Which factors are involved in the Darcy-Weisbach head loss equation?

• A. Volume of fluid
• B. Temperature
• C. Friction factor, length, diameter, velocity, and gravitational acceleration
• D. Density only

Answer: (C)

The head loss in a pipe comes from friction converting some of the fluid’s energy into heat as it flows. The Darcy-Weisbach form for this loss is h_f = f (L/D) (V^2 / (2g)). The factors here are:

• Friction factor f: this dimensionless number encapsulates how rough the pipe is and the flow regime (laminar or turbulent). It determines how strongly friction reduces the energy of the flow.

• Length L and diameter D: the ratio L/D scales the amount of frictional work. Longer pipes increase loss, and smaller diameters raise loss for a given flow because the flow path is constricted, increasing friction per unit length.

• Velocity V and gravitational acceleration g: head loss grows with the square of the flow speed, so doubling velocity increases loss by four. The term V^2/(2g) converts this energy into a head (a height of fluid) using g.

Density and temperature aren’t explicit terms in this equation (though density can appear in related pressure-head relationships or when relating Q to V). The explicit factors that control the head loss are the friction factor, the pipe’s length and diameter, the flow velocity, and gravity.