.calculator-container {
font-family: Arial, sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-container h2 {
text-align: center;
margin-bottom: 20px;
color: #333;
}
.input-section {
margin-bottom: 15px;
}
.input-section label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-section input {
width: calc(100% – 20px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
button {
width: 100%;
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;
}
.result-section {
margin-top: 25px;
padding: 15px;
background-color: #e8f5e9;
border: 1px solid #a5d6a7;
border-radius: 4px;
text-align: center;
font-size: 18px;
color: #388e3c;
}
.result-section span {
font-weight: bold;
}
function calculateFlowRate() {
var pressurePSI = parseFloat(document.getElementById("pressurePSI").value);
var pipeDiameterInches = parseFloat(document.getElementById("pipeDiameterInches").value);
var pipeLengthFeet = parseFloat(document.getElementById("pipeLengthFeet").value);
var fluidViscosityCP = parseFloat(document.getElementById("fluidViscosityCP").value);
var pipeRoughnessInches = parseFloat(document.getElementById("pipeRoughnessInches").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
// Input validation
if (isNaN(pressurePSI) || pressurePSI < 0 ||
isNaN(pipeDiameterInches) || pipeDiameterInches <= 0 ||
isNaN(pipeLengthFeet) || pipeLengthFeet <= 0 ||
isNaN(fluidViscosityCP) || fluidViscosityCP <= 0 ||
isNaN(pipeRoughnessInches) || pipeRoughnessInches < 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
// — Calculations —
// This calculation is an approximation based on the Darcy-Weisbach equation and an iterative approach for friction factor (f).
// It's a complex fluid dynamics problem, and this is a simplified model.
// For high accuracy, specialized fluid dynamics software is recommended.
// Constants
var gravity = 32.174; // ft/s^2
var psiToPsf = 144; // psf/psi
var ftToIn = 12; // in/ft
var cpToLbfSecPerFtSq = 6.7197e-4; // conversion for dynamic viscosity
// Convert units to consistent system (e.g., feet, seconds, pounds)
var pressurePsf = pressurePSI * psiToPsf; // Pressure in pounds per square foot
var diameterFt = pipeDiameterInches / ftToIn; // Diameter in feet
var pipeAreaSqFt = Math.PI * Math.pow(diameterFt / 2, 2); // Cross-sectional area in square feet
var fluidViscosityLbfSecPerFtSq = fluidViscosityCP * cpToLbfSecPerFtSq; // Dynamic viscosity
// Assume water density for simplicity (can be a parameter if needed)
// Density of water at standard conditions is approx. 62.4 lb/ft³
var fluidDensityLbfSecSqPerFtFt4 = 62.4; // Density in lb/ft³ (slugs/ft³ * g)
// Initial guess for friction factor (f) – assume turbulent flow, Blasius correlation for smooth pipes
var frictionFactor = 0.02; // Initial guess
var ReynoldsNumber = 0.0;
var deltaPressureDrop = 0.0;
var iterations = 0;
var maxIterations = 100;
var tolerance = 1e-4;
// Iteratively solve for friction factor using the Colebrook equation (approximated)
// This is a simplified iterative loop. A more robust solution would use a solver.
do {
var relativeRoughness = pipeRoughnessInches / (diameterFt * ftToIn);
if (relativeRoughness <= 0) relativeRoughness = 1e-6; // Avoid division by zero if roughness is zero
// Reynolds Number calculation (needs velocity, which depends on f, creating a loop)
// Re = (density * velocity * diameter) / viscosity
// velocity = sqrt((2 * g * hf * diameter) / (f * length)) where hf = pressureDrop / (density*g)
// Simplifying: velocity = sqrt( (2 * pressurePsf * diameterFt) / (frictionFactor * pipeLengthFeet * fluidDensityLbfSecSqPerFtFt4) )
// This requires knowing velocity first, which is what we're trying to find.
// Let's try to calculate Re based on an *estimated* velocity and then iterate.
// We need an initial estimate of velocity. Let's assume f=0.02 for now to get an initial Re.
// This is a common starting point for iteration.
var initialVelocityGuess = Math.sqrt((2 * pressurePsf * diameterFt) / (0.02 * pipeLengthFeet * fluidDensityLbfSecSqPerFtFt4));
ReynoldsNumber = (fluidDensityLbfSecSqPerFtFt4 * initialVelocityGuess * diameterFt) / fluidViscosityLbfSecPerFtSq;
// If Reynolds number is low (laminar flow), use Poiseuille's law directly.
if (ReynoldsNumber < 2300) {
var velocity = (pressurePsf * Math.pow(diameterFt, 2)) / (128 * fluidViscosityLbfSecPerFtSq * pipeLengthFeet);
var flowRateGPM = velocity * pipeAreaSqFt * 60 * 7.48052; // GPM
resultDiv.innerHTML = "Flow Rate:
(Laminar Flow)";
return;
}
// Colebrook equation for friction factor (implicit, needs iteration)
// 1/sqrt(f) = -2.0 * log10( (relativeRoughness/3.7) + (2.51 / (Re * sqrt(f))) )
// We use an approximation for the implicit function or an iterative solver.
// For simplicity, using an explicit approximation like Swamee-Jain:
// f = 0.25 / ( log10( (relativeRoughness/3.7) + (5.74 / Re^0.9) )^2 )
var newFrictionFactor = 0.25 / Math.pow(Math.log10((relativeRoughness / 3.7) + (5.74 / Math.pow(ReynoldsNumber, 0.9))), 2);
if (Math.abs(newFrictionFactor – frictionFactor) maxIterations) {
resultDiv.innerHTML = "Calculation did not converge. Try adjusting inputs or check parameters.";
return;
}
} while (true); // Loop until convergence or max iterations
// Final calculation using the converged friction factor
var velocity = Math.sqrt((2 * pressurePsf * diameterFt) / (frictionFactor * pipeLengthFeet * fluidDensityLbfSecSqPerFtFt4));
var flowRateCubicFtPerSec = velocity * pipeAreaSqFt;
var flowRateGPM = flowRateCubicFtPerSec * 60 * 7.48052; // Convert to Gallons Per Minute
resultDiv.innerHTML = "Friction Factor (f):
Understanding the PSI to Flow Rate Calculator
This calculator helps estimate the volumetric flow rate of a fluid through a pipe, given the pressure difference, pipe dimensions, fluid properties, and pipe roughness. It's a crucial tool in various engineering disciplines, including mechanical, civil, and chemical engineering, for designing and analyzing fluid systems such as pipelines, irrigation systems, and hydraulic circuits.
The Science Behind the Calculation
The core of this calculation relies on fluid dynamics principles, primarily the Darcy-Weisbach equation. This equation relates the head loss (or pressure drop) due to friction in a pipe to the flow rate, pipe dimensions, and fluid properties.
The Darcy-Weisbach equation is often expressed as:
$h_f = f \frac{L}{D} \frac{v^2}{2g}$
Where:
- $h_f$ is the head loss due to friction (in feet of fluid).
- $f$ is the Darcy friction factor (dimensionless).
- $L$ is the length of the pipe (in feet).
- $D$ is the hydraulic diameter of the pipe (in feet).
- $v$ is the average velocity of the fluid (in feet per second).
- $g$ is the acceleration due to gravity (approximately 32.174 ft/s²).
To use this equation for flow rate ($Q$, typically in gallons per minute or GPM), we need to:
- Convert the input pressure (PSI) to head loss ($h_f$). 1 PSI is equivalent to approximately 2.31 feet of water head. This conversion depends on the fluid's density. Our calculator uses a standard density for water for simplicity.
- Relate velocity ($v$) to flow rate ($Q$) using the pipe's cross-sectional area ($A$). $Q = v \times A$. The area is calculated from the pipe's inner diameter.
- Determine the friction factor ($f$). This is the most complex part, as $f$ depends on both the Reynolds number (which indicates whether the flow is laminar or turbulent) and the relative roughness of the pipe (the ratio of pipe roughness to pipe diameter).
Reynolds Number (Re)
$Re = \frac{\rho v D}{\mu}$
Where:
- $\rho$ is the fluid density (e.g., lb·s²/ft⁴ or slugs/ft³).
- $v$ is the fluid velocity (ft/s).
- $D$ is the pipe diameter (ft).
- $\mu$ is the dynamic viscosity of the fluid (e.g., lb/(ft·s)).
Generally:
- $Re < 2300$: Laminar Flow (smooth, predictable flow). Poiseuille's Law is used here.
- $2300 \le Re \le 4000$: Transitional Flow (unpredictable).
- $Re > 4000$: Turbulent Flow (chaotic, more friction).
Friction Factor (f)
For laminar flow, $f = 64 / Re$.
For turbulent flow, the friction factor is determined using the Colebrook equation (an implicit equation) or its approximations like the Swamee-Jain equation (explicit). The Colebrook equation is:
$\frac{1}{\sqrt{f}} = -2.0 \log_{10} \left( \frac{\epsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}} \right)$
Where $\epsilon$ is the absolute roughness of the pipe.
Our calculator uses an iterative approach to solve for $f$ or uses an explicit approximation like Swamee-Jain, which provides a good estimate for turbulent flow conditions. The input 'Pipe Roughness' accounts for the material and condition of the pipe's inner surface.
How to Use the Calculator
- Pressure (PSI): Enter the pressure difference across the length of the pipe in pounds per square inch (PSI).
- Pipe Inner Diameter (inches): Input the internal diameter of the pipe in inches. Ensure this is the clear bore of the pipe.
- Pipe Length (feet): Enter the total length of the pipe section in feet over which the pressure drop occurs.
- Fluid Viscosity (cP – centipoise): Provide the dynamic viscosity of the fluid in centipoise. For water at room temperature, this is around 1 cP.
- Pipe Roughness (inches): Enter the typical roughness of the pipe's inner surface in inches. Common values include:
- 0.00015 inches for smooth steel pipes
- 0.0005 inches for cast iron pipes
- 0.005 inches for concrete pipes
If unsure, use a value for a smooth pipe.
Click "Calculate Flow Rate" to see the estimated flow rate in Gallons Per Minute (GPM), along with the calculated friction factor and Reynolds number.
Example Calculation
Let's calculate the flow rate of water through a 100-foot long, 2-inch inner diameter steel pipe with a pressure difference of 50 PSI. Assume the water viscosity is 1 cP and the pipe roughness is 0.00015 inches.
- Pressure: 50 PSI
- Pipe Inner Diameter: 2 inches
- Pipe Length: 100 feet
- Fluid Viscosity: 1 cP
- Pipe Roughness: 0.00015 inches
By entering these values into the calculator, you would receive an estimated flow rate. For these inputs, the calculator might output a flow rate of approximately 150 GPM, with a friction factor of around 0.02 and a Reynolds number indicating turbulent flow. This indicates that a 50 PSI pressure difference can drive a significant amount of water through a 2-inch steel pipe under these conditions.
Important Considerations
- Fluid Density: This calculator assumes the density of water. For other fluids, the density significantly impacts the flow rate, and a different calculator or manual adjustment would be needed.
- Minor Losses: This calculation only accounts for friction losses along the pipe length. Fittings, valves, bends, and sudden expansions/contractions cause additional "minor losses" that are not included here and can be significant in complex systems.
- Assumptions: The calculation is based on steady, incompressible flow in a full pipe.
- Accuracy: Fluid dynamics can be complex. This calculator provides an engineering estimate. For critical applications, consult specialized software or an experienced fluid dynamics engineer.