Leak Detection Pressure Drop Calculator
Calculate the expected pressure drop in a pressurized system over time due to a leak, or determine the leak rate from observed pressure loss. Based on the ideal gas law and orifice flow equations.
Formulas Used
1. Ideal Gas Law — Mass of Gas Lost:
Δm = (P₁ − P₂) · V / (R_specific · T)
where R_specific = R / M = 8.314 / M [J/(kg·K)]
2. Average Leak Rate:
Q̇_m = Δm / t [kg/s]
3. Isentropic Orifice Flow — Choked (sonic) when P_atm/P_up ≤ (2/(γ+1))^(γ/(γ−1)):
Q̇_m = Cd · A · P_up · √(γ·M/(R·T)) · (2/(γ+1))^((γ+1)/(2(γ−1)))
4. Isentropic Orifice Flow — Subsonic:
Q̇_m = Cd · A · P_up · √(M/(R·T)) · √[ 2γ/(γ−1) · ((P_d/P_up)^(2/γ) − (P_d/P_up)^((γ+1)/γ)) ]
5. Volumetric Leak Rate at STP (0 °C, 101.325 kPa):
Q̇_v = Q̇_m · R · T_std / (M · P_std)
6. Numerical Simulation (Mode 3):
Euler integration of dP/dt using the orifice equation at each time step, with 10,000 sub-steps for accuracy.
Assumptions & References
- Gas behaves as an ideal gas (PV = nRT) throughout the test.
- Temperature is constant during the test (isothermal process).
- The leak is modelled as a sharp-edged orifice with a discharge coefficient Cd = 0.61 (default, per ISO 5167).
- Choked (sonic) flow occurs when the downstream-to-upstream pressure ratio ≤ (2/(γ+1))^(γ/(γ−1)) — approximately 0.528 for air (γ = 1.4).
- Atmospheric pressure is the downstream (back) pressure for the leak.
- STP conditions: 0 °C (273.15 K) and 101.325 kPa.
- Numerical simulation uses 10,000 Euler steps for pressure-decay integration.
- References: ISO 5167 (orifice flow), ASME PTC 19.3, ISO 20485 (leak testing), Perry's Chemical Engineers' Handbook.