Pipe Leak Flow Rate Calculator
ANA›Life Services Authority›National Calculator Authority›Pipe Leak Flow Rate Calculator
.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
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.
Discharge Coefficient (Cd)
Typical values: 0.61 (sharp-edged hole), 0.80 (rounded edge), 0.98 (short nozzle)
Leak Opening Area (mm²)
Cross-sectional area of the crack or hole
Internal Gauge Pressure (kPa)
Pressure difference between pipe interior and atmosphere
Fluid Density (kg/m³)
Water ≈ 1000 kg/m³ | Oil ≈ 850–900 kg/m³ | Air ≈ 1.225 kg/m³
Calculate
function pipCalc() { const resultDiv = document.getElementById('pip-result');
const Cd = parseFloat(document.getElementById('pip-cd').value); const areaMm2 = parseFloat(document.getElementById('pip-area').value); const pressKPa = parseFloat(document.getElementById('pip-pressure').value); const rho = parseFloat(document.getElementById('pip-density').value);
// --- Validation --- const errors = []; if (isNaN(Cd) || Cd 1) errors.push("Discharge coefficient must be between 0 and 1."); if (isNaN(areaMm2) || areaMm2 0) { resultDiv.style.display = 'block'; resultDiv.className = 'calc-result calc-error'; resultDiv.innerHTML = 'Please fix the following:' + errors.map(e => '').join('') + ''; return; }
// --- Unit conversions --- const A = areaMm2 * 1e-6; // mm² → m² const dP = pressKPa * 1000; // kPa → Pa
// --- Orifice flow equation --- // Q = Cd * A * sqrt(2 * dP / rho) const velocity = Math.sqrt(2 * dP / rho); // m/s (Torricelli velocity) const Q_m3s = Cd * A * velocity; // m³/s const Q_Ls = Q_m3s * 1000; // L/s const Q_Lmin = Q_Ls * 60; // L/min const Q_m3h = Q_m3s * 3600; // m³/h
// Mass flow rate const mdot_kgs = rho * Q_m3s; // kg/s
// Daily volume loss const dailyLitres = Q_Ls * 86400; // L/day
resultDiv.style.display = 'block'; resultDiv.className = 'calc-result calc-success'; resultDiv.innerHTML = ` ### Results
Effective Leak Velocity${velocity.toFixed(3)} m/s Volumetric Flow Rate${Q_m3s.toExponential(4)} m³/s ${Q_Ls.toFixed(4)} L/s ${Q_Lmin.toFixed(3)} L/min ${Q_m3h.toFixed(4)} m³/h Mass Flow Rate${mdot_kgs.toFixed(4)} kg/s Daily Volume Loss${dailyLitres.toFixed(1)} L/day
Inputs used — Cd: ${Cd} | Area: ${areaMm2} mm² | ΔP: ${pressKPa} kPa | ρ: ${rho} 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
- The leak behaves as a sharp-edged orifice; Cd = 0.61 is the standard default (ISO 5167).
- 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.
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