Short Answer:

The cavitation number is a dimensionless number used in fluid mechanics to indicate the likelihood of cavitation occurring in a fluid system. It compares the difference between local pressure and vapor pressure to the dynamic pressure of the fluid.

A low cavitation number means the fluid is close to vaporizing, so the risk of cavitation is high. A high cavitation number means cavitation is unlikely. This number helps engineers assess and design pumps, turbines, and valves to avoid cavitation damage in hydraulic systems.

Detailed Explanation:

Significance of Cavitation Number

The cavitation number (σ) is an important parameter used to predict and analyze cavitation in various hydraulic machines and fluid flow systems. It provides a measure of how close the local fluid pressure is to the vapor pressure of the liquid, which determines whether vapor bubbles will form and collapse — the key condition for cavitation.

The cavitation number is calculated using the formula:

σ = (P – Pv) / (½ × ρ × V²)

Where:

• σ = Cavitation number
• P = Local or reference pressure (usually at pump inlet or flow location)
• Pv = Vapor pressure of the fluid
• ρ = Density of the fluid
• V = Flow velocity

This formula shows the ratio of the pressure difference (between actual pressure and vapor pressure) to the dynamic pressure of the flow.

Why Cavitation Number is Significant

1. Predicting Cavitation Risk

The cavitation number helps identify the risk of cavitation in a system.

• If σ is small, it means the local pressure is close to vapor pressure — high chance of cavitation.
• If σ is large, the pressure is much higher than vapor pressure — low chance of cavitation.

This makes the cavitation number a useful early indicator for engineers to take preventive actions.

2. Designing Hydraulic Machines

In pumps, turbines, propellers, and other devices, the cavitation number is used during design to ensure the system operates safely.

• Designers aim to maintain a minimum required cavitation number to avoid bubble formation.
• The shape and position of components (like impeller blades or nozzles) are adjusted based on expected σ values.

3. Testing and Performance Evaluation

Cavitation number is used in laboratory and field testing to evaluate performance under different operating conditions.

• It helps compare results from scaled models with actual machines by ensuring similarity in cavitation behavior.

4. Similitude and Model Studies

In fluid model testing, such as testing turbines or propellers in labs, the cavitation number must be the same for the model and prototype to ensure accurate results.

• This ensures cavitation effects observed in small-scale models match those in real-world equipment.

Effects of Varying Cavitation Number

• Low Cavitation Number (σ < 1):
  High risk of cavitation. Vapor bubbles likely to form, causing noise, erosion, and efficiency loss.
• High Cavitation Number (σ > 1):
  Safe operation. Pressure is well above vapor pressure. No risk of bubble formation.

The goal in design is to keep the cavitation number above a critical value based on the type of machine and fluid conditions.

Conclusion:

The cavitation number is a crucial indicator used to determine the possibility of cavitation in fluid systems. By comparing local pressure, vapor pressure, and flow velocity, it helps engineers predict, avoid, and control cavitation. Maintaining a safe cavitation number is essential for the reliable and long-term operation of pumps, turbines, and other hydraulic equipment.