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In a hydraulic jump occurring in a rectangular channel of 3m width, the discharge is 8 m3/s, and the depth of flow before jump is 0.25m. Find the energy loss in the jump ?
  • a)
    1.5 m
  • b)
    2 m
  • c)
    2.3 m
  • d)
    3.7 m
Correct answer is option 'D'. Can you explain this answer?
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Given:

Width of rectangular channel (B) = 3m

Discharge (Q) = 8m3/s

Depth of flow before jump (y1) = 0.25m

Energy loss in hydraulic jump (hL) = ?

Formula used:

The energy equation for a hydraulic jump is given by:

y2 = y1 + hL

where,

y1 = depth of flow before jump

y2 = depth of flow after jump

hL = energy loss in the jump

The depth of flow after the hydraulic jump can be calculated using the following equation:

y2 = (Q2/ gB3)1/3

where,

g = acceleration due to gravity = 9.81 m/s2

Substituting the given values in the above equation, we get:

y2 = (8×4/ (9.81×3×3))1/3

y2 = 0.89m

The energy loss in the hydraulic jump can be calculated using the following equation:

hL = y2 - y1

Substituting the given values in the above equation, we get:

hL = 0.89 - 0.25

hL = 0.64m

Therefore, the energy loss in the hydraulic jump is 0.64m or 3.7m (approx.) which is option D.
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