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# Science Fair Project Encyclopedia

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# Hydraulic jump

In the animation, you can see a hydraulic jump appear on the downstream side of the sill. The water flows from the left to the right, and just over the sill, the flow velocity of the water exceeds the celerity with which a wave would move. The standing wave that can be seen on the right side of the sill would want to move in an upward direction, but the high flow velocities do not allow that. Thus, the 'wave' will remain standing there for some time. Only after the discharge is decreased, the flow celerities decrease, and the wave is allowed to splash against the sill. The animation was made using the simulation program from http://www.sobek.nl.

A hydraulic jump is a phenomenon from the science of hydraulics.

A hydraulic jump represents a wave that desires to move in upstream direction, but which it is unable to do, as the flow velocity of the water is larger than the wave's celerity (the speed of individual waves). A hydraulic jump can be recognised as a waterlevel that becomes larger in downstream direction. Tidal bores are a formed in this manner, and can be thought of as a moving hydraulic jump.

A hydraulic jump marks the border between supercritical and subcritical flow.

The wave celerity in shallow water is given by:

• $c = \sqrt{gd}\sqrt{\frac{\tanh{(kd)}}{kd}}$ which is similar to $\sqrt{gd}$ for small d;

In which:

• c = wave celerity (m/s)
• g = gravitational acceleration (9.81 m/s²)
• d = water depth (m)
• $k = \frac{2\pi}{\lambda}$ wave number

A daily example of a hydraulic jump can be seen when brushing your teeth: in the sink. Around the place where the tap water hits the sink, you will see a smooth looking flow pattern. A little further away, you will see a sudden 'jump' in the water level. This too, is a hydraulic jump.