What is the Darcy-Weisbach equation used for in piping networks?

• A. To compute pump head.
• B. To compute minor losses.
• C. To calculate head loss due to friction along a pipe: Δh_f = f (L/D) (V^2/2g).
• D. To estimate gas expansion.

Answer: (C)

The main idea is that this equation quantifies the energy lost as fluid slides along the inside of a pipe due to viscous friction. It gives the head loss, Δh_f, from friction as the flow travels a length L in a pipe of diameter D, with velocity V, using the dimensionless friction factor f: Δh_f = f (L/D) (V^2/2g). This shows how losses grow with longer pipes and higher flow velocity, and how they decrease with a larger diameter. The factor f, called the Darcy friction factor, encapsulates the flow regime and surface roughness; for laminar flow it’s 64/Re, while for turbulent flow it depends on Reynolds number and roughness and is found from charts or correlations.

In practice, this equation isolates the frictional loss along straight pipe segments. Minor losses from fittings, valves, bends, and contractions are not included in this term; those are usually added separately with Δh = K (V^2/2g). Likewise, pump head is not given directly by this formula, but the friction loss it must overcome is one part of the total head requirement; the pump head would need to cover Δh_f plus any minor losses and any elevation changes.

It isn’t about gas expansion or other non-friction phenomena, which is why the Darcy-Weisbach equation is used specifically to calculate the head loss due to friction along a pipe.