Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations
Question Statement:
Which of the following statements regarding pipe flow and open channel flow hydraulics is/are CORRECT?
Options:
(A) In laminar pipe flow, the Darcy friction factor $f$ depends only on the Reynolds number ($f = 64/Re$)
(B) The hydraulic grade line (HGL) is always higher than the total energy line (TEL) by the velocity head $\frac{v^2}{2g}$
(C) In an open channel, critical flow occurs when the Froude number $Fr = 1$, representing minimum specific energy for a given discharge
(D) In a hydraulic jump on a horizontal floor, the sequent depth ratio depends solely on the initial Froude number
Answer Key:
A, C, D
Step-by-Step Solution & Explanation
- Statement A is correct: In Hagen-Poiseuille laminar flow, $f = 64/Re$, completely independent of pipe roughness.
- Statement B is incorrect: TEL is the sum of pressure head, elevation head, and velocity head, while HGL is pressure head plus elevation head. Therefore, TEL is always higher than HGL by $\frac{v^2}{2g}$.
- Statement C is correct: At critical state ($Fr = 1$), specific energy $E = y + \frac{Q^2}{2g A^2}$ is minimized for a given discharge $Q$.
- Statement D is correct: By the Bélanger equation for rectangular channels, $\frac{y_2}{y_1} = \frac{1}{2}\left( \sqrt{1 + 8Fr_1^2} - 1 \right)$, which is a function of $Fr_1$ only.