Re: Pressure Drop for Compressible Flow

On Jan 27, 2008, at 11:56 PM, indra pratisto wrote:

> I'm assuming isothermal compressible flow. Using pressure and
> temperature at the safety valve's discharge point I obtain the
> fluid properties (density, viscosity, Cp, Cv, etc). Afterwards, my
> step-by-step calculation is as follows:
> - Check for Mach number of inlet fluid: max possible velocity of
> a compressible fluid in a pipe is sonic.
> - Calculate friction loss using Reynolds number and relative
> roughness
> - Calculate loss coefficient due to fittings using Darcy's 3-K
> method
> - Calculate total loss (friction loss + loss due to fittings)
> - Calculate outlet pressure using Darcy's equation for
> compressible fluid
> - Get the pressue drop (Inlet pressure - Outlet pressure)
> - Check for Mach number of outlet fluid: max possible velocity of
> a compressible fluid in a pipe is sonic.
This is covered pretty well in my old undergraduate fluid mechanics textbook by V. L. Streeter. Your best bet is to find a reasonably good book on the subject to see the form of the relationships involved and get some caveats on the limitations of the process. Marks' Handbook is an excellent desk reference. The steps you've outlined are correct, but the procedure is iterative--perfect for a spreadsheet.

If it were me, I'd start by assuming that the entire pressure drop takes place across the valve and determining the first guess at a flow rate from that. Then I'd figure what the flow rate would be with zero pressure loss across the valve. The lower of the two figures is an upper bound to the overall flow rate. Provided the pressure ratio across the system is less than that for sonic flow in the valve, which will be the absolute maximum flow rate. If that's the case your problem is solved already. In that case the chances are that the effect of the line will be small. In fact the line should be chosen short enough and big enough so that the pressure drop will be an absolute minimum--otherwise the pressure relief will allow the the steam drum pressure to rise above the valve set point. You really don't want that.

Otherwise use the upper bound to estimate reynolds number and the friction factor in the pipe and solve for the flow rate through the system, then iterate until the Reynolds number and friction factor are consistent with the flow rate.

Christopher Wright P.E. |"They couldn't hit an elephant at chrisw@skypoint.com | this distance" (last words of Gen.

.......................................| John Sedgwick, Spotsylvania