Leak Flow Rate Calculation

Leak Flow Rate Calculator

Calculated Results:

Liters per Minute (L/min): 0

Cubic Meters per Hour (m³/h): 0

Gallons per Minute (GPM): 0

function calculateLeakFlow() { var d = parseFloat(document.getElementById('holeDiameter').value); var pBar = parseFloat(document.getElementById('pressure').value); var cd = parseFloat(document.getElementById('dischargeCoeff').value); var rho = parseFloat(document.getElementById('fluidDensity').value); if (isNaN(d) || isNaN(pBar) || isNaN(cd) || isNaN(rho) || d <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Convert Diameter mm to meters var d_m = d / 1000; // Area A = PI * (d/2)^2 var area = Math.PI * Math.pow((d_m / 2), 2); // Convert Pressure bar to Pascals (1 bar = 100,000 Pa) var p_pa = pBar * 100000; // Bernoulli's derived formula: Q = Cd * A * sqrt(2 * deltaP / rho) // Result in cubic meters per second (m3/s) var flowM3s = cd * area * Math.sqrt((2 * p_pa) / rho); // Convert to various units var flowLpm = flowM3s * 1000 * 60; // 1 m3/s = 1000 L, 60s/min var flowM3h = flowM3s * 3600; // 1 m3/s = 3600 m3/h var flowGpm = flowLpm * 0.264172; // 1 Liter = 0.264172 US Gallons document.getElementById('flowLpm').innerText = flowLpm.toFixed(2); document.getElementById('flowM3h').innerText = flowM3h.toFixed(3); document.getElementById('flowGpm').innerText = flowGpm.toFixed(2); document.getElementById('resultDisplay').style.display = 'block'; }

Understanding Leak Flow Rate Calculation

Calculating the flow rate of a leak is critical for maintenance engineers, safety inspectors, and water utility managers. Whether you are dealing with a punctured pipe or a faulty valve, knowing the volume of fluid lost per minute helps in quantifying economic loss and environmental impact.

The Physics Behind the Formula

This calculator utilizes a derivation of Bernoulli's Principle and the Orifice Flow Equation. The primary factors influencing the leak rate are:

• Orifice Area: The physical size of the hole. Larger holes allow significantly more volume to pass through.
• Pressure Differential: The difference between the internal pipe pressure and the external atmospheric pressure. Higher pressure pushes fluid through the opening faster.
• Discharge Coefficient (Cd): A factor that accounts for the geometry of the hole and fluid friction. For a sharp-edged circular hole, 0.62 is a common standard.
• Fluid Density: The thickness of the fluid. Water has a density of approximately 1000 kg/m³, while oils or gases will differ.

Standard Formula

Q = Cd × A × √(2 × ΔP / ρ)

Where:

• Q: Volumetric flow rate (m³/s)
• Cd: Discharge coefficient (dimensionless)
• A: Cross-sectional area of the leak (m²)
• ΔP: Pressure difference (Pascals)
• ρ: Density of the fluid (kg/m³)

Practical Example

Imagine a water pipe with an internal pressure of 4 Bar that develops a small puncture of 3 mm in diameter. Using the standard discharge coefficient for water (0.62):

1. Area: π × (0.0015)² = 0.000007068 m²
2. Pressure: 400,000 Pascals
3. Calculation: 0.62 × 0.000007068 × √(800,000 / 1000)
4. Result: Approximately 7.35 Liters per minute.

In just one hour, this "tiny" 3mm leak would waste over 440 liters of water!

Typical Discharge Coefficients

Hole Type	Cd Value (Approx)
Sharp Edged Orifice	0.61 – 0.65
Short Tube	0.80 – 0.82
Rounded Orifice	0.95 – 0.98