Pipe Leak Flow Rate Calculator
Estimate the volumetric flow rate of fluid leaking through a pipe crack or hole using the orifice (Torricelli-based) flow equation.
Typical values: 0.61 (sharp-edged hole), 0.80 (rounded edge), 0.98 (short nozzle)
Cross-sectional area of the crack or hole
Pressure difference between pipe interior and atmosphere
Water ≈ 1000 kg/m³ | Oil ≈ 850–900 kg/m³ | Air ≈ 1.225 kg/m³
Formula
Orifice / Torricelli Flow Equation:
Q = Cd · A · √(2 · ΔP / ρ)
- Q — Volumetric flow rate (m³/s)
- Cd — Discharge coefficient (dimensionless)
- A — Leak opening area (m²)
- ΔP — Gauge pressure differential (Pa)
- ρ — Fluid density (kg/m³)
The term √(2ΔP/ρ) is the theoretical fluid velocity at the orifice (Torricelli's theorem extended to pressurised flow). Cd accounts for vena contracta and viscous losses.
Assumptions & References
- Steady, incompressible, single-phase flow through the leak opening.
- The leak behaves as a sharp-edged orifice; Cd = 0.61 is the standard default (ISO 5167).
- Gauge pressure (pipe internal pressure minus atmospheric) drives the leak — atmospheric back-pressure is assumed.
- Fluid density is treated as constant (valid for liquids; use with caution for compressible gases at high ΔP).
- Gravitational head contribution is neglected (conservative for horizontal pipes; add ρgh to ΔP for vertical cases).
- References: ISO 5167-1:2003 (Measurement of fluid flow by orifice plates); Munson, Young & Okiishi, Fundamentals of Fluid Mechanics, 8th ed.; Crane Technical Paper 410.