In the Darcy-Weisbach equation h_f = f (L/D) (V^2/(2g)), h_f is proportional to which combination?

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Multiple Choice

In the Darcy-Weisbach equation h_f = f (L/D) (V^2/(2g)), h_f is proportional to which combination?

Explanation:
The head loss from friction scales with the combination f (L/D) V^2 because the equation is h_f = f (L/D) (V^2/(2g)). The factor 1/(2g) is just a constant, so the essential proportional part is f (L/D) V^2. Friction factor and the length-to-diameter ratio are dimensionless, so the velocity term appears as V^2, not V or V^3. The option with f squared would wrongly imply a squared friction factor, which isn’t part of the formula.

The head loss from friction scales with the combination f (L/D) V^2 because the equation is h_f = f (L/D) (V^2/(2g)). The factor 1/(2g) is just a constant, so the essential proportional part is f (L/D) V^2. Friction factor and the length-to-diameter ratio are dimensionless, so the velocity term appears as V^2, not V or V^3. The option with f squared would wrongly imply a squared friction factor, which isn’t part of the formula.

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