Please enter valid positive numbers for all fields.
Calculation Results
Flow Velocity:–
Reynolds Number (Re):–
Flow Regime:–
Pressure Drop (Friction Loss):–
Pressure Drop (PSI):–
function calculatePressure() {
// 1. Get Input Values
var flowRateInput = document.getElementById('flowRate').value;
var diameterInput = document.getElementById('pipeDiameter').value;
var lengthInput = document.getElementById('pipeLength').value;
var densityInput = document.getElementById('fluidDensity').value;
var viscosityInput = document.getElementById('fluidViscosity').value;
var errorDiv = document.getElementById('errorMsg');
var resultDiv = document.getElementById('resultBox');
// 2. Validation
if (flowRateInput === "" || diameterInput === "" || lengthInput === "" || densityInput === "" || viscosityInput === "") {
errorDiv.style.display = "block";
resultDiv.style.display = "none";
return;
}
var Q_lmin = parseFloat(flowRateInput);
var D_mm = parseFloat(diameterInput);
var L_m = parseFloat(lengthInput);
var rho = parseFloat(densityInput);
var mu_cP = parseFloat(viscosityInput);
if (Q_lmin <= 0 || D_mm <= 0 || L_m <= 0 || rho <= 0 || mu_cP m³/s
var Q_si = Q_lmin / 60000;
// Diameter: mm -> m
var D_si = D_mm / 1000;
// Viscosity: cP -> Pa·s (kg/(m·s)) (1 cP = 0.001 Pa·s)
var mu_si = mu_cP / 1000;
// 4. Calculate Area and Velocity
var area = Math.PI * Math.pow((D_si / 2), 2);
var velocity = Q_si / area;
// 5. Calculate Reynolds Number (Re = (rho * v * D) / mu)
var reynolds = (rho * velocity * D_si) / mu_si;
// 6. Calculate Friction Factor (f)
// Darcy friction factor
var f = 0;
var regime = "";
if (reynolds < 2300) {
// Laminar Flow: f = 64 / Re
f = 64 / reynolds;
regime = "Laminar";
} else if (reynolds < 4000) {
// Transition zone – approximation
regime = "Transition";
// Blasius approximation often used for smooth pipes in turbulent/transition
f = 0.3164 * Math.pow(reynolds, -0.25);
} else {
// Turbulent Flow
regime = "Turbulent";
// Blasius approximation for smooth pipes (simplification for general web calculator)
f = 0.3164 * Math.pow(reynolds, -0.25);
}
// 7. Calculate Pressure Drop (Darcy-Weisbach Equation)
// Delta P = f * (L/D) * (rho * v² / 2)
var deltaP_Pa = f * (L_m / D_si) * (0.5 * rho * Math.pow(velocity, 2));
// 8. Convert Pressure Results
var deltaP_Bar = deltaP_Pa / 100000;
var deltaP_Psi = deltaP_Pa * 0.000145038;
// 9. Display Results
document.getElementById('resVelocity').innerText = velocity.toFixed(2) + " m/s";
document.getElementById('resReynolds').innerText = reynolds.toFixed(0);
document.getElementById('resRegime').innerText = regime;
document.getElementById('resPressureBar').innerText = deltaP_Bar.toFixed(4) + " Bar";
document.getElementById('resPressurePsi').innerText = deltaP_Psi.toFixed(2) + " PSI";
resultDiv.style.display = "block";
}
Understanding Pressure from Flow Rate
In fluid dynamics, calculating "pressure" from "flow rate" typically involves determining the pressure drop required to push a specific volume of fluid through a pipe of a certain size. This calculator uses the properties of the fluid, the dimensions of the pipe, and the velocity of the flow to estimate pressure loss due to friction.
The Relationship Between Flow and Pressure
Contrary to common intuition, high flow rate does not always mean high pressure. In fact, according to Bernoulli's principle, as the speed of a fluid increases, its static pressure actually decreases (assuming no energy is added). However, to maintain a high flow rate through a pipe, a significant pressure difference (pressure drop) is required to overcome friction against the pipe walls.
Formulas Used in This Calculator
This calculator primarily utilizes the Darcy-Weisbach equation, which is the standard engineering formula for calculating pressure loss in pipe flow:
ΔP = f · (L / D) · (½ ρ v²)
Where:
ΔP: Pressure Drop (Pascals)
f: Darcy Friction Factor (dimensionless)
L: Length of the pipe (meters)
D: Hydraulic diameter of the pipe (meters)
ρ (rho): Fluid Density (kg/m³)
v: Flow Velocity (m/s)
Why Velocity and Reynolds Number Matter
Before calculating the pressure drop, we must determine the Flow Velocity ($v = Q/A$). Once velocity is known, we calculate the Reynolds Number (Re) to determine if the flow is Laminar (smooth) or Turbulent (chaotic).
Laminar Flow (Re < 2300): The fluid moves in smooth layers. Friction is lower, and calculated using $f = 64/Re$.
Turbulent Flow (Re > 4000): The fluid undergoes irregular fluctuations and mixing. Friction is higher. This calculator uses the Blasius approximation for smooth pipes to estimate the friction factor in this regime.
Applications
This calculation is critical for:
Plumbing: Ensuring pipes are large enough to deliver water without excessive pressure loss.
Irrigation: Sizing pumps to ensure sprinklers receive adequate pressure at the end of a line.
Industrial Process: Calculating energy requirements for pumping fluids through long pipelines.