To calculate the volumetric flow of a fluid driven by a piston in a cylinder, the Hagen-Poiseuille equation is a relevant consideration, particularly for laminar flow scenarios. The discussion highlights the importance of continuity and momentum equations, emphasizing the balance of forces acting on the fluid. For duct flow, the continuity equation indicates that the velocity gradient in the y-direction is zero, while the momentum equation incorporates gravitational forces and pressure gradients. In the context of a circular pipe, the continuity equation shows that the axial velocity is constant, and the momentum equation addresses the effects of pressure and viscous forces. Understanding these equations is crucial for accurately determining fluid flow in various geometries.
