CAVITATION

Overview

The CAVITATION function calculates the Cavitation number (Ca, also denoted σ or σc), a dimensionless parameter used in fluid dynamics to characterize the potential for cavitation in a flowing liquid. Cavitation occurs when local pressure in a fluid drops below the vapor pressure, causing vapor bubbles to form—a phenomenon that can lead to noise, vibration, erosion, and performance degradation in hydraulic systems, pumps, turbines, and valves.

This implementation uses the fluids library, an open-source Python package for fluid mechanics calculations. For detailed documentation, see the fluids.core.Cavitation reference.

The Cavitation number represents the ratio of the pressure margin above vaporization to the inertial (dynamic) pressure of the flow:

\text{Ca} = \sigma = \frac{P - P_{sat}}{\frac{1}{2}\rho V^2}

where P is the local fluid pressure, P_{sat} is the vapor (saturation) pressure, \rho is the fluid density, and V is the fluid velocity. A low Cavitation number indicates that the flow is more susceptible to cavitation, while a high value suggests a greater margin against bubble formation.

Engineers use this dimensionless number to evaluate flow restrictions such as orifices, control valves, and venturi sections. Note that some definitions omit the factor of 2 in the denominator; this implementation follows the standard form used in Perry’s Chemical Engineers’ Handbook and Cengel & Cimbala’s Fluid Mechanics textbook.

This example function is provided as-is without any representation of accuracy.

Excel Usage

=CAVITATION(P, Psat, rho, V)

• P (float, required): Internal pressure in Pascals (Pa)
• Psat (float, required): Vapor pressure in Pascals (Pa)
• rho (float, required): Fluid density in kilograms per cubic meter (kg/m³)
• V (float, required): Fluid velocity in meters per second (m/s)

Returns (float): Cavitation number (float), or error message string.

Examples

Example 1: Demo case 1

Inputs:

P	Psat	rho	V
200000	10000	1000	10

Excel formula:

=CAVITATION(200000, 10000, 1000, 10)

Expected output:

3.8

Example 2: Demo case 2

Inputs:

P	Psat	rho	V
250000	15000	950	20

Excel formula:

=CAVITATION(250000, 15000, 950, 20)

Expected output:

1.237

Example 3: Demo case 3

Inputs:

P	Psat	rho	V
120000	10000	998	8

Excel formula:

=CAVITATION(120000, 10000, 998, 8)

Expected output:

3.444

Example 4: Demo case 4

Inputs:

P	Psat	rho	V
300000	50000	1020	15

Excel formula:

=CAVITATION(300000, 50000, 1020, 15)

Expected output:

2.179

Python Code

import micropip
await micropip.install(["fluids"])
from fluids.core import Cavitation as fluids_cavitation

def cavitation(P, Psat, rho, V):
    """
    Calculate the Cavitation number (Ca) for a flowing fluid.

    See: https://fluids.readthedocs.io/fluids.core.html#fluids.core.Cavitation

    This example function is provided as-is without any representation of accuracy.

    Args:
        P (float): Internal pressure in Pascals (Pa)
        Psat (float): Vapor pressure in Pascals (Pa)
        rho (float): Fluid density in kilograms per cubic meter (kg/m³)
        V (float): Fluid velocity in meters per second (m/s)

    Returns:
        float: Cavitation number (float), or error message string.
    """
    try:
        P = float(P)
        Psat = float(Psat)
        rho = float(rho)
        V = float(V)
    except (ValueError, TypeError):
        return "Error: All parameters must be numeric values."

    if V == 0:
        return "Error: velocity (V) must be nonzero."
    if rho == 0:
        return "Error: density (rho) must be nonzero."

    try:
        result = fluids_cavitation(P, Psat, rho, V)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

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