Re: [PipingDesign] flow calculation in case of pipeline rupture

From: <Christopher>
Date: Sat Dec 13 2003 - 00:59:00 EST

>Suppose I have a pipe containing gas at a pressure higher than atmospheric
>pressure. (Pl. note that there is no feeding source to the pipe).
You have to integrate the relationship between flow and pressure. I don't think there's a simple formula because the pressure difference across th opening is changing constantly over time. but you can go back to your fluids book and work out the variation over time. You don't have to use calculus if you don't feel like it, but the arithmetic is easy with a spreadsheet.

In a short interval Dt a little bit of gas, Dm, comes out. The instantaneous mass flow is Dm/Dt. The relationship between mass flow for low pressure is DM/Dt = Cd*(density)*(Area)*root(P-Patm/density). All this is in your fluids book, BTW. The outflow drops the density to a new density and the pressure, P, to a new pressure P1 during the interval Dt. You refigure the new mass flow Dm/Dt from the new pressure and density and get the amoumt of mass which flows out during the second interval. Just repeat the calculation stepwise until the pressure drops to atmospheric. If the pressure is high enough for compressibility effects, there's a more complicated pressure -mass flow relationship, but the calculation goes the same way.

Christopher Wright P.E.    |"They couldn't hit an elephant at        | this distance"   (last words of Gen.
___________________________| John Sedgwick, Spotsylvania 1864) Received on Sat Dec 13 00:59:00 2003

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