In closed pipe flow, which equation is primarily used?

In closed pipe flow, the Darcy-Weisbach Equation is primarily used because it quantifies the head loss due to friction along a given length of pipe caused by the viscous nature of the fluid. This equation takes into account factors like pipe length, diameter, flow velocity, and the friction factor, which is a function of the flow regime (laminar or turbulent) and the roughness of the pipe's interior surface.

While the Hazen-Williams Equation is indeed a practical formula used for estimating pressure losses in water flow through pipes, it is specifically formulated for water and assumes a turbulent flow regime, which limits its applicability. Manning's Equation is generally used for open channel flow, and the Continuity Equation is fundamental in analyzing fluid dynamics but does not directly address the losses associated with flow in a closed pipeline system.