# How pressure and velocity is related? And its effect in cavitation

As per my knowledge I think when velocity increases and discharge is constant,the fluid(liquid) molecules get away from each other in the region where velocity is high and that's why they get converted into vapor . Am I correct? Please help to clear my confusion regarding cavitation at end of turbine blade.

• What kind of turbine? If a steam turbine, there shouldn't be any cavitation. – David White Mar 6 at 18:50
• Francis turbine – Ravi Pandey Mar 7 at 16:04

## 2 Answers

Cavitation occurs when the flowing liquid's pressure drops below the vapor pressure of that liquid (in this case, water). This happens inside pump and turbine cases when the liquid gets "squeezed" through a reduced cross-sectional area, the velocity increases, and the pressure decreases per the Bernoulli equation.

At the point where the cavitation occurs, very small steam bubbles form. These bubbles typically don't last very long, as they soon encounter a higher pressure fluid region where fluid velocities decrease. When this happens, the bubble collapses violently. If the cavitation bubble collapses on metal surfaces, it will chip away a very small piece of metal and erode the metal in that spot. Continued operation of pumps and turbines in a cavitating condition will destroy equipment.

There are several things to think about in order to either avoid cavitation, or engineer a solution where the cavitation is not destructive.

• If velocities in the turbine can be decreased, the maximum pressure drop inside the turbine will be reduced, and cavitation will be avoided. Obviously, for a Francis turbine, this may not be possible, but if it is, it will result in a reduction in power produced

• If you can increase the upstream pressure on the Francis turbine and keep the water flow through the turbine constant, the pressure throughout the turbine should increase, hopefully to the point where cavitation is eliminated

• If there is a way to introduce water into the Francis turbine that has a lower temperature, cavitation can be eliminated by lowering the vapor pressure of the water to a point that is lower than the lowest pressure that the water experiences as it goes through the turbine

• In some cases, the water flow path can be redirected such that the lowest pressures are encountered inside the water stream. When this happens, cavitation still occurs, but the collapsing vapor bubbles never touch a metal surface, which eliminates equipment damage

• It may be possible to apply a thin coating of a material that has "rubber like" properties. Such a surface would tend to rebound when a cavitation bubble strikes it, rather than "flake off" like a metal does

As a start for investigating cavitation in Francis turbines, see https://caeai.com/resources/analysis-cavitation-inside-francis-turbine.

For a better idea of when cavitation occurs, consult the Antoine equation. This equation calculates the vapor pressure of water at any given temperature, and it will tell you the minimum pressure that the Francis turbine can operate at and still avoid cavitation. See https://en.wikipedia.org/wiki/Antoine_equation

In addition to the above, assuming that your Francis turbine is experiencing turbine blade erosion, you will want to get with the manufacturer and let him know what is happening. Your cavitation problem is undoubtedly not unique, and there are probably solutions to this problem that have already been successfully implemented.

• Thank you for the answer,still I am not satisfied.I want the relation between velocity and pressure at molecular level. My question is what happened at cavitation point how increase in velocity decreases pressure at molecular level.Is at higher velocity water get stretched and molecules get detached and become vapor?? – Ravi Pandey Mar 8 at 8:23
• The molecules don't get "detached" or "stretched". The liquid boils when the pressure goes below the vapor pressure. Are you familiar with the Bernoulli equation? – David White Mar 8 at 16:05
• I am getting what you meant sir,but I want to know how pressure get affected as velocity increases,how inside a liquid as velocity increases pressure decreases.what is behind this? – Ravi Pandey Mar 9 at 10:46
• And if talking about Bernoulli's equation,this question arises from Bernoulli's equation,I understood Bernoulli's but can't feel it that how pressure and velocity are related what happened when velocity increases pressure comes down.Same is happening in Venturi meter cavitation occurs at throat what happened at throat how increase in velocity cause decease in pressure,please explain not mathematically or by Bernoulli's principle. – Ravi Pandey Mar 9 at 17:13
• Pressure is energy per unit volume. The Bernoulli equation accounts for fluid pressure, fluid gravitational potential energy per unit volume, and fluid kinetic energy per unit volume, and it accounts for changes in those variables. This means that the Bernoulli equation involves conservation of energy per unit volume of liquid. As one of the variables in the Bernoulli equation changes, other variables change as well in order to conserve fluid energy. For a constant fluid height, as fluid velocity increases, fluid pressure must decrease. – David White Mar 9 at 17:41

Based on Bernoulli's principle of fluid flow, the pressure experienced by a moving fluid is inversely proportional to it's velocity. What causes that isn't clear, but from my standpoint I think the fluid being being stretched out over more length might have something to do with why there's pressure drop.

• conservation of energy causes a decrease in pressure when velocity increases. – David White Mar 6 at 20:41
• Is there a mathematical expression for that? – TechDroid Mar 6 at 20:43
• @TechDroid The most basic example is Bernoulli's principle; but that's really just energy conservation over different flow conditions. – JMac Mar 6 at 20:53
• TechDroid, the terms in the Bernoulli equation are all equivalent to pressure, and pressure is equivalent to energy per unit volume. Look at the term $1/2 \rho v^2$. This is CLEARLY kinetic energy per unit volume. Thus, the Bernoulli equation represents energy conservation. – David White Mar 7 at 1:10
• The pressure is inversely related to velocity, but isn't inversely proportional to velocity. If it were, zero velocity fluids would have infinite pressure. And answers are for communicating established physics knowledge, not speculation. – Acccumulation Mar 7 at 22:21