# Darcy Friction Factor

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Darcy friction factor, abbreviated as f, a dimensionless number, used in fluid mechanics to characterize the level of friction or resistance to flow in a pipe or conduit.  The Darcy friction factor is commonly used in fluid mechanics to calculate the pressure drop or head loss that occurs due to the friction between the fluid and the walls of a pipe or channel.  It's particularly important in determining the flow of fluids through pipes, tubes, or other conduits, and it is essential for designing and analyzing piping systems, water distribution networks, and various types of fluid transportation systems.

The Darcy friction factor depends on several factors, including the Reynolds number, the roughness of the pipe's inner surface, and the geometry of the pipe.  It is often used in the Darcy-Weisbach equation, which relates the pressure drop or head loss to the flow rate, pipe diameter, fluid properties, and the Darcy friction factor.

Calculating the Darcy friction factor can involve complex equations, especially for turbulent flows.  For laminar flows, the Darcy friction factor is straightforward and can be directly calculated based on the Hagen-Poiseuille equation.  However, for turbulent flows, the calculation often requires the use of empirical correlations, charts, or numerical methods due to the nonlinear and complex nature of turbulent fluid dynamics.

In turbulent flow, the Darcy friction factor can be determined using the Colebrook equation or other empirical relationships based on experimental data. The choice of method for calculating the friction factor depends on the flow conditions and the available information about the system.

### Darcy friction factor formula

$$f \;=\; 2 \; h_l \; d \; g \;/\; l \; v^2$$     (Darcy friction factor)

$$h_l \;=\; f \; l \; v^2 \;/\; 2 \; d \; g$$

$$d \;=\; f \; l \; v^2 \;/\; 2 \; h \; g$$

$$g \;=\; f \; l \; v^2 \;/\; 2 \; h \; d$$

$$l \;=\; 2 \; h_l \; d \; g \;/\; f \; v^2$$

$$v \;=\; \sqrt{ 2 \; h_l \; d \; g \;/\; f \; l }$$

Symbol English Metric
$$f$$ = Darcy friction factor $$dimensionless$$
$$h_l$$ = head loss $$ft$$ $$m$$
$$d$$ = pipe inside diameter $$in$$ $$mm$$
$$g$$ = gravitational acceleration $$ft \;/\; sec^2$$ $$m \;/\; s^2$$
$$l$$ = lenght of the pipe $$ft$$ $$m$$
$$v$$ = velocity of the fluid $$ft \;/\; sec$$  $$m \;/\; s$$