Hydraulic Jump Calculator
Calculate the downstream depth after a hydraulic jump: y2 = (y1/2) * (sqrt(1 + 8*Fr1^2) - 1), where Fr1 is the upstream Froude number.
Upstream Froude Number
2.2580
Upstream Froude Number vs Upstream Depth (y1)
सूत्र
## Hydraulic Jump A hydraulic jump occurs when supercritical flow (fast, shallow) abruptly transitions to subcritical flow (slow, deep). ### Downstream Depth **y2 = (y1/2) * [sqrt(1 + 8 Fr1^2) - 1]** where Fr1 = v1 / sqrt(g y1) is the upstream Froude number (must be > 1 for a jump to occur). Energy is dissipated in the turbulent roller, making hydraulic jumps useful for energy dissipation in spillways.
हल किया गया उदाहरण
y1 = 0.5 m, v1 = 5 m/s.
- 01Fr1 = 5 / sqrt(9.807 * 0.5) = 5 / 2.214 = 2.259
- 02y2 = (0.5/2) * (sqrt(1 + 8*5.103) - 1)
- 03y2 = 0.25 * (sqrt(41.82) - 1)
- 04y2 = 0.25 * (6.467 - 1) = 1.367 m
अक्सर पूछे जाने वाले प्रश्न
Where do hydraulic jumps occur in nature?
At the base of dams and spillways, in tidal bores (like the Severn Bore), and when a fast stream enters a deeper, slower pool.
Can a hydraulic jump be used to mix fluids?
Yes. The intense turbulence in the jump is excellent for mixing, aeration, and chemical treatment in wastewater facilities.
What happens to the energy?
Kinetic energy is converted to turbulent mixing and heat. The energy loss increases with the Froude number.
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