Which law relates to the kinetic, pressure, and potential energy in a fluid flow?

• A. Bernoulli's theorem
• B. Newton's laws
• C. Charles's law
• D. Boyle's law

Answer: (A)

Bernoulli’s principle describes how mechanical energy is distributed in a flowing fluid. It links pressure, kinetic energy, and potential energy along a streamline. The relation is expressed as P + 1/2 ρ v^2 + ρ g z = constant, where P is static pressure, ρ is density, v is flow speed, and z is elevation. The kinetic energy term (1/2 ρ v^2) and the potential energy term (ρ g z) represent energy per unit volume, so when the flow speeds up (v increases) the pressure term must drop to keep the total energy constant, and vice versa. This explains why narrow sections of a pipe have lower pressure and why faster flows can generate lift, as in an airfoil or venturi meter.

This relationship holds along a streamline for steady, incompressible, non-viscous flow. In real systems with viscosity, turbulence, or compressibility, there are losses and deviations, but Bernoulli’s principle captures the essential energy balance. The other laws describe different gas behaviors or force laws and do not directly express how pressure, speed, and height energies trade off in a flowing fluid.