[Physics] Maximum liquid velocity in a siphon

bernoulli-equationfluid dynamics

According to wikipedia: Siphon, the velocity of liquid in a siphon is equal to $\sqrt{2gh}$, where h is the difference in level between the water surface and the opening of the siphon.

But it also mentions that there exists a maximum velocity which can be attained; hence the velocity of the liquid coming out of the opening of the siphon cannot be increased beyond a particular limit by merely increasing $h$.

But wouldn't this violate Bernoulli's equation if applied for the water surface and the opening if $h$ is taken beyond the value at which maximum velocity is obtained?

Best Answer

That formula is simplified by

ignoring viscosity
ignoring that $h$ could be greater than what could be supported by atmospheric pressure (about 10 meters in the case of water), at which point the fluid separates.

Related Solutions

[Physics] Application of Bernoulli’s equation to siphon

In this case, it is allowed. As a thought experiment, you can replace the top bucket with the siphon hose by an S-shaped tube that has a gradual change in diameter, like this:

           _
         /   \
|www|   |     |
\www|   |     |
 \ww|   |     |
  \w|   |     |
   \|__/      |
              |
              |

With this type of analysis, it is more important that the downstream side of the tube makes a gradual transition to a large cross section. If you don't, then the kinetic energy of the high-velocity stream will be converted to heat rather than back to a pressure rise. This is not an issue at the upstream (tube inlet) side.

[Physics] Static Pressure in a Venturi vs a Free stream

Pressure reduction in high flow speed regions, by virtue of Bernoulli principle, occurs whether or not the flow is exposed to atmosphere. Bernoulli principle is a consequence of energy conservation in the absence of viscous dissipation, and must hold true wherever the approximation of inviscid flow may be applied.

This last paragraph is really irrelevant to your question I suppose, but I shall retain it here because it tells you another way in which pressure inside a free stream can vary. When a flow is exposed to atmosphere, its pressure becomes atmospheric (neglecting surface tension effects) only if its flow streamlines are straight. If the flow streamlines are curved, then pressure within the flow can be greater or lower than atmospheric pressure, depending on the sign of curvature. If the flow streamlines are convex looking from inside the flow, then pressure would be higher than atmospheric there, and if concave, pressure would be lower than atmospheric there. Significant deviation from atmospheric pressure requires large curvature, which seldom occurs in practice, so people straightaway assume that a flow exposed to atmosphere must have atmospheric pressure within, to a good approximation.

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Related Solutions

[Physics] Application of Bernoulli’s equation to siphon

[Physics] Static Pressure in a Venturi vs a Free stream

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