In pipe flow, the average velocity is established as half of the maximum velocity under specific conditions. This relationship can be derived by solving the Navier-Stokes equations in cylindrical coordinates, assuming incompressible flow, linear pressure decrease, finite flow rate, unidirectional flow, and zero velocity at the pipe walls. These assumptions simplify the analysis and lead to the conclusion that the average velocity is indeed half of the maximum velocity. Understanding this derivation is crucial for fluid dynamics applications. The principles outlined are fundamental for engineers and scientists working with pipe flow systems.
