Calculate Flow Rate from Pressure Drop and Diameter

Pipe Flow Rate Calculator

Calculate volumetric flow rate based on pipe diameter, pressure drop, and fluid properties using the Darcy-Weisbach equation.

mm

bar

meters

kg/m³

Water ≈ 1000, Oil ≈ 850

(unitless)

Typical Steel Pipe: 0.02 – 0.05

Calculation Results

Flow Rate (Cubic Meters/Hour)

0.00 m³/h

Flow Rate (Liters/Minute)

0.00 L/min

Flow Rate (Gallons/Minute)

0.00 GPM

Fluid Velocity

0.00 m/s

function calculateFlowRate() { // Get inputs by ID var d_mm = parseFloat(document.getElementById("pipeDiameter").value); var p_bar = parseFloat(document.getElementById("pressureDrop").value); var l_m = parseFloat(document.getElementById("pipeLength").value); var density = parseFloat(document.getElementById("fluidDensity").value); var friction = parseFloat(document.getElementById("frictionFactor").value); // Validation if (isNaN(d_mm) || isNaN(p_bar) || isNaN(l_m) || isNaN(density) || isNaN(friction) || l_m <= 0 || density <= 0 || friction <= 0 || d_mm meters var d_m = d_mm / 1000; // Pressure: bar -> Pascals (Pa) var p_pa = p_bar * 100000; // Radius var radius_m = d_m / 2; // Area (A = pi * r^2) var area_m2 = Math.PI * Math.pow(radius_m, 2); // Calculation using Darcy-Weisbach rearranged for Velocity (v) // DeltaP = f * (L/D) * (rho * v^2 / 2) // v = Sqrt( (2 * DeltaP * D) / (f * L * rho) ) var numerator = 2 * p_pa * d_m; var denominator = friction * l_m * density; if (denominator === 0) { return; // Prevent divide by zero } var velocity_squared = numerator / denominator; var velocity = Math.sqrt(velocity_squared); // Calculate Flow Rate (Q = v * A) var flow_m3s = velocity * area_m2; // Convert Results var flow_m3h = flow_m3s * 3600; // m3 per hour var flow_lpm = flow_m3s * 60000; // liters per minute var flow_gpm = flow_lpm * 0.264172; // US gallons per minute // Display Results document.getElementById("resultsSection").style.display = "block"; document.getElementById("res_m3h").innerText = flow_m3h.toFixed(2) + " m³/h"; document.getElementById("res_lpm").innerText = flow_lpm.toFixed(2) + " L/min"; document.getElementById("res_gpm").innerText = flow_gpm.toFixed(2) + " GPM"; document.getElementById("res_velocity").innerText = velocity.toFixed(2) + " m/s"; }

How to Calculate Flow Rate from Pressure Drop and Diameter

Calculating the flow rate of a fluid through a pipe based on pressure drop and diameter is a fundamental task in fluid mechanics and engineering. Whether you are designing an irrigation system, an industrial hydraulic circuit, or residential plumbing, understanding the relationship between these variables is critical for efficient system performance.

This calculator utilizes the Darcy-Weisbach equation, which is widely considered the most accurate method for determining pressure loss and flow rate in pipes ranging from laminar to turbulent flow regimes.

The Physics: The Darcy-Weisbach Equation

While the simplified Hagen-Poiseuille law is often cited for laminar flow, real-world applications usually involve turbulent flow. The Darcy-Weisbach equation connects the pressure drop ($\Delta P$) to the flow characteristics:

ΔP = f &cdot; (L / D) &cdot; (ρ &cdot; v² / 2)

Where:

• ΔP: Pressure Drop (Pa)
• f: Darcy Friction Factor (dimensionless)
• L: Pipe Length (m)
• D: Hydraulic Diameter (m)
• ρ: Fluid Density (kg/m³)
• v: Fluid Velocity (m/s)

Why Pipe Diameter Matters Most

The diameter of the pipe has the most significant impact on flow rate. In fluid dynamics, flow capacity is proportional to the diameter raised to the power of 4 (in laminar conditions) or approximately 2.5 to 3 in turbulent conditions. This means a small increase in pipe diameter can lead to a massive increase in flow rate for the same pressure drop.

Key Input Variables Explained

• Internal Diameter: The actual opening inside the pipe. Note that a "2-inch pipe" often has a different internal diameter depending on its schedule (wall thickness).
• Pressure Drop: The difference in pressure between the inlet and outlet of the pipe segment. This is the driving force that pushes the fluid.
• Friction Factor: A coefficient that represents the roughness of the pipe's interior surface. New, smooth plastic pipes have a lower friction factor (approx 0.015-0.02) compared to old, corroded steel pipes (0.04+).

Frequently Asked Questions

Does this calculator work for air or gas?

This calculator assumes an incompressible fluid (liquids like water or oil). For gases with significant pressure drops (where density changes), you need a compressible flow calculator. However, for low-pressure drop ventilation systems, this approximation is often acceptable if the correct density for air (approx 1.2 kg/m³) is used.

How do I find the Friction Factor?

The Darcy friction factor depends on the Reynolds number and relative roughness. For estimation purposes in turbulent flow, a value of 0.02 is a standard average for commercial steel or smooth concrete pipes.

Why is pipe length required?

You cannot calculate flow rate from pressure and diameter alone. Pressure drop occurs over a distance. A 0.5 bar drop over 1 meter implies a violent, high-speed flow, whereas a 0.5 bar drop over 10 kilometers implies a mere trickle. Length is mathematically essential to the equation.