What principle establishes the equivalence of flow rate and velocity in pipe flow?

The continuity principle is fundamental in fluid mechanics and establishes the relationship between flow rate and velocity in pipe flow. This principle states that for an incompressible, steady flow of fluid, the mass flow rate must remain constant from one cross-sectional area of a pipe to another. Mathematically, it can be expressed as the product of the cross-sectional area of the pipe and the fluid velocity at that cross-section, which must remain constant along the flow path.

When a fluid flows through a pipe that has varying diameters, the continuity principle indicates that if the diameter decreases, the velocity of the fluid must increase to maintain the same flow rate, and vice versa. This principle is crucial for understanding how fluids behave in confined systems, such as piping networks in hydraulic systems.

The other principles, while important in the study of fluids, apply to different concepts. The Bernoulli principle relates pressure, velocity, and elevation in fluid flow but does not directly establish a direct relationship between flow rate and velocity. The Pascal principle focuses on the transmission of pressure in incompressible fluids, and the Archimedes principle relates to buoyancy and the forces experienced by objects submerged in fluids. Therefore, the continuity principle is the key concept that accurately describes the equivalence of