but it depends on pressure, not velocity. There is no single “cavitation velocity”.ellenb899 said:
Post the whole question please. Is there a diagram?ellenb899 said:
Do you have a relationship for the total pressure?ellenb899 said:
Please, see:ellenb899 said:
No I donterobz said:
But you have in the relevant equations section "Bernoulli's"?ellenb899 said:
But that is the relevant equation... Imagining a single location of a flow having total pressure ##P_{total} = 30 \rm{hPa}##. The Static Pressure ##P_s## cannot drop below the vapor pressure of the liquid ( i.e. ##P_{static} > P_{vapor}##), or cavitation can occur. Since we are examining at a single location, the elevation ##h## can be taken as the ##0## datum without consequence.ellenb899 said:
Lets take this one step at a time:ellenb899 said:
It's an inequality. We need to end with ##V < \text{something}##. And, that is not one step...ellenb899 said:
Incorrect. There should be nothing on the lefthand side other than the variables ##P_{total}## and ##V##. try again.ellenb899 said:
You have to think a bit here about what things mean. You're just ( rather poorly - without care) throwing variables around...its a waste of time.ellenb899 said:
No. use the equation in post #13... This step needs to look like:ellenb899 said:
The key equations governing cavitation include the Rayleigh-Plesset equation, which describes the dynamics of a spherical gas bubble in a liquid, and Bernoulli's equation, which relates the pressure, velocity, and height in a flowing fluid. The Rayleigh-Plesset equation is given by: \[ R\ddot{R} + \frac{3}{2}\dot{R}^2 = \frac{1}{\rho} \left( p_g - p_\infty - \frac{2\sigma}{R} - 4\mu \frac{\dot{R}}{R} \right) \]where \( R \) is the bubble radius, \( \dot{R} \) and \( \ddot{R} \) are the first and second time derivatives of the radius, \( \rho \) is the liquid density, \( p_g \) is the gas pressure inside the bubble, \( p_\infty \) is the far-field pressure, \( \sigma \) is the surface tension, and \( \mu \) is the liquid viscosity.
Flow speed affects cavitation through its influence on local pressure. According to Bernoulli's principle, as the flow speed increases, the pressure in the fluid decreases. When the local pressure drops below the vapor pressure of the liquid, cavitation occurs, forming vapor bubbles. The relationship can be described by Bernoulli's equation:\[ p + \frac{1}{2}\rho v^2 + \rho gh = \text{constant} \]where \( p \) is the pressure, \( \rho \) is the fluid density, \( v \) is the flow velocity, and \( h \) is the height above a reference point. Higher flow speeds lead to lower pressures, which can induce cavitation if the pressure falls below the vapor pressure.
Delta vapor pressure (ΔP) is the difference between the local pressure in the fluid and the vapor pressure of the liquid. Cavitation occurs when the local pressure drops below the vapor pressure, creating a negative ΔP. Mathematically, it is expressed as:\[ \Delta P = P_{\text{local}} - P_{\text{vapor}} \]When ΔP is negative, vapor bubbles can form, leading to cavitation. Controlling ΔP is crucial in preventing cavitation in various engineering applications.
Cavitation can have several detrimental effects on fluid flow and mechanical components. It can cause significant damage to surfaces through pitting and erosion when