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  • Submitted: Feb 03 2011 09:18 AM
  • Last Updated: Feb 03 2011 09:18 AM
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Download Darcy-Weisbach Pipe Sizing

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This sheet calculates the pressure drop for liquid flow in a pipe using the Darcy-Weisbach equation. This equation was derived based on water flow and therefore assumes that the fluid density remains constant along the length of the pipe.
dP = f * (L / D) * r * v2 / 2
In the turbulent zone (Re > 3000) friction factor, f, is solved iteratively using the Colebrook-White equation (which represents the familiar Moodey chart):
1 / f 0.5 = -0.86 * Log[ (e/D) / 3.71 + 2.51 / ( Re * f 0.5 ) ]
In the laminar zone (Re <2000) friction factor is solved using the Hagen-Poiseuille equation:
f = 64 / Re
Note that other variations on the general flow equation such as the Weymouth or Panhandle equations are simplifications of the above approach to allow an analytical (non-iterative) solution. These equations are not applicable over the full range of flow conditions/ pipe sizes and were developed prior to personel computers.

Wall thickness
Minimum pipe wall thickness is calculated based on the hoop stress caused by the pressurised fluid in the pipe. Several slightly different equations are in use depending on the service (pipeline or plant process piping) and the standard that you are working to. ISO13623 uses Lame's formula, Sy = (Pint - Pext).(D - t)/(2t.F); ASME B31.4 uses Barlow's equation which is a simplification of Lame's equation, Sy = P.Do/(2t.F); For process piping, ASME B31.3 uses Sy = PDo/(2t.F) - P.F2. Sy is the minimum yield strength at the maximum design temperature, D is the nominal outer diameter, Do is the actual outer diameter and F is a design factor (not exactly the same in each case). The general form of the equation is similar and given that the minimum wall thickness is then translated into a standard wall thickness the end result is likely to be similar.

Based on the minimum wall thickness a standard wall thickness can then be selected from a table of standard pipe sizes (c/- ANSI 36.10). This is done automatically via a lookup to allow quick sensitivities on diameter to be carried out without having to revisit the wall thickness calculation each time. However, if you want to consider a specific wall thickness or pipe schedule then it is also possible to enter an overwrite.

Note 1: The diameter term in Lame's equation (D - t) is correct - ie. it is not (D - 2t). This is because the stress in the pipe wall varies across it's thickness. The average stress occurs at the centre of the pipe wall (ie. D - t).

Note 2: There appears to be no good reason for using the nominal diameter instead of the actual outer diameter other than perhaps convenience.

Note 3: For plastic pipe standard sizes are based on the ratio of diameter to wall thickness so the pressure rating is the same across all sizes (a more useful approach than the schedule numbers in use for steel pipe which are essentially arbitrary and have no relationship to the pressure rating).

Note 4: The wall thickness calculation provided here is sufficient for a preliminary sizing only - other stresses may need to be considered and the relevant code should be refered to for any detailed sizing.

Submitted by yalcin

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