This calculator helps you estimate the volumetric flow rate of a fluid through a pipe or orifice when you know the pressure difference across it, the fluid properties, and the dimensions of the flow path. This is based on principles derived from Bernoulli's equation and considers factors like viscosity and pipe resistance.
function calculateFlowRate() {
var pressureDifference = parseFloat(document.getElementById("pressureDifference").value);
var pipeDiameter = parseFloat(document.getElementById("pipeDiameter").value);
var pipeLength = parseFloat(document.getElementById("pipeLength").value);
var fluidViscosity = parseFloat(document.getElementById("fluidViscosity").value);
var fluidDensity = parseFloat(document.getElementById("fluidDensity").value);
var frictionFactor = parseFloat(document.getElementById("frictionFactor").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(pressureDifference) || isNaN(pipeDiameter) || isNaN(pipeLength) || isNaN(fluidViscosity) || isNaN(fluidDensity) || isNaN(frictionFactor)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (pipeDiameter <= 0 || pipeLength <= 0 || fluidViscosity <= 0 || fluidDensity <= 0 || frictionFactor <= 0 || pressureDifference < 0) {
resultDiv.innerHTML = "Please enter positive values for dimensions, viscosity, density, and friction factor, and a non-negative pressure difference.";
return;
}
// Calculate pipe radius
var pipeRadius = pipeDiameter / 2;
// Calculate pipe cross-sectional area
var pipeArea = Math.PI * Math.pow(pipeRadius, 2);
// Use Hagen-Poiseuille equation for laminar flow, but this calculator uses a more general approach considering friction factor for turbulent flow.
// The general formula for flow rate (Q) is often approximated using the Darcy-Weisbach equation for pressure drop,
// and then relating pressure drop back to flow rate. A common way to express flow rate from pressure difference, accounting for friction:
// Q = sqrt( (DeltaP * D^5) / (128 * mu * L) ) for laminar flow
// For turbulent flow, the Darcy-Weisbach equation for pressure drop is: DeltaP = f * (L/D) * (rho * V^2 / 2)
// where V = Q/A. Substituting V: DeltaP = f * (L/D) * (rho * (Q/A)^2 / 2)
// Rearranging for Q: Q = A * sqrt( (2 * DeltaP * D) / (f * L * rho) )
// This formula is a simplification and assumes turbulent flow or a known friction factor applicable to the flow regime.
// The friction factor itself depends on Reynolds number, which depends on flow rate, creating an iterative problem for precise turbulent flow.
// This calculator provides a direct calculation using a provided friction factor.
var flowRate = pipeArea * Math.sqrt((2 * pressureDifference * pipeDiameter) / (frictionFactor * pipeLength * fluidDensity));
// Convert to more common units for display if desired (e.g., Liters per minute)
var flowRateLPM = flowRate * 60 / 0.001; // m³/s to L/min
resultDiv.innerHTML = "