How to Calculate Flow Rate from Differential Pressure

Flow Rate from Differential Pressure Calculator

Calculate the volumetric flow rate based on the pressure drop across an orifice plate, venturi meter, or flow nozzle using Bernoulli's principle.

Water is ~1000 kg/m³
Standard orifice is ~0.61

Calculation Results:

Volumetric Flow Rate (m³/s): 0
Flow Rate (Liters per min): 0
Flow Rate (m³/hour): 0

Understanding Differential Pressure and Flow Rate

The relationship between differential pressure (ΔP) and flow rate (Q) is a fundamental concept in fluid mechanics, primarily derived from Bernoulli's Equation. When a fluid passes through a restriction (like an orifice plate or a venturi meter), its velocity increases, and its pressure decreases.

The Mathematical Formula

Q = Cd × A × √(2 × ΔP / ρ)

  • Q: Volumetric Flow Rate (m³/s)
  • Cd: Discharge Coefficient (accounts for energy losses and flow contraction)
  • A: Cross-sectional area of the opening (m²)
  • ΔP: Differential pressure across the restriction (Pa)
  • ρ (rho): Density of the fluid (kg/m³)

Key Factors Affecting Results

Discharge Coefficient (Cd): This value varies depending on the type of device used. A sharp-edged orifice plate typically has a Cd of approximately 0.61, while a smooth Venturi tube can have a Cd as high as 0.98.

Fluid Density: Temperature and pressure affect fluid density. For liquid water at room temperature, 1000 kg/m³ is standard. For gases, the density must be calculated at the specific operating pressure and temperature.

Practical Example

Suppose you have an orifice plate with a diameter of 50mm (0.05m) installed in a water line. The differential pressure transmitter reads 5,000 Pascals (Pa). Using a discharge coefficient of 0.61:

  1. Area (A) = π × (0.025)² = 0.001963 m²
  2. Flow (Q) = 0.61 × 0.001963 × √(2 × 5000 / 1000)
  3. Q = 0.61 × 0.001963 × √10 ≈ 0.00378 m³/s
  4. Converted to Liters/min: 0.00378 × 60,000 ≈ 226.8 L/min
function calculateFlowRate() { var dp = parseFloat(document.getElementById('diffPressure').value); var diameterMm = parseFloat(document.getElementById('orificeDiameter').value); var density = parseFloat(document.getElementById('fluidDensity').value); var cd = parseFloat(document.getElementById('dischargeCoeff').value); if (isNaN(dp) || isNaN(diameterMm) || isNaN(density) || isNaN(cd) || density <= 0 || diameterMm <= 0) { alert('Please enter valid positive numbers for all fields.'); return; } // Convert diameter from mm to meters var diameterM = diameterMm / 1000; // Calculate Area (A) = PI * r^2 var radiusM = diameterM / 2; var area = Math.PI * Math.pow(radiusM, 2); // Formula: Q = Cd * A * sqrt(2 * DP / rho) var flowRateM3s = cd * area * Math.sqrt((2 * dp) / density); // Conversions var flowRateLpm = flowRateM3s * 60000; var flowRateM3h = flowRateM3s * 3600; // Display results document.getElementById('resM3s').innerText = flowRateM3s.toFixed(6); document.getElementById('resLpm').innerText = flowRateLpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resM3h').innerText = flowRateM3h.toLocaleString(undefined, {minimumFractionDigits: 3, maximumFractionDigits: 3}); document.getElementById('flow-results').style.display = 'block'; }

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