The Darcy Friction Factor is used when solving the Darcy Weisbach Equation, one of the three commonly used relationships for determining hf due to the flow of fluid through pipes. The resultant friction factor is determined based on what type of flow you're dealing with (by using Reynolds Number) and also what type of pipe you're dealing with.

How to solve for the Darcy Weisbach Friction Factor:

The Generic Term for the Darcy Friction Factor is:

f = f \left(\frac{e}{D} , Re \right)

where:

e = size of surface imperfections
D = diameter of pipe
e/D = relative roughness of the pipe

How to Determine Friction Factor:

Moody Diagram

One way to determine friction factor is to use Moody's Diagram. Pressure drops seen for fully-developed flow of fluids through pipes can be predicted using the Moody diagram which plots the friction factor(f) against Reynolds number (Re) and relative roughness (ε / D). The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases.

Figure 1: Moody Diagram
Figure 1: Moody Diagram (Click to Enlarge)

To use the Moody diagram to find the friction factor, choose the curve for a specific relative roughness. Follow the curve (you'll be starting from the right) and stop when you get directly above the Reynolds Number (shown on the bottom) or direcly below VD (shown on the top and only applicable if the water temperature is 60F). Go straight to the left axis and the value read is the appropriate friction factor.

Tables

Tables are another common method of finding the friction factor. The CERM Appendix 17.B (starting on page A-27) lists friction factors for various Re and e/D.

Equations:

The friction factor can also be determined by equation depending on condition of the flow as shown in the following table:

Table 1: Equations to solve for Darcy's Friction Factor
Type of Flow Range of Application Solving for f
Laminar Re < 2000 f = \frac{64}{Re}
Hydraulically Smooth or Turbulent Smooth 4000 < Re < 100,000 f = \frac{0.316}{Re^{0.25}}
Re > 4000 \frac{1}{\sqrt{f}} = 2log_{10}(Re \sqrt{f} ) - 0.8
Transition between Hydraulically Smooth and Wholly Rough Re > 4000 \frac{1}{\sqrt{f}} = 1.14-2log_{10} \left(\frac{e}{D} + \frac{9.35}{Re\sqrt{f}}\right)
Hydraulically Rough or Turbulent Rough Re > 4000 \frac{1}{\sqrt{f}} = 1.14-2log_{10} \left(\frac{e}{D}\right)

where:

Note: In situations where Re falls between 2100 and 400 (an area between laminar and turbulent flow) eddies will be present which cause critical flow. It is difficult to design for this region since fluid behavior is not consistent.


Swamee-Jain equation:

For fully turbulent flow, the Swamee-Jain equation[1] can be used to solve for the friction factor. The Swamee–Jain equation is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation.

f = 1.325\left(ln \left(\frac{\frac{e}{D}}{3.7} + \frac{5.74}{Re^{0.9}} \right)\right)^{-2}

References:

  1. http://docs.bentley.com/en/HMStormCAD/Bentley_WaterGEMS_Help-10-039.html

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