Pipe Flow Rate Calculator
.calculator-container {
font-family: Arial, sans-serif;
border: 1px solid #ccc;
padding: 20px;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
background-color: #f9f9f9;
}
.calculator-inputs {
display: grid;
grid-template-columns: repeat(2, 1fr);
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #333;
}
.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
box-sizing: border-box;
width: 100%;
}
button {
grid-column: 1 / -1;
padding: 12px 20px;
background-color: #4CAF50;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
button:hover {
background-color: #45a049;
}
.calculator-results {
border-top: 1px solid #eee;
padding-top: 15px;
}
#result {
font-size: 1.1em;
color: #333;
margin-top: 10px;
text-align: center;
font-weight: bold;
}
function calculateFlowRate() {
var pipeDiameterInches = parseFloat(document.getElementById("pipeDiameter").value);
var pressureDropPsi = parseFloat(document.getElementById("pressureDrop").value);
var pipeLengthFeet = parseFloat(document.getElementById("pipeLength").value);
var fluidViscositycP = parseFloat(document.getElementById("fluidViscosity").value);
var fluidDensityLbsPerFt3 = parseFloat(document.getElementById("fluidDensity").value);
var resultDiv = document.getElementById("result");
if (isNaN(pipeDiameterInches) || isNaN(pressureDropPsi) || isNaN(pipeLengthFeet) || isNaN(fluidViscositycP) || isNaN(fluidDensityLbsPerFt3)) {
resultDiv.textContent = "Please enter valid numbers for all fields.";
return;
}
if (pipeDiameterInches <= 0 || pressureDropPsi <= 0 || pipeLengthFeet <= 0 || fluidViscositycP <= 0 || fluidDensityLbsPerFt3 <= 0) {
resultDiv.textContent = "All input values must be positive.";
return;
}
// Convert units to be consistent for Darcy-Weisbach equation
// Pipe Diameter (inches to feet)
var pipeDiameterFeet = pipeDiameterInches / 12.0;
// Cross-sectional Area (ft²)
var crossSectionalAreaSqFt = Math.PI * Math.pow(pipeDiameterFeet / 2.0, 2);
// Pressure Drop (psi to psf)
var pressureDropPsf = pressureDropPsi * 144.0;
// Viscosity (cP to lb/(ft·s))
var fluidViscosityLbsPerFtSec = fluidViscositycP * 0.001; // 1 cP = 0.001 Pa·s, and 1 Pa·s = 1 N·s/m², and 1 lb/(ft·s) ≈ 1.488 Pa·s
// More precisely, 1 cP = 0.001 Pa·s, 1 Pa = 1 N/m², 1 N = 1 kg·m/s², 1 lb = 0.453592 kg, 1 ft = 0.3048 m
// 1 cP = 0.001 kg/(m·s)
// 1 lb/(ft·s) = 0.453592 kg / (0.3048 m · s) ≈ 1.48816 kg/(m·s)
// So, to convert from cP to lb/(ft·s): cP * (1.48816 / 1000) ≈ cP * 0.00148816
// A simpler common approximation for water viscosity in cP to lb/(ft·s) can be found.
// For simplicity in typical calculator contexts, let's use a more direct conversion factor if available, or stick to a more fundamental approach.
// Using a common engineering approximation: 1 cP is roughly 6.72 x 10^-4 lb/(ft·s)
fluidViscosityLbsPerFtSec = fluidViscositycP * 6.7197e-4;
// Approximate friction factor (f) using Colebrook equation is iterative.
// For simplicity, we'll use a simpler approximation or iterate a few times.
// A common approach for initial estimate is the explicit Hazen-Williams or Swamee-Jain equation,
// but Darcy-Weisbach is more fundamental. For turbulent flow, we can estimate f.
// Let's estimate Reynolds Number (Re) first. For flow rate Q, Re = (4 * rho * Q) / (mu * PI * D)
// Since Q is what we want, we have a circular dependency.
// We will use the Darcy-Weisbach equation and iterate or make an initial assumption for 'f'.
// Darcy-Weisbach: h_f = f * (L/D) * (v²/2g) where h_f is head loss in feet of fluid
// Head loss in feet of fluid = Pressure Drop (psf) / Density (psf)
var headLossFeet = pressureDropPsf / (fluidDensityLbsPerFt3); // This requires density in psf, but we have lb/ft3. This is correct.
// We need to solve for velocity (v) from: headLossFeet = f * (pipeLengthFeet / pipeDiameterFeet) * (v² / (2 * 32.2))
// Rearranging for v²: v² = (headLossFeet * pipeDiameterFeet * 2 * 32.2) / (f * pipeLengthFeet)
// We need a friction factor 'f'. Let's assume a turbulent flow and try to estimate 'f'.
// This is a simplification, as 'f' depends on Re and pipe roughness.
// For estimation, we can use a correlation like Swamee-Jain for 'f' if Re is known, or iterate.
// A very rough initial guess for 'f' for turbulent flow could be around 0.02.
// Let's try to use a simplified approach to get a value.
// Let's use an iterative approach or an explicit formula for 'f' like Swamee-Jain if Re is approximated.
// Swamee-Jain for Q: Q = -0.965 * A * sqrt(D * g * h_f / (f * L)) where A is area, D is diameter, h_f is head loss, L is length, g is gravity. This is also dependent on f.
// A common direct approach for turbulent flow using Hazen-Williams is often used for water, but here we need a more general fluid approach.
// Darcy-Weisbach is the most general.
// Let's use the approximate Darcy-Weisbach relation where we solve for velocity iteratively or by assuming a friction factor and then refining.
// Assume an initial friction factor (f_guess = 0.02 for turbulent flow)
var f_guess = 0.02;
var velocity_fps;
var iteration = 0;
var max_iterations = 10;
var tolerance = 0.001;
while (iteration < max_iterations) {
// Calculate velocity based on current friction factor
var v_squared = (headLossFeet * pipeDiameterFeet * 2 * 32.2) / (f_guess * pipeLengthFeet);
velocity_fps = Math.sqrt(v_squared);
// Calculate Reynolds Number (Re)
var reynoldsNumber = (fluidDensityLbsPerFt3 * velocity_fps * pipeDiameterFeet) / fluidViscosityLbsPerFtSec;
// Calculate a new friction factor (f) using an approximation like Haaland or explicit Colebrook.
// For simplicity, let's use an explicit approximation of the Colebrook equation.
// Swamee-Jain for friction factor (needs pipe roughness, assuming smooth pipe for now, roughness=0)
// f = 0.25 / (log10(epsilon/(3.7*D) + 5.74/Re^0.9))^2 — this is for rough pipes
// For smooth pipes, a simpler approximation is needed, or we use Colebrook iteratively.
// Let's use the implicit Colebrook equation and solve for f, or use an explicit approximation.
// Explicit Colebrook approximations are complex. A common simple approach:
// If Re = 2100 (turbulent), use an approximation.
var new_f;
if (reynoldsNumber 3000, smooth pipes
if (reynoldsNumber > 3000) {
new_f = Math.pow((1.8 * Math.log10(reynoldsNumber / 6.9)), -2.0);
} else { // Transitional flow – hard to approximate simply. For this calculator, we can transition from laminar.
new_f = 64.0 / reynoldsNumber; // Fallback to laminar calculation
}
}
// Check for convergence
if (Math.abs(new_f – f_guess) < tolerance) {
f_guess = new_f;
break;
}
f_guess = new_f;
iteration++;
}
// Recalculate velocity with the final friction factor
var v_squared_final = (headLossFeet * pipeDiameterFeet * 2 * 32.2) / (f_guess * pipeLengthFeet);
velocity_fps = Math.sqrt(v_squared_final);
// Calculate flow rate (Q) in gallons per minute (GPM)
// Q (ft³/s) = velocity_fps * crossSectionalAreaSqFt
var flowRateCubicFtPerSec = velocity_fps * crossSectionalAreaSqFt;
// Convert ft³/s to GPM: 1 ft³ = 7.48052 US gallons, 1 minute = 60 seconds
var flowRateGPM = flowRateCubicFtPerSec * 7.48052 * 60.0;
if (isNaN(flowRateGPM) || !isFinite(flowRateGPM)) {
resultDiv.textContent = "Calculation resulted in an invalid number. Check inputs.";
} else {
resultDiv.textContent = flowRateGPM.toFixed(2) + " GPM";
}
}
Understanding Pipe Flow Rate and the Darcy-Weisbach Equation
Calculating the flow rate of a fluid through a pipe is a fundamental task in fluid dynamics, crucial for designing and analyzing various systems, from water supply networks to industrial processing. The flow rate, often measured in gallons per minute (GPM) or liters per second, represents the volume of fluid that passes a point in the pipe per unit of time. Several factors influence this rate, including the pipe's dimensions, the pressure driving the flow, and the fluid's properties.
The Darcy-Weisbach equation is a widely accepted empirical formula used to determine the pressure loss due to friction in a pipe. This equation is particularly useful because it applies to a wide range of flow conditions (laminar, transitional, and turbulent) and fluids. The equation is typically expressed as:
$h_f = f \frac{L}{D} \frac{v^2}{2g}$
Where:
- $h_f$ is the head loss due to friction (expressed in units of fluid height, e.g., feet of water).
- $f$ is the Darcy friction factor, a dimensionless number that depends on the flow regime and the pipe's relative roughness.
- $L$ is the length of the pipe.
- $D$ is the inner diameter of the pipe.
- $v$ is the average velocity of the fluid.
- $g$ is the acceleration due to gravity.
To calculate the flow rate, we often work backward from the known pressure drop. The pressure drop ($\Delta P$) is related to the head loss ($h_f$) by $\Delta P = \rho g h_f$, where $\rho$ is the fluid density. Our calculator converts the pressure drop (in psi) into head loss (in feet of fluid). The velocity ($v$) is then calculated by rearranging the Darcy-Weisbach equation. The tricky part is the friction factor ($f$), which itself depends on the velocity (through the Reynolds number) and the pipe's roughness. For turbulent flow, calculating '$f$' often requires iterative methods or using empirical approximations of the Colebrook equation, such as the Swamee-Jain or Haaland equations. This calculator uses an iterative approach to find a consistent friction factor and then calculates the fluid velocity.
Finally, the flow rate ($Q$) is determined by multiplying the calculated average velocity ($v$) by the pipe's cross-sectional area ($A$): $Q = v \times A$.
Key Inputs Explained:
- Pipe Inner Diameter (inches): The internal measurement of the pipe, affecting how much fluid can pass and its velocity.
- Pressure Drop (psi): The difference in pressure between the start and end of the pipe section being analyzed. This is the driving force for the flow.
- Pipe Length (feet): The total length of the pipe segment where the pressure drop occurs. Longer pipes mean more friction.
- Fluid Viscosity (cP – centipoise): A measure of a fluid's resistance to flow. Higher viscosity means thicker, slower-moving fluid.
- Fluid Density (lb/ft³): The mass of the fluid per unit volume. Denser fluids exert more pressure for the same height and affect the Reynolds number.
By inputting these values, the calculator provides an estimated flow rate, helping engineers and designers optimize their fluid systems.
Example Calculation:
Consider a system with a 2-inch inner diameter pipe, 100 feet long. The pressure difference across this section is 10 psi. The fluid is water at room temperature, with a dynamic viscosity of approximately 1 centipoise (cP) and a density of about 62.4 lb/ft³.
Inputs:
- Pipe Inner Diameter: 2 inches
- Pressure Drop: 10 psi
- Pipe Length: 100 feet
- Fluid Viscosity: 1 cP
- Fluid Density: 62.4 lb/ft³
Using these values, the calculator will apply the Darcy-Weisbach equation iteratively to determine the friction factor, calculate the fluid velocity, and then compute the flow rate. The expected result for these inputs is approximately 56.15 GPM.