the right direction on how I actually do this question?
I have done questions where we were asked the mass flow rate before but we were not given values for pressure etc in them. I know that i have to use the moody diagram but do not know what to do with the pressure values given.
Also came across this formula in my notes: μ = [(∏*d^4)/(128*Q*l)]*(P1-P2) but surely it could not be that easy?


Thanks for any help in advance!

 

[Travis_King]

http://www.engineeringtoolbox.com/air-duct-friction-loss-diagram-d_328.html

This might serve as a good approximate, unless you need to do it analytically.

 

[256bits]

You might have to do it by iterations.
Start -assume a friction factor - Pick a random flow rate ( or velocity ) - find Reynolds number - calculate pressure drop - does it match - yes you are done - if not increase or decrease flow rate depending upon calculated pressure drop and go back to start.

How close should the match be - I guess you decide but 1% to 5% should be OK and how many iterations you would like to do, Afterall you are ignoring losses other than friction, so maybe a resulting flow on the low side would be more reasonable.

 

[RTW69]

I think "bits" is correct. This problem requires an iterative solution. Basically the pipe pressure drop equals the head loss (h-L). To calculate h-L assume a velocity, calculate Re, look up (or calculate) a friction factor. Compare h_l to ΔP. If ΔP≠h-L, assume new velocity. If you don't like looking up the friction factor from the moody diagram you can use the Colebrook equation (assumes you are in the nonlaminar range) which as empirical fit for the Moody diagram.

 

[RTW69]

The units of dynamic viscosity are Pa*s

Forget the Colebrook equation. Plug in all your constants and you get a simple equation in the form const=f*v^2 where f is the friction factor and v is velocity.Get your moody diagram out. Look up the absolute roughness ε for stainless steel pipe and calculate ε/D. Assume a reasonable velocity for natural gas in a pipe. Calculate Re, look up f from Moody diagram. See if f*v^2 = the constant. If it doesn't, assume another value for v, calculate Re, look up new f. You get the idea. After 3-4 iterations you will approach the correct value of velocity and can calculate the mass flow rate.