Calculate fluid flow rate based on pressure drop, pipe diameter, and length.
Unit: Bar
Unit: Bar (must be lower than P₁)
Unit: Millimeters (mm)
Unit: Meters (m)
kg/m³ (Water = 1000)
Approx: 0.02 (Steel/Clean), 0.01 (PVC)
Volumetric Flow Rate (m³/h):–
Flow Rate (Liters/min):–
Fluid Velocity:–
Pressure Drop:–
function calculateFlowRate() {
// 1. Get Input Values
var p1 = parseFloat(document.getElementById("inletPressure").value);
var p2 = parseFloat(document.getElementById("outletPressure").value);
var d_mm = parseFloat(document.getElementById("pipeDiameter").value);
var length = parseFloat(document.getElementById("pipeLength").value);
var density = parseFloat(document.getElementById("fluidDensity").value);
var friction = parseFloat(document.getElementById("frictionFactor").value);
// 2. Element References
var resultBox = document.getElementById("resultBox");
var errorMsg = document.getElementById("errorMsg");
// 3. Validation
errorMsg.style.display = "none";
resultBox.style.display = "none";
if (isNaN(p1) || isNaN(p2) || isNaN(d_mm) || isNaN(length) || isNaN(density) || isNaN(friction)) {
errorMsg.innerText = "Please fill in all fields with valid numbers.";
errorMsg.style.display = "block";
return;
}
if (p2 >= p1) {
errorMsg.innerText = "Outlet pressure must be lower than Inlet pressure to create flow.";
errorMsg.style.display = "block";
return;
}
if (d_mm <= 0 || length <= 0 || density <= 0 || friction <= 0) {
errorMsg.innerText = "Diameter, Length, Density, and Friction factor must be positive values.";
errorMsg.style.display = "block";
return;
}
// 4. Unit Conversions & Calculation (Darcy-Weisbach derived)
// Formula: v = sqrt( (2 * deltaP * D) / (f * L * rho) )
// deltaP in Pascals
// D in meters
var deltaP_bar = p1 – p2;
var deltaP_pa = deltaP_bar * 100000; // Convert Bar to Pascals
var d_m = d_mm / 1000; // Convert mm to meters
// Calculate Velocity (v) in m/s
var numerator = 2 * deltaP_pa * d_m;
var denominator = friction * length * density;
var velocity = Math.sqrt(numerator / denominator);
// Calculate Area (A) in m²
var radius = d_m / 2;
var area = Math.PI * Math.pow(radius, 2);
// Calculate Flow Rate (Q) in m³/s
var flow_m3s = area * velocity;
// Convert Results
var flow_m3h = flow_m3s * 3600; // m³/s to m³/h
var flow_lpm = flow_m3s * 60000; // m³/s to Liters/min
// 5. Display Results
document.getElementById("resM3h").innerText = flow_m3h.toFixed(2) + " m³/h";
document.getElementById("resLpm").innerText = flow_lpm.toFixed(1) + " L/min";
document.getElementById("resVelocity").innerText = velocity.toFixed(2) + " m/s";
document.getElementById("resDrop").innerText = deltaP_bar.toFixed(2) + " Bar";
resultBox.style.display = "block";
}
How to Calculate Flow Rate Through a Pipe Using Pressure
Calculating the flow rate of a fluid through a pipe is a fundamental task in engineering, plumbing, and fluid dynamics. When a fluid moves through a pipe, friction against the pipe walls causes a loss of energy, resulting in a pressure drop ($\Delta P$) from the inlet to the outlet. By knowing this pressure difference, along with the pipe's physical dimensions and the fluid's properties, we can determine the velocity and volumetric flow rate.
The Physics: Darcy-Weisbach Equation
The most accurate method to link pressure drop to flow rate in pipes is derived from the Darcy-Weisbach equation. While the equation is typically used to find head loss or pressure drop given a known flow rate, it can be rearranged to solve for velocity ($v$) when the pressure drop is known.
The formula for fluid velocity based on pressure drop is:
v = √ [ (2 · ΔP · D) / (f · L · ρ) ]
Where:
v = Fluid Velocity (m/s)
ΔP = Pressure Drop (Pascals)
D = Pipe Hydraulic Diameter (meters)
f = Darcy Friction Factor (dimensionless)
L = Pipe Length (meters)
ρ (Rho) = Fluid Density (kg/m³)
Steps to Calculate Volumetric Flow Rate
Once the velocity ($v$) is determined using the formula above, the volumetric flow rate ($Q$) is calculated by multiplying the velocity by the cross-sectional area of the pipe ($A$).
Pressure Drop ($\Delta P$): The driving force of the flow. A higher pressure difference between the inlet and outlet results in a higher flow rate.
Diameter ($D$): Small changes in diameter have a massive impact on flow rate. Doubling the diameter can increase the flow rate by a factor of 4 or more, depending on the flow regime.
Friction Factor ($f$): This represents the roughness of the pipe. Smooth pipes (like PVC or Copper) have lower friction factors (approx 0.010-0.015), while rougher pipes (like Concrete or rusted Steel) have higher values (0.020-0.050).
Fluid Density ($\rho$): Heavier fluids require more pressure to achieve the same velocity. Water is approximately 1000 kg/m³, while oil might be 850 kg/m³.
Example Calculation
Let's say you have a water pipe setup with the following parameters:
Inlet Pressure: 5 Bar
Outlet Pressure: 4.5 Bar (Drop of 0.5 Bar = 50,000 Pa)
Pipe Diameter: 50mm (0.05m)
Length: 10 meters
Friction Factor: 0.02
Density: 1000 kg/m³
Using the calculator above, the fluid velocity would be approximately 5.0 m/s, resulting in a flow rate of roughly 35.3 m³/h (or about 589 Liters/minute).