In which flow regime is friction head loss proportional to velocity rather than velocity squared?

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Study for the PE Environmental Qualitative Exam. Practice with flashcards and multiple choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

In which flow regime is friction head loss proportional to velocity rather than velocity squared?

Explanation:
In laminar pipe flow, friction head loss grows linearly with velocity. This happens because the Darcy friction factor is f = 64/Re, and Re = ρ v D / μ. Substituting into h_f = f L v^2 /(2 g D) yields h_f ∝ v, since the 1/v from f cancels one of the v's in v^2. In turbulent flow, the friction factor is roughly constant for a given roughness, so head loss scales with v^2. Non-Newtonian fluids can change the relationship depending on shear, and pipe smoothness mainly affects pressure loss in the turbulent regime. So the linear relationship is a hallmark of laminar flow.

In laminar pipe flow, friction head loss grows linearly with velocity. This happens because the Darcy friction factor is f = 64/Re, and Re = ρ v D / μ. Substituting into h_f = f L v^2 /(2 g D) yields h_f ∝ v, since the 1/v from f cancels one of the v's in v^2. In turbulent flow, the friction factor is roughly constant for a given roughness, so head loss scales with v^2. Non-Newtonian fluids can change the relationship depending on shear, and pipe smoothness mainly affects pressure loss in the turbulent regime. So the linear relationship is a hallmark of laminar flow.

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