Head loss due to friction is proportional to velocity squared in which regime?

Head loss due to friction is proportional to velocity squared in which regime?

• A. Laminar flow
• B. Transitional flow
• C. Turbulent flow
• D. Non-Newtonian flow

Answer: (C)

In pipe flow, the way friction losses scale with flow velocity depends on the flow regime. For fully developed laminar flow, the pressure drop along a length is governed by Poiseuille’s law and is proportional to velocity, so head loss increases linearly with speed. In contrast, when the flow is turbulent, the frictional energy dissipation behaves such that the head loss follows the Darcy–Weisbach form hf = f (L/D)(V^2/2g). For a given pipe and roughness, the friction factor f stays roughly constant as velocity changes, so the head loss rises with the square of the velocity. This quadratic relationship is a hallmark of turbulent regimes. Transitional flow doesn’t follow a clean square-law, and non-Newtonian fluids introduce variations because viscosity depends on the shear rate. So the regime where head loss due to friction is proportional to velocity squared is turbulent flow.

In pipe flow, the way friction losses scale with flow velocity depends on the flow regime. For fully developed laminar flow, the pressure drop along a length is governed by Poiseuille’s law and is proportional to velocity, so head loss increases linearly with speed. In contrast, when the flow is turbulent, the frictional energy dissipation behaves such that the head loss follows the Darcy–Weisbach form hf = f (L/D)(V^2/2g). For a given pipe and roughness, the friction factor f stays roughly constant as velocity changes, so the head loss rises with the square of the velocity. This quadratic relationship is a hallmark of turbulent regimes. Transitional flow doesn’t follow a clean square-law, and non-Newtonian fluids introduce variations because viscosity depends on the shear rate. So the regime where head loss due to friction is proportional to velocity squared is turbulent flow.