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Robin | Mechanical Engineer
Robin | Mechanical Engineer

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Pressure Decay Leak Rate Calculation with Temperature Compensation — Implementation Guide

#engineering #python #testing #aerospace

Pressure decay is the standard method for leak testing sealed pneumatic assemblies. Getting accurate leak rate figures requires more than just watching a pressure gauge fall — you need temperature compensation, correct volume calculation, and proper units conversion.

The Physics

Pressure decay in a sealed volume with a small leak follows:

dP/dt = -Q_leak × P_atm / V_system
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Where Q_leak is volumetric leak rate (cc/s at atmospheric), P_atm is atmospheric pressure, V_system is system volume.

But temperature changes cause pressure changes too (ideal gas: PV = nRT). A temperature rise of just 0.1°C in a 350 bar system causes a pressure increase of ~0.3 bar — easily masking a small leak.

Temperature-Compensated Leak Rate 

import numpy as np

def temp_compensated_leak_rate(
    pressure_bar,      # array: pressure measurements in bar absolute
    temp_kelvin,       # array: temperature measurements in K
    time_s,            # array: timestamps in seconds
    system_volume_cc,  # total sealed volume in cc
    p_atm_bar=1.01325  # atmospheric pressure
):
    """
    Calculate leak rate in standard cc/min (sccm) with temperature compensation.
    """
    # Compensate pressure for temperature changes using ideal gas law
    # P_corrected = P_measured × (T_reference / T_measured)
    T_ref = temp_kelvin[0]  # Use initial temperature as reference
    P_corrected = pressure_bar * (T_ref / temp_kelvin)

    # Fit linear trend to corrected pressure vs time
    # Slope = dP/dt (bar/s)
    coeffs = np.polyfit(time_s, P_corrected, 1)
    dP_dt = coeffs[0]  # bar/s (negative = pressure falling = leak present)

    # Convert to volumetric leak rate at atmospheric conditions
    # Q_leak (cc/s at atm) = |dP/dt| × V_system / P_atm
    leak_rate_cc_per_s = abs(dP_dt) * system_volume_cc / p_atm_bar
    leak_rate_sccm = leak_rate_cc_per_s * 60  # convert to per minute

    return leak_rate_sccm, dP_dt

# Example usage:
# pressure = np.array([350.00, 349.97, 349.94, ...])  # bar abs
# temp = np.array([293.15, 293.18, 293.20, ...])  # Kelvin
# time = np.array([0, 10, 20, ...])  # seconds
# volume = 250  # cc
# rate, slope = temp_compensated_leak_rate(pressure, temp, time, volume)
# print(f"Leak rate: {rate:.2f} sccm")
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Typical Aerospace Leak Specifications

System Max Leak Rate Standard
Aircraft oxygen system 1 sccm MIL-PRF-27210
Pneumatic brake line 5 sccm OEM specification
Missile actuation 2 sccm MIL-PRF-27422
Aircraft tyre valve 10 sccm ASME

Test Duration for Statistical Confidence

For very small leak rates, longer test duration improves detection confidence:

def min_test_duration(target_rate_sccm, volume_cc, resolution_bar=0.001):
    """
    Calculate minimum test time to detect a target leak rate
    given pressure measurement resolution.
    """
    # Minimum detectable dP/dt based on sensor resolution
    # Need at least 3× resolution change to distinguish from noise
    min_detectable_dP_dt = 3 * resolution_bar / 60  # bar/s

    # Required dP for target leak rate
    required_dP_dt = target_rate_sccm * 1.01325 / (volume_cc * 60)

    if required_dP_dt < min_detectable_dP_dt:
        # Need to wait for enough pressure change to be statistically significant
        min_time = (10 * resolution_bar) / required_dP_dt
        return min_time
    else:
        return 60  # 60 seconds sufficient for detectable rates
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Neometrix High Pressure Air Test Systems implement this compensation and calculation in the PLC for real-time leak rate display and automated pass/fail.
→ https://neometrixgroup.com/products/high-pressure-air-test-system

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