In a hydraulic jump occurring in a horizontal rectangular channel, the sequent depths are 0.25 m and 1.25 m. The energy loss in this jump is:
- A1.25 m
- B1.5 m
- C1 m
- D0.80 mCorrect
Solution
Concept
Energy loss in a hydraulic jump in a horizontal rectangular channel depends only on the two sequent depths.
Formula
EL = (y2 - y1)3 / (4 y1 y2)
Step-by-step solution
1. Given y1 = 0.25 m and y2 = 1.25 m. 2. y2 - y1 = 1.25 - 0.25 = 1.0 m. 3. (y2 - y1)3 = 1.03 = 1.0 m³. 4. 4 y1 y2 = 4 × 0.25 × 1.25 = 1.25 m². 5. EL = 1.0 / 1.25 = 0.80 m.
Explanation
In a hydraulic jump, some energy is lost in eddies and turbulence. For a horizontal rectangular channel, this loss is (y2 - y1)3 / (4 y1 y2). With the given depths, the loss is 0.80 m.
Why the other options are wrong
A: 1.25 m is just y2, not the loss. B: 1.5 m is y1 + y2, which has no meaning here. C: 1 m is y2 - y1, the jump height, not the energy loss.
Shortcut
Find (y2 - y1) first; if it is 1, then EL = 1/(4 y1 y2).
Common mistake
Taking the height of the jump (y2 - y1) as the energy loss.
Correct answer: D) 0.80 m