How to Calculate Flow Rate Using Differential Pressure

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Differential Pressure Flow Rate Calculator

Standard Orifice: 0.61 | Venturi: 0.98

Volumetric Flow Rate (Q):

How to Calculate Flow Rate Using Differential Pressure

Measuring flow rate via differential pressure is one of the most common methods in industrial processing. This technique relies on Bernoulli's Principle, which states that as the speed of a moving fluid increases, the pressure within the fluid decreases.

The Mathematical Formula

The relationship between differential pressure (ΔP) and flow rate (Q) is expressed by the following equation:

Q = Cd * A * √(2 * ΔP / ρ)

Where:

  • Q: Volumetric Flow Rate (m³/s)
  • Cd: Discharge Coefficient (accounts for energy losses)
  • A: Cross-sectional area of the orifice or throat (m²)
  • ΔP: Differential Pressure (P1 – P2) in Pascals
  • ρ: Density of the fluid (kg/m³)

Practical Example

Imagine you have water (density 1000 kg/m³) flowing through a pipe with an orifice plate. You measure a differential pressure of 5000 Pa. The orifice diameter is 40mm (0.04m), and the discharge coefficient is 0.61.

  1. Calculate Area: A = π * (0.02)² = 0.001256 m²
  2. Calculate Flow: Q = 0.61 * 0.001256 * √(2 * 5000 / 1000)
  3. Result: Q = 0.61 * 0.001256 * √10 = 0.00242 m³/s

Common Discharge Coefficients (Cd)

The coefficient of discharge varies based on the geometry of the restriction:

  • Orifice Plate: Typically 0.60 to 0.65. It is popular because it is inexpensive but causes high pressure loss.
  • Venturi Tube: Typically 0.95 to 0.99. It is highly efficient with low pressure loss but more expensive to install.
  • Flow Nozzle: Typically 0.92 to 0.98. A middle ground between orifice and venturi.

Why is ΔP used for Flow?

Differential pressure flow meters are preferred because they have no moving parts, are well-understood, and can be used for a wide variety of liquids, gases, and steam. By simply measuring the pressure drop across a known restriction, you can derive the exact velocity and volume of the fluid passing through the system.

function calculateDPFlow() { var dp = parseFloat(document.getElementById("diff_pressure").value); var rho = parseFloat(document.getElementById("fluid_density").value); var diameterMM = parseFloat(document.getElementById("orifice_diameter").value); var cd = parseFloat(document.getElementById("discharge_coeff").value); var resultContainer = document.getElementById("dp_result_container"); if (isNaN(dp) || isNaN(rho) || isNaN(diameterMM) || isNaN(cd) || rho <= 0 || diameterMM <= 0) { alert("Please enter valid positive numbers for all fields."); return; } if (dp < 0) { alert("Differential pressure must be positive to calculate flow."); return; } // Convert diameter from mm to meters var diameterM = diameterMM / 1000; // Calculate Area A = pi * r^2 var radius = diameterM / 2; var area = Math.PI * Math.pow(radius, 2); // Bernoulli flow formula: Q = Cd * A * sqrt(2 * dP / rho) var q_m3s = cd * area * Math.sqrt((2 * dp) / rho); // Convert m3/s to L/min (1 m3 = 1000 L, 1 sec = 1/60 min) var q_lmin = q_m3s * 1000 * 60; // Display results document.getElementById("q_cubic_meters").innerText = q_m3s.toFixed(6) + " m³/s"; document.getElementById("q_liters_min").innerText = "Equivalent to: " + q_lmin.toFixed(2) + " Liters per minute (L/min)"; resultContainer.style.display = "block"; }

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