Which of the following equations is/are used in deriving equations for the hydraulic jump in a rectangular channel in terms of the conjugate depths and initial Froude number? i. continuity equation ii. momentum equation iii. energy equation
- AOnly (i)
- BOnly (i) and (ii)Correct
- COnly (ii) and (iii)
- D(i), (ii) and (iii)
Solution
Concept
Governing equations for hydraulic jump analysis
Formula
NONE
Step-by-step solution
1. The analysis of hydraulic jump in open channels applies continuity and momentum equations to derive relations for conjugate depths and initial Froude number. 3. Therefore, option D is selected. Answer: B
Explanation
Due to significant energy dissipation in a hydraulic jump, the energy equation cannot be directly applied across it. Instead, the continuity equation and momentum principle are used to derive relationships between conjugate depths and Froude number. Therefore, option B is correct.
Why the other options are wrong
A) Momentum and energy equations are also required to derive hydraulic jump parameters. C) The continuity equation is essential to relate flow velocities and channel depths.
Shortcut
Hydraulic jump derivations use Continuity and Momentum equations (Energy is lost in the jump).
Common mistake
Selecting option D by incorrectly including the energy equation, ignoring the head loss across a hydraulic jump.
Correct answer: B) Only (i) and (ii)