Plastic / PVC (Smooth) – 0.0015 mm
Commercial Steel – 0.045 mm
Galvanized Iron – 0.15 mm
Cast Iron – 0.26 mm
Copper / Brass – 0.0015 mm
Concrete – 0.6 mm
Material Absolute Roughness (ε)
kg/m³ (Water = 998.2)
Pa·s (Water @ 20°C = 0.001002)
Pressure Drop
0.00 Bar
(0.00 PSI)
Fluid Velocity:0.00 m/s
Reynolds Number (Re):0
Flow Regime:Turbulent
Friction Factor (Darcy):0.0000
Head Loss:0.00 m
function calculatePressureDrop() {
var flowRateInput = document.getElementById('flowRate').value;
var diameterInput = document.getElementById('pipeInnerDiameter').value;
var lengthInput = document.getElementById('pipeLength').value;
var roughnessInput = document.getElementById('pipeMaterial').value;
var densityInput = document.getElementById('fluidDensity').value;
var viscosityInput = document.getElementById('fluidViscosity').value;
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('resultsArea');
// Reset errors and results
errorDiv.innerHTML = "";
resultsDiv.style.display = "none";
// Validate Inputs
if (!flowRateInput || !diameterInput || !lengthInput || !densityInput || !viscosityInput) {
errorDiv.innerHTML = "Please fill in all input fields correctly.";
return;
}
var Q_lpm = parseFloat(flowRateInput);
var D_mm = parseFloat(diameterInput);
var L_m = parseFloat(lengthInput);
var epsilon_mm = parseFloat(roughnessInput);
var rho = parseFloat(densityInput);
var mu = parseFloat(viscosityInput);
if (Q_lpm <= 0 || D_mm <= 0 || L_m <= 0 || rho <= 0 || mu m³/s
var Q_m3s = Q_lpm / 60000;
// Diameter: mm -> m
var D_m = D_mm / 1000;
// Roughness: mm -> m
var epsilon_m = epsilon_mm / 1000;
// — Step 2: Calculate Velocity —
// Area = pi * r^2 = pi * (D/2)^2
var area = Math.PI * Math.pow((D_m / 2), 2);
var velocity = Q_m3s / area; // m/s
// — Step 3: Calculate Reynolds Number —
// Re = (rho * v * D) / mu
var Re = (rho * velocity * D_m) / mu;
// — Step 4: Calculate Friction Factor (f) —
// Using Darcy-Weisbach friction factor
var f = 0;
var regime = "";
if (Re = 2300 && Re < 4000) {
regime = "Transition";
} else {
regime = "Turbulent";
}
// Swamee-Jain Equation (Direct solution for Darcy friction factor)
var term1 = epsilon_m / (3.7 * D_m);
var term2 = 5.74 / Math.pow(Re, 0.9);
var logVal = Math.log10(term1 + term2);
f = 0.25 / Math.pow(logVal, 2);
}
// — Step 5: Calculate Pressure Drop (Darcy-Weisbach) —
// Delta P = f * (L/D) * (rho * v^2 / 2)
// Result in Pascals
var pressureDropPa = f * (L_m / D_m) * (rho * Math.pow(velocity, 2) / 2);
// Convert Pascals to Bar (1 Bar = 100,000 Pa)
var pressureDropBar = pressureDropPa / 100000;
// Convert Pascals to PSI (1 Bar = 14.5038 PSI)
var pressureDropPsi = pressureDropBar * 14.5038;
// Calculate Head Loss (meters of fluid)
// h_f = Delta P / (rho * g)
var g = 9.81;
var headLoss = pressureDropPa / (rho * g);
// — Step 6: Display Results —
document.getElementById('resPressureBar').innerHTML = pressureDropBar.toFixed(4) + " Bar";
document.getElementById('resPressurePsi').innerHTML = pressureDropPsi.toFixed(2);
document.getElementById('resVelocity').innerHTML = velocity.toFixed(2) + " m/s";
document.getElementById('resReynolds').innerHTML = Re.toFixed(0);
document.getElementById('resRegime').innerHTML = regime;
document.getElementById('resFriction').innerHTML = f.toFixed(5);
document.getElementById('resHeadLoss').innerHTML = headLoss.toFixed(2) + " m";
resultsDiv.style.display = "block";
}
How to Calculate Pressure in a Pipe with Flow Rate
Calculating the pressure drop in a pipe given a specific flow rate is a fundamental task in fluid dynamics and engineering. This calculation helps in sizing pumps, selecting pipe diameters, and ensuring that a system delivers fluids efficiently without excessive energy loss due to friction.
The Relationship Between Flow and Pressure
Contrary to common intuition, flow rate and static pressure are inversely related in terms of energy conservation (Bernoulli's principle), but in pipe flow, the primary concern is Pressure Loss (or Pressure Drop) due to friction. To push a specific volume of fluid through a pipe (Flow Rate), you must overcome the friction caused by the fluid rubbing against the pipe walls. This energy loss manifests as a drop in pressure from the start of the pipe to the end.
The Governing Formula: Darcy-Weisbach Equation
The most accurate method to calculate pressure loss in a pipe is the Darcy-Weisbach equation. This formula accounts for fluid properties, pipe geometry, and the flow regime (laminar or turbulent).
ΔP = f · (L / D) · (ρ · v² / 2)
Where:
ΔP: Pressure Drop (Pascals)
f: Darcy Friction Factor (dimensionless)
L: Length of the pipe (m)
D: Hydraulic diameter of the pipe (m)
ρ (rho): Fluid density (kg/m³)
v: Fluid velocity (m/s)
Step-by-Step Calculation Process
1. Determine Fluid Velocity
First, convert your flow rate (Q) into velocity (v). Since Flow Rate = Area × Velocity:
v = Q / (π · (D/2)²)
2. Calculate the Reynolds Number (Re)
The Reynolds number determines if the flow is Laminar (smooth) or Turbulent (chaotic). It is calculated using the fluid's density, velocity, pipe diameter, and dynamic viscosity (μ).
Re = (ρ · v · D) / μ
Re < 2300: Laminar Flow
Re > 4000: Turbulent Flow
3. Find the Friction Factor (f)
This is the most complex step.
For Laminar flow, f = 64 / Re.
For Turbulent flow, the friction factor depends on the pipe's relative roughness. The calculator above uses the Swamee-Jain equation (an approximation of the Colebrook equation) to solve for f without needing iteration.
Example Calculation
Let's look at a realistic scenario for a residential water line:
Parameter
Value
Flow Rate
50 L/min
Pipe Diameter
25 mm (Plastic)
Length
20 meters
Fluid
Water (Density: 998 kg/m³, Viscosity: 0.001 Pa·s)
Result: Using the calculator, the velocity is approximately 1.7 m/s. The Reynolds number is roughly 42,300 (Turbulent). The resulting Pressure Drop is approximately 0.22 Bar (3.19 PSI). This means if you start with 4 Bar of pressure, you will have 3.78 Bar at the end of the 20-meter run.
Factors Increasing Pressure Loss
Higher Flow Rate: Pressure drop increases with the square of the velocity. Doubling flow quadruples pressure loss.
Smaller Diameter: Reducing pipe size dramatically increases velocity and friction.
Rougher Pipes: Old, corroded iron pipes create more friction than smooth new PVC.
Viscosity: Thicker fluids (like oil) resist flow more than water, causing higher pressure drops.