免费水跃计算器
计算明渠水跃的共轭深度和能量损失。
Upstream Froude Number
2.2580
Upstream Froude Number vs Upstream Depth (y1)
公式
## 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.
计算示例
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
常见问题
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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