Introduction

If you want to obtain an Excel spreadsheet to use for pipe flow/friction factor calculation, visit our download page.  Read on for information about the Darcy Weisbach equation and its use in an Excel spreadsheet as a friction factor/pipe flow calculator.

The Darcy Weisbach equation is widely used for pipe flow calculations.  This equation is applicable to pressure flow in pipes, rather than gravity flow, which is handled by open channel flow equations like the Manning equation.  The Darcy Weisbach equation can be used for fully developed, turbulent flow of a gas or liquid.  It provides the relationship among several parameters of interest: pipe diameter and length, frictional head loss or pressure drop, and pipe flow rate.  Any one of these can be calculated if the others are known along with the density and viscosityof the fluid.

The Darcy Weisbach Equation and a Friction Factor Calculator

The Darcy Weisbach equation is h_L = f*(L/D)(V²/2g), where h_L is the frictional head loss for flow of a fluid at average velocity, V, through a pipe of length, L, and diameter, D.  The Reynolds number for the flow and the relative roughness of the pipe (e/D) are needed to get a value for the friction factor, f.  The Moody Diagram at the left shows the general relationship among the friction factor, f, the Reynolds number, Re, and the relative pipe roughness, e/D.

For calculations with an Excel spreadsheet, equations for f as a function of Re and e/D are more convenient than using a graph like the Moody diagram.   A set of equations for friction factor as a function of Re and e/D for four different flow regimes is shown in the boc at the right.  The four different flow regimes appear as different portions of the Moody diagram as follows:

• laminar flow (Re < 2100) - the straight line at the left side of the Moody diagram
• Smooth pipe turbulent flow - the dark curve labeled "smooth pipe' in the Moody diagram - f is a function of Re only in this region
• Completely turbulent region - the portion of the diagram above and to the right of the dashed line labeled "complete turbulence" - f is a function of e/D only in this region
• Transition region - the portion of the diagram betweeen the "smooth pipe" solid line and the "complete turbulence" dashed line - f is a function of both Re and e/D in this region and this is not an explicit equation for f)

 The table at the right shows pipe roughness values for some common pipe materials, for use in calculating the pipe roughness ratio, e/D.

For a low cost Moody friction factor calculator download, that will calculate f for Reynolds number above 2100, visit our download page.

Frictional Head Loss and Frictional Pressure Drop Calculations

 After a value of the friction factor, f, is obtained with the Moody friction factor calculator, it is quite straightforward to calculate frictional head loss and pressure drop, if the pipe length & diameter and average flow velocity are known.  One simply needs to substitute values for L, D, V and f into the Darcy Weisbach equation [ h_L = f(L/D)(V²/2g)  ].  The Darcy Weisbach equation is a dimensionally consistent equation, so any consistent set of units can be used.  For U.S. units,  h_L, L, and D are typically in ft, V is in ft/sec, and g is 32.2   ft/sec² .  For S.I. units,   are typically in m, V is in m/s, and g is 9.81 m/s² .  If volumetric flow rate, Q, is known rather than average velocity, V, then V can be calculated from

Frictional pressure drop can be calculated from frictional head loss, using the equation:

The Excel spreadsheet screenshot below shows a spreadsheet available as part of the "Pipe Flow-Friction Factor Calculations Package,"  from our download page in either U.S. units or S.I. units.  This spreadsheet package has three worksheets: one to calculate frictional head loss and pressure drop for known pipe diameter, length, & material and flow rate; one to calculate flow rate for known head loss or pressure drop, and pipe diameter, length & material; and one to calculate pipe diameter for known head loss or pressure drop, flow rate, and pipe length & material.

 References

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

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

3. Source for pipe roughness values – http://www.efunda.com/formulae/fluids/roughness.cfm

4. Bengtson, H.H., Pipe Flow/Friction Factor Calculations with Excel, an online continuing education course for Professional Engineers

 5. Bengtson, Harlan, "Advantages of Spreadsheets for Pipe Flow/Friction Factor Calculations", Available as an Amazon Kindle e-book and as a paperback.

6. Bengtson, Harlan, Pipe Flow-Friction Factor Calculator Excel Spreadsheet, an online blog article