P_CRITICAL_FLOW

Overview

Calculate critical flow pressure for a fluid at Mach 1.

Excel Usage

=P_CRITICAL_FLOW(p_stag, k_isentropic)

• p_stag (float, required): Stagnation pressure of a fluid with Ma=1 [Pa]
• k_isentropic (float, required): Isentropic exponent [-]

Returns (float): Critical flow pressure at Ma=1 [Pa]

Examples

Example 1: Textbook example (P=1.4MPa, k=1.289)

Inputs:

p_stag	k_isentropic
1400000	1.289

Excel formula:

=P_CRITICAL_FLOW(1400000, 1.289)

Expected output:

766812.9022792266

Example 2: Air at standard conditions (k=1.4)

Inputs:

p_stag	k_isentropic
500000	1.4

Excel formula:

=P_CRITICAL_FLOW(500000, 1.4)

Expected output:

264140.8938585871

Example 3: High pressure nozzle

Inputs:

p_stag	k_isentropic
5000000	1.3

Excel formula:

=P_CRITICAL_FLOW(5000000, 1.3)

Expected output:

2728638.6690703253

Example 4: Steam conditions (k=1.135)

Inputs:

p_stag	k_isentropic
1000000	1.135

Excel formula:

=P_CRITICAL_FLOW(1000000, 1.135)

Expected output:

577430.4000110733

Python Code

import micropip
await micropip.install(["fluids"])
from fluids.compressible import P_critical_flow as fluids_p_crit

def p_critical_flow(p_stag, k_isentropic):
    """
    Calculate critical flow pressure for a fluid at Mach 1.

    See: https://fluids.readthedocs.io/fluids.compressible.html#fluids.compressible.P_critical_flow

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

    Args:
        p_stag (float): Stagnation pressure of a fluid with Ma=1 [Pa]
        k_isentropic (float): Isentropic exponent [-]

    Returns:
        float: Critical flow pressure at Ma=1 [Pa]
    """
    # Validate and convert inputs
    try:
        p_stag = float(p_stag)
    except (ValueError, TypeError):
        return "Invalid input: p_stag must be a number."

    try:
        k_isentropic = float(k_isentropic)
    except (ValueError, TypeError):
        return "Invalid input: k_isentropic must be a number."

    # Validation
    if p_stag <= 0:
        return "Invalid input: p_stag must be positive."
    if k_isentropic <= 1:
        return "Invalid input: k_isentropic must be greater than 1."

    try:
        result = fluids_p_crit(P=p_stag, k=k_isentropic)
        return float(result)
    except Exception as e:
        return f"Error: Failed to compute critical flow pressure: {str(e)}"

Online Calculator