function calculateFlowRate() {
var pressure = parseFloat(document.getElementById("pressure").value);
var diameter = parseFloat(document.getElementById("diameter").value);
var pipeLength = parseFloat(document.getElementById("pipeLength").value);
var pipeRoughness = parseFloat(document.getElementById("pipeRoughness").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(pressure) || isNaN(diameter) || isNaN(pipeLength) || isNaN(pipeRoughness) ||
pressure <= 0 || diameter <= 0 || pipeLength <= 0 || pipeRoughness < 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields. Pipe roughness can be zero or positive.";
return;
}
// Constants
var gravity = 32.174; // ft/s^2
var waterDensity = 62.4; // lb/ft^3
var viscosity = 1.0e-5; // ft^2/s (approx. kinematic viscosity of water at room temp)
var conversionFactorGPM = 448.831; // to convert ft^3/s to GPM
// Convert pressure from psi to psf (pounds per square foot)
var pressure_psf = pressure * 144; // psf
// Calculate pipe radius
var radius = diameter / 24.0; // feet
// Calculate cross-sectional area
var area = Math.PI * radius * radius; // ft^2
// Calculate Reynolds number (Re) – initial guess for turbulent flow
// Re = (density * velocity * diameter) / viscosity
// We don't know velocity yet, so we'll use an iterative approach or a simplified equation.
// For simplicity and a common engineering approach, we'll use the Darcy-Weisbach equation
// and iterate or use a Moody diagram approximation implicitly.
// Hazen-Williams equation is often used for water flow, but Darcy-Weisbach is more fundamental for pressure/diameter.
// Let's use a simplified Darcy-Weisbach approach assuming turbulent flow and estimate friction factor.
// A common simplification for turbulent flow is to assume a friction factor.
// However, a more robust approach involves iteration or using a solver for the Colebrook equation.
// For this calculator, we'll implement a simplified approach that approximates the Colebrook equation.
// Initial guess for friction factor (e.g., using Blasius correlation for smooth pipes in turbulent flow)
// Or a rough initial guess for turbulent flow in rough pipes
var frictionFactor = 0.02; // Initial guess
// Iterative calculation for friction factor using Colebrook equation approximation (or simplified methods)
// Colebrook equation: 1/sqrt(f) = -2.0 * log10( (relative_roughness/3.7) + (2.51/Re)/sqrt(f) )
// where relative_roughness = pipeRoughness / diameter
var relativeRoughness = pipeRoughness / diameter;
var iterationLimit = 100;
var tolerance = 1e-6;
for (var i = 0; i v = sqrt( (2*g*h_L) / (f * L/D) )
// Head loss (h_L) in feet of water is P / density
var headLoss = pressure_psf / waterDensity; // feet of water
if (headLoss <= 0) {
resultDiv.innerHTML = "Pressure is too low to overcome head loss.";
return;
}
// Velocity (v) from Darcy-Weisbach: v = sqrt( (2 * g * D * h_L) / (f * L) )
// Substitute h_L = P_psf / rho
// v = sqrt( (2 * g * D * (P_psf / rho)) / (f * L) )
var velocity_m_s = Math.sqrt((2 * gravity * (diameter / 12.0) * headLoss) / (frictionFactor * pipeLength));
var reynoldsNumber = (waterDensity * velocity_m_s * (diameter / 12.0)) / (viscosity * waterDensity); // Using dynamic viscosity * density = kinematic viscosity
// Re = (velocity * diameter) / kinematic_viscosity
reynoldsNumber = (velocity_m_s * (diameter / 12.0)) / viscosity;
var calculatedFrictionFactor;
if (reynoldsNumber < 2300) { // Laminar flow
calculatedFrictionFactor = 64 / reynoldsNumber;
} else if (reynoldsNumber 4000.
// If Re is in this range, we might estimate using turbulent formulas and flag it.
// For this calc, let's just use a turbulent approximation here if Re is above laminar.
if (relativeRoughness === 0) { // Smooth pipe turbulent
calculatedFrictionFactor = 0.316 / Math.pow(reynoldsNumber, 0.25);
} else { // Rough pipe turbulent approximation
calculatedFrictionFactor = Math.pow(1.14 + 2 * Math.log10(diameter / (7.4 * pipeRoughness)), -2);
}
} else { // Turbulent flow
if (relativeRoughness === 0) { // Smooth pipe turbulent (Blasius for lower Re, or others for higher)
// Using explicit approximations for smooth pipes
if (reynoldsNumber < 100000) {
calculatedFrictionFactor = 0.316 / Math.pow(reynoldsNumber, 0.25);
} else {
// Haaland equation is a good explicit approximation for turbulent flow
calculatedFrictionFactor = Math.pow(1.8 * Math.log10(6.9 / reynoldsNumber) + 1.10, -2);
}
} else { // Rough pipe turbulent (Colebrook or explicit approximations like Haaland/Swamee-Jain)
// Using Haaland equation as an explicit approximation for Colebrook
calculatedFrictionFactor = Math.pow(1.8 * Math.log10((relativeRoughness / 3.7) + (6.9 / reynoldsNumber)) + 1.10, -2);
}
}
var diff = Math.abs(calculatedFrictionFactor – frictionFactor);
frictionFactor = calculatedFrictionFactor;
if (diff < tolerance) {
break; // Converged
}
if (i === iterationLimit – 1) {
resultDiv.innerHTML = "Calculation did not converge. Try adjusting inputs or use more advanced tools.";
return;
}
}
// Recalculate velocity with the converged friction factor
var velocity = Math.sqrt((2 * gravity * (diameter / 12.0) * headLoss) / (frictionFactor * pipeLength));
// Calculate flow rate in ft^3/s
var flowRate_ft3s = area * velocity;
// Convert to GPM
var flowRate_gpm = flowRate_ft3s * conversionFactorGPM;
resultDiv.innerHTML =
"Estimated Flow Rate: " + flowRate_gpm.toFixed(2) + " GPM" +
"Reynolds Number: " + reynoldsNumber.toFixed(0) + "" +
"Friction Factor: " + frictionFactor.toFixed(4) + "";
}
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font-family: sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ddd;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
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.calculator-inputs {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 15px;
margin-bottom: 20px;
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.input-group {
display: flex;
flex-direction: column;
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.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
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display: block;
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.calculator-container button:hover {
background-color: #0056b3;
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#result {
margin-top: 25px;
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border: 1px solid #eee;
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Understanding Water Flow Rate: Pressure, Pipe Diameter, and Friction
Calculating water flow rate is crucial for many applications, from plumbing and irrigation to industrial processes and firefighting. The flow rate, often measured in Gallons Per Minute (GPM), is not solely determined by the pressure at the source. Several other factors play a significant role, most notably the diameter of the pipe and the resistance to flow caused by friction. This calculator helps you estimate the flow rate by considering these key parameters.
Key Factors Influencing Flow Rate:
Pressure (psi): This is the force pushing the water through the pipe. Higher pressure generally leads to higher flow rates, assuming all other factors remain constant. It's typically measured in pounds per square inch (psi).
Pipe Inner Diameter (inches): The width of the inside of the pipe is a critical determinant of flow. A larger diameter pipe offers less resistance to flow, allowing more water to pass through at a given pressure compared to a smaller diameter pipe.
Pipe Length (feet): The longer the pipe, the more surface area there is for water to interact with, leading to increased frictional losses. Therefore, longer pipes will result in lower flow rates for the same pressure and diameter.
Pipe Roughness (inches): The internal surface of a pipe is never perfectly smooth. Roughness, whether from the material itself (like PVC vs. cast iron) or from sediment buildup over time, causes turbulence and friction, slowing down the water flow. This is often represented by a roughness height (e.g., in inches or millimeters).
The Physics Behind the Calculation (Darcy-Weisbach Equation):
This calculator utilizes principles derived from the Darcy-Weisbach equation, a fundamental formula in fluid dynamics used to calculate the head loss (energy loss due to friction) in pipes. The equation is:
$h_f = f \frac{L}{D} \frac{v^2}{2g}$
Where:
$h_f$ is the head loss due to friction (in feet of water).
$f$ is the Darcy friction factor (dimensionless).
$L$ is the pipe length (in feet).
$D$ is the pipe inner diameter (in feet).
$v$ is the average flow velocity (in feet per second).
$g$ is the acceleration due to gravity (approx. 32.174 ft/s²).
The head loss ($h_f$) can be directly related to the input pressure. The challenge in calculating flow rate is that the friction factor ($f$) itself depends on the flow velocity and the pipe's relative roughness (roughness divided by diameter). This relationship is often described by the Colebrook equation, which is implicit and requires iterative methods or approximations. This calculator employs an iterative approach to find a suitable friction factor.
Once the friction factor is determined, the velocity ($v$) can be calculated, and then the flow rate can be found using:
$Q = A \times v$
Where:
$Q$ is the volumetric flow rate (in cubic feet per second).
$A$ is the cross-sectional area of the pipe (in square feet).
The result is then converted to Gallons Per Minute (GPM) for common usability.
Example Calculation:
Let's consider a scenario:
Pressure: 60 psi
Pipe Inner Diameter: 1 inch
Pipe Length: 200 feet
Pipe Roughness (e.g., for PVC): 0.0005 inches
Inputting these values into the calculator will provide an estimated flow rate in GPM, taking into account the pressure available and the resistance from the pipe's diameter, length, and surface roughness. For these inputs, the calculator might yield approximately 14.5 GPM. This value indicates that about 14.5 gallons of water would flow through the pipe per minute under these specific conditions.
Important Considerations:
Units: Ensure consistency in units. This calculator uses psi for pressure, inches for diameter and roughness, and feet for length. The output is in GPM.
Fittings and Valves: This calculation primarily accounts for friction within straight pipe sections. Elbows, tees, valves, and other fittings add additional resistance (minor losses) that can significantly reduce flow rate, especially in systems with many fittings or complex layouts. For precise calculations, these must be accounted for separately.
Water Temperature: Water viscosity changes with temperature, which can slightly affect the Reynolds number and friction factor, particularly in transitional flow regimes. This calculator uses an average viscosity.
Actual vs. Theoretical: Real-world conditions can vary. The pipe roughness value is an approximation, and actual pipe conditions might differ due to wear, debris, or installation quality.
By understanding these factors and using this calculator, you can gain a better estimate of water flow rates for your specific projects.