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Flying circus of physics

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Circular water-flow pattern in a sink

When a smoothly flowing water stream from a faucet hits a flat sink with an open drain, why does a circle form around the impact point, with deeper water on the outside of the circle?

Answer 
When the water from a faucet hits the sink, it spreads radially at a rate that is said to be supercritical because the water moves faster than waves can move over the water. Initially, the flow is stable because any chance disturbance is quickly eliminated. However, as the water spreads outward, the effects of the water’s viscosity become important and the flow becomes unstable. In one description, the viscous flow begins along the sink surface and then gradually extends upward. At a certain radius from the impact point, the viscous flow reaches the surface and the water depth suddenly increases, an effect known as a hydraulic jump. Beyond this wall, the water speed is slower (subcritical). Thus the hydraulic jump is the transition from faster, shallower flow to slower, deeper flow.    

Hydraulic jumps often appear on many common streams, such as where water flows down a driveway, along a curb, through underground drainage pipes, and along tilted irrigation cannels. Look for a stationary wave on the flow, especially where an obstacle lies in the flow. Waves are created as the water flows over or past the obstacle. Most of those waves merely lose their energy and disappear but one wave, with a particular wavelength, moves up the stream as fast as the water moves down the stream, and so the wave is stationary. The continuous disturbance of the water by the obstacle continuously feeds energy into the wave, allowing it to persist. You might see a stationary series of crests and valleys instead of a single wall as you do in a sink. Hydraulic jumps on fast moving streams can be a serious (or even fatal) problem for white-water rafting, because a raft can become trapped at the jump and over turned by the turbulence.

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