How to Calculate Flow Rate from Pressure Drop

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Flow Rate from Pressure Drop Calculator

Water is approx. 1000 kg/m³
Typically 0.6 to 0.98 (Standard orifice is ~0.62)

Calculation Results:

Volumetric Flow Rate (L/min): 0 L/min

Volumetric Flow Rate (m³/h): 0 m³/h

Flow Velocity: 0 m/s

function calculateFlowRate() { var dp_bar = parseFloat(document.getElementById("pressureDrop").value); var d_mm = parseFloat(document.getElementById("orificeDiameter").value); var rho = parseFloat(document.getElementById("fluidDensity").value); var cd = parseFloat(document.getElementById("dischargeCoeff").value); if (isNaN(dp_bar) || isNaN(d_mm) || isNaN(rho) || isNaN(cd) || d_mm <= 0 || rho <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Convert Pressure Drop from Bar to Pascals (N/m²) var dp_pa = dp_bar * 100000; // Convert Diameter from mm to meters var d_m = d_mm / 1000; // Calculate Area (m²) var area = Math.PI * Math.pow((d_m / 2), 2); // Bernoulli based formula for flow rate: Q = Cd * A * sqrt(2 * ΔP / ρ) // This assumes flow through an orifice or across a restriction var q_m3s = cd * area * Math.sqrt((2 * dp_pa) / rho); // Convert m³/s to L/min (1 m³/s = 60000 L/min) var q_lpm = q_m3s * 60000; // Convert m³/s to m³/h (1 m³/s = 3600 m³/h) var q_m3h = q_m3s * 3600; // Calculate Velocity V = Q / A var velocity = q_m3s / area; document.getElementById("flowLPM").innerText = q_lpm.toFixed(2); document.getElementById("flowM3H").innerText = q_m3h.toFixed(2); document.getElementById("velocityMS").innerText = velocity.toFixed(2); document.getElementById("flowResult").style.display = "block"; }

How to Calculate Flow Rate from Pressure Drop

In fluid dynamics, the relationship between flow rate and pressure drop is fundamental for sizing pumps, pipes, and control valves. When a fluid passes through a restriction (like an orifice plate, a valve, or a narrow pipe section), its velocity increases, and its pressure decreases. This phenomenon is described by Bernoulli's principle.

The Basic Formula

The standard formula used to calculate the volumetric flow rate ($Q$) based on a pressure differential ($\Delta P$) is:

Q = Cd × A × √(2 × ΔP / ρ)

Variables Explained:

  • Q: Volumetric flow rate (m³/s).
  • Cd: Discharge Coefficient. This accounts for energy losses and flow contraction. For a sharp-edged orifice, it is usually around 0.62.
  • A: Cross-sectional area of the opening (m²).
  • ΔP: Pressure drop across the restriction (Pascals).
  • ρ (rho): Density of the fluid (kg/m³).

Real-World Example

Suppose you have a water pipe with an orifice diameter of 50mm. You measure a pressure drop of 0.5 Bar across a specific section. How much water is flowing?

  1. Convert Units: 0.5 Bar = 50,000 Pascals. 50mm = 0.05m diameter.
  2. Calculate Area: Area = π × (0.025)² = 0.001963 m².
  3. Assume Constants: Cd = 0.62, Density = 1000 kg/m³.
  4. Apply Formula: Q = 0.62 × 0.001963 × √(2 × 50,000 / 1000) = 0.62 × 0.001963 × 10 = 0.01217 m³/s.
  5. Final Result: Approximately 730 Liters per minute (L/min).

Factors Affecting Accuracy

While the calculator provides a precise mathematical result, several factors can influence actual field measurements:

  • Viscosity: Highly viscous fluids (like heavy oils) require a different calculation method involving the Reynolds number.
  • Pipe Roughness: Internal friction in older pipes causes higher pressure drops that aren't purely related to flow velocity.
  • Turbulence: The formula assumes relatively steady flow. High turbulence can lead to fluctuations in pressure readings.
  • Fluid Compressibility: This calculator is designed for liquids (incompressible). For gases, expansion factors must be considered.

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