Flow Rate Pressure Calculator

Calculate the volumetric flow rate of a fluid through a pipe or orifice based on the pressure drop (differential pressure), pipe diameter, and fluid density.

Pressure Drop (Differential Pressure) in Pascals (Pa): The difference in pressure between the inlet and outlet driving the flow.

Internal Pipe/Orifice Diameter in millimeters (mm):

Fluid Density in kg/m³: Common densities: Water ≈ 1000 kg/m³, Air (at STP) ≈ 1.225 kg/m³.

Calculation Results:

Flow Rate (m³/s): m³/s

Flow Rate (Liters/minute): LPM

Flow Velocity: m/s

function calculateFlowRate() { // Get input values var pressureDropPa = parseFloat(document.getElementById("pressureDrop").value); var diameterMm = parseFloat(document.getElementById("pipeDiameter").value); var densityKgM3 = parseFloat(document.getElementById("fluidDensity").value); var resultDiv = document.getElementById("flowResult"); // Validate inputs if (isNaN(pressureDropPa) || pressureDropPa < 0 || isNaN(diameterMm) || diameterMm <= 0 || isNaN(densityKgM3) || densityKgM3 <= 0) { alert("Please enter valid positive numbers for all fields. Density and Diameter must be greater than zero."); resultDiv.style.display = "none"; return; } // Perform calculations based on simplified Bernoulli equation principles for flow through an area // 1. Convert diameter from mm to meters var diameterMeters = diameterMm / 1000; var radiusMeters = diameterMeters / 2; // 2. Calculate Cross-Sectional Area (A = π * r²) in square meters var areaM2 = Math.PI * Math.pow(radiusMeters, 2); // 3. Calculate Velocity (v = sqrt((2 * ΔP) / ρ)) in m/s // This assumes the pressure drop is entirely converted to kinetic energy (ideal scenario) var velocityMs = Math.sqrt((2 * pressureDropPa) / densityKgM3); // 4. Calculate Volumetric Flow Rate (Q = A * v) in m³/s var flowRateM3s = areaM2 * velocityMs; // 5. Convert Flow Rate to Liters Per Minute (LPM) // 1 m³/s = 60,000 Liters/minute var flowRateLPM = flowRateM3s * 60000; // Display results formatting to 4 decimal places for precision document.getElementById("resultM3s").innerHTML = flowRateM3s.toFixed(5); document.getElementById("resultLPM").innerHTML = flowRateLPM.toFixed(2); document.getElementById("resultVelocity").innerHTML = velocityMs.toFixed(2); // Show result container resultDiv.style.display = "block"; }

Understanding the Relationship Between Pressure and Flow Rate

In fluid dynamics, the relationship between flow rate and pressure is fundamental to engineering applications ranging from plumbing systems to industrial pipelines. While often complex, the basic principle is that a pressure difference (often called pressure drop or differential pressure) is required to move fluid through a pipe or orifice.

Fluid flows from an area of high pressure to an area of low pressure. The magnitude of this pressure drop ($\Delta P$), combined with the physical properties of the fluid (density) and the conduit it is flowing through (diameter/area), determines how fast the fluid moves (velocity) and how much volume passes per unit of time (volumetric flow rate).

Key Factors Influencing Flow:

Pressure Drop ($\Delta P$): The driving force. A larger pressure difference generally results in a higher flow rate.
Pipe Diameter/Area ($A$): A wider pipe offers less resistance and allows for a greater volume of fluid to pass through at a given velocity.
Fluid Density ($\rho$): Heavier, denser fluids (like water) require more pressure to accelerate to the same velocity compared to lighter fluids (like air).

This calculator uses a simplified application of Bernoulli's principle, which relates pressure, velocity, and elevation. For horizontal flow driven through an orifice or pipe section by pressure differential, the relationship determines that velocity increases as the square root of the pressure drop divided by density.

Practical Example: Water Flowing Through a Pipe

Let's assume you have a scenario where water is being pushed through a pipe with an internal diameter of 50 mm. You measure a pressure drop across a specific section of the pipe to be 10,000 Pascals (Pa) (which is roughly 0.1 bar or 1.45 PSI).

To calculate the theoretical flow rate, we use the known density of water, which is approximately 1000 kg/m³.

By inputting these values into the calculator above:

Pressure Drop: 10000 Pa
Diameter: 50 mm
Density: 1000 kg/m³

The calculator determines that the fluid velocity would be approximately 4.47 m/s, resulting in a volumetric flow rate of roughly 0.00878 m³/s, which is equivalent to roughly 526.8 Liters per minute (LPM).

Note: This calculator provides theoretical values based on ideal fluid dynamics principles. Real-world systems experience additional friction losses dependent on pipe roughness, viscosity, and turbulence, which may result in actual flow rates being slightly lower than calculated here.