written by: Harlan Bengtson • edited by: Lamar Stonecypher • updated: 10/11/2010

Calculation of frictional head loss or pressure drop for pipe flow, using the Darcy Weisbach/ friction factor equation, can be done with downloadable Excel spreadsheet templates given in this article. A template is also given for calculation of pipe diameter needed for given flow rate and head loss.

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Darcy Weisbach equation/pipe flow calculations like head loss, pressure drop, or required pipe diameter, using Excel spreadsheet templates, are illustrated in this article. The Darcy Weisbach equation [ hL = f (L/D)(V2/2g) ] gives a relationship among pipe length and diameter (L and D); average velocity in the pipe (V); frictional head loss (hL); and friction factor (f), where the friction factor is, in general, a function of Reynolds number (Re) and the ratio of pipe roughness to pipe diameter (ε/D). More details about the Darcy Weisbach equation and the variable listed here are available in the article, "Pipe Flow Calculations 3: The Friction Factor and Frictional Head Loss." The friction factor, f, may be determined with the use of a graph or from equations. The graph and equations for f are given in the article just mentioned. Also the equations that will be used for f in these Excel spreadsheet templates are given later in this article.

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### Calculation of Frictional Head Loss or Pressure Drop

The Excel spreadsheet template shown in the image at the left is set up to calculate the frictional head loss and pressure drop for a specified volumetric flow rate in a pipe of known diameter, length, and roughness. Also, the fluid density and viscosity need to be known. (Clicking on the image will enlarge it so it can be read.) The table at the right gives typical pipe roughness values for use with the Darcy Weisbach equation.

The calculations in this example spreadsheet proceed in three steps, after the needed data has been input. The first step is calculating the friction factor, f, using the equation for 'completely turbulent flow,' f = 1.14 + 2log10(D/ε)-2. The second step is an iterative calculation with the more general equation for friction factor: f = {-2log10[((ε/D)/3.7) + (2.51/(Re*(f1/2))]}-2, which gives f as a function of both ε/D and Reynolds number, to zero in on a better estimate for f. The third step, calculating frictional head loss and frictional pressure drop is quite straightforward after the value of f is determined.

The example spreadsheet in the image uses U.S. units, but both U.S. and S.I. versions can be downloaded below.

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### Calculation of Required Pipe Diameter

The Excel spreadsheet template shown in this section will calculate the pipe diameter needed to carry a specified flow rate of fluid with  known density and viscosity, with a specified maximum head loss. The same iterative procedure is used to calculate the friction factor, f, however an assumed value of pipe diameter, D, is needed to start the process, because a value for D is needed to determine a value for f. After a value for f is found using the assumed D, then another set of iterative calculations are needed to find the required minimum pipe diameter, D.

As noted on the Excel spreadsheet template, the iterative calculation for D, doesn't converge very smoothly. The best way to proceed with it is to try standard pipe diameters until you find the smallest standard diameter for which the calculated required diameter is less than the assumed value.

U.S. standard pipe diameters for most types of pipe material are as follows (in inches):

1/2, 3/4, 1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 54, 60, (then 6" increments up to 180")

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### Summary

The Excel spreadsheet templates presented and discussed in this article can be used to calculate frictional head loss and pressure drop for a given pipe flow rate, pipe diameter and length, and fluid density and viscosity, or to calculate the required minimum pipe diameter to carry a specified pipe flow rate at a given maximum head loss, with known pipe length and fluid density and viscosity. In both cases an iterative calculation is used to find a value of the friction factor, which is a function of both Reynolds number and the ratio of pipe roughness to pipe diameter.

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### References

1. Source for pipe roughness values - http://www.efunda.com/formulae/fluids/roughness.cfm

2. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

3. Darcy Weisbach equation history - http://biosystems.okstate.edu/darcy/DarcyWeisbach/Darcy-WeisbachHistory.htm

#### Pipe Flow Calculations

Pipe flow calculations include using Reynolds number to find if the flow is laminar flow or turbulent flow. Frictional head loss can be found using the Darcy Weisbach equation and the friction factor. The entrance length for fully developed flow can be found for turbulent flow and for laminar flow.