Flow Rate Through Orifice Calculator

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Orifice Flow Rate Calculator

Calculate liquid flow rate through an orifice plate or restrictor.

Diameter of the hole in millimeters (mm).
Pressure drop across the orifice in bar.
Density in kg/m³. Water is approx 1000.
Typically 0.60 – 0.65 for sharp-edged orifices.
Please enter valid positive numbers for all fields.

Calculation Results

Volumetric Flow Rate (LPM): –
Volumetric Flow Rate (m³/h): –
Orifice Velocity: –
Orifice Area: –

Understanding Orifice Flow Rate Calculations

Calculating the flow rate through an orifice is a fundamental task in fluid dynamics and engineering. This calculator determines the volumetric flow rate of an incompressible fluid (liquid) passing through a restriction or hole (orifice) based on the pressure difference across it. This is commonly used in hydraulic systems, water treatment, and pipeline metering.

The Flow Rate Formula

The calculation relies on Bernoulli's principle, modified with a discharge coefficient to account for real-world fluid losses and vena contracta effects. The formula used is:

Q = Cd × A × √(2 × ΔP / ρ)

Where:

  • Q = Volumetric Flow Rate (m³/s)
  • Cd = Discharge Coefficient (dimensionless)
  • A = Cross-sectional Area of the Orifice (m²)
  • ΔP = Pressure Difference across the orifice (Pa or N/m²)
  • ρ = Fluid Density (kg/m³)

Key Parameters Explained

Orifice Diameter (d)

This is the physical diameter of the hole through which the fluid flows. Even small changes in diameter have a significant impact on flow rate because the area is proportional to the square of the diameter.

Pressure Difference (ΔP)

This represents the driving force of the flow. It is the difference between the upstream pressure (before the orifice) and the downstream pressure (after the orifice). In this calculator, the input is in bar, which is converted to Pascals for calculation (1 bar = 100,000 Pa).

Discharge Coefficient (Cd)

In an ideal world, fluids would flow without friction or contraction. In reality, the flow stream contracts (vena contracta) and energy is lost. The Discharge Coefficient corrects theoretical flow to actual flow.

  • 0.60 – 0.65: Common for sharp-edged orifices / thin plates.
  • 0.95 – 0.98: Common for well-rounded nozzles.

Fluid Density (ρ)

The mass per unit volume of the fluid.

  • Water: ~1000 kg/m³
  • Oil: ~850-900 kg/m³
  • Fuel (Gasoline): ~720-775 kg/m³

Example Calculation

Let's say you have a water tank creating a pressure of 3 bar against a drain hole with a diameter of 15 mm.

  1. Convert Units: 15mm = 0.015m. 3 bar = 300,000 Pa. Density = 1000 kg/m³.
  2. Calculate Area: A = π × (0.015/2)² ≈ 0.0001767 m².
  3. Calculate Velocity Term: √(2 × 300,000 / 1000) = √600 ≈ 24.49 m/s.
  4. Apply Coefficient (0.62): Q = 0.62 × 0.0001767 × 24.49 ≈ 0.00268 m³/s.
  5. Convert to LPM: 0.00268 × 60,000 ≈ 160.8 Liters per Minute.
function calculateFlowRate() { // 1. Get DOM elements var dInput = document.getElementById("orificeDiameter"); var pInput = document.getElementById("pressureDiff"); var rhoInput = document.getElementById("fluidDensity"); var cdInput = document.getElementById("dischargeCoeff"); var resultDiv = document.getElementById("frcResults"); var errorDiv = document.getElementById("frcError"); var resLPM = document.getElementById("resLPM"); var resM3H = document.getElementById("resM3H"); var resVelocity = document.getElementById("resVelocity"); var resArea = document.getElementById("resArea"); // 2. Parse values var d_mm = parseFloat(dInput.value); var p_bar = parseFloat(pInput.value); var rho = parseFloat(rhoInput.value); var cd = parseFloat(cdInput.value); // 3. Validation if (isNaN(d_mm) || isNaN(p_bar) || isNaN(rho) || isNaN(cd) || d_mm <= 0 || rho <= 0 || cd <= 0 || p_bar < 0) { errorDiv.style.display = "block"; resultDiv.style.display = "none"; return; } errorDiv.style.display = "none"; // 4. Unit Conversion for Calculation (SI Units) // Diameter: mm to meters var d_m = d_mm / 1000; // Pressure: bar to Pascals (N/m^2) var p_pa = p_bar * 100000; // 5. Calculate Area (m^2) // A = pi * r^2 = pi * (d/2)^2 var area_m2 = Math.PI * Math.pow((d_m / 2), 2); // 6. Calculate Velocity (Theoretical Bernoulli velocity) // v = sqrt(2 * deltaP / rho) // Note: Actual velocity at the vena contracta relates to Cv, but for simplified Q calculation: // Q = Cd * A * sqrt(2dP/rho) // We will calculate Q first, then derive effective velocity v = Q/A_effective or keep theoretical. // Standard engineering approach: Q = Cd * A_orifice * sqrt(2 * dP / rho) var termInsideSqrt = (2 * p_pa) / rho; var sqrtTerm = Math.sqrt(termInsideSqrt); // Flow Rate in Cubic Meters per Second (m^3/s) var q_m3s = cd * area_m2 * sqrtTerm; // Velocity through the orifice (m/s) // v = Q / (Cd * A) ?? No, usually v = sqrt(2dP/rho) is ideal. // Actual average velocity at orifice plane = Q / A_orifice var velocity_ms = q_m3s / area_m2; // 7. Convert Results for Display // Liters per Minute (LPM) // 1 m^3/s = 60,000 L/min var q_lpm = q_m3s * 60000; // Cubic Meters per Hour (m^3/h) // 1 m^3/s = 3600 m^3/h var q_m3h = q_m3s * 3600; // Area in mm^2 for display var area_mm2 = area_m2 * 1000000; // 8. Output Results resLPM.innerText = q_lpm.toFixed(2) + " LPM"; resM3H.innerText = q_m3h.toFixed(2) + " m³/h"; resVelocity.innerText = velocity_ms.toFixed(2) + " m/s"; resArea.innerText = area_mm2.toFixed(2) + " mm²"; resultDiv.style.display = "block"; }

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