Calculate Flow Rate from Pressure and Pipe Size

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Flow Rate Calculator (Hazen-Williams Formula)

Results:

.calculator-container { font-family: sans-serif; border: 1px solid #ccc; padding: 20px; border-radius: 8px; max-width: 500px; margin: 20px auto; background-color: #f9f9f9; } .calculator-inputs { display: grid; grid-template-columns: 1fr; gap: 15px; } .input-group { display: flex; flex-direction: column; } .input-group label { margin-bottom: 5px; font-weight: bold; color: #333; } .input-group input { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1rem; } .calculator-inputs button { background-color: #4CAF50; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 1.1rem; transition: background-color 0.3s ease; } .calculator-inputs button:hover { background-color: #45a049; } .calculator-results { margin-top: 25px; padding-top: 20px; border-top: 1px solid #eee; } .calculator-results h3 { margin-bottom: 10px; color: #333; } #result { font-size: 1.1rem; color: #007bff; font-weight: bold; } function calculateFlowRate() { var diameterInches = parseFloat(document.getElementById("pipeDiameter").value); var lengthFeet = parseFloat(document.getElementById("pipeLength").value); var pressureDropPsi = parseFloat(document.getElementById("pressureDrop").value); var roughnessC = parseFloat(document.getElementById("pipeRoughness").value); var resultElement = document.getElementById("result"); resultElement.innerHTML = ""; // Clear previous results // Input validation if (isNaN(diameterInches) || diameterInches <= 0) { resultElement.innerHTML = "Please enter a valid pipe diameter (greater than 0)."; return; } if (isNaN(lengthFeet) || lengthFeet <= 0) { resultElement.innerHTML = "Please enter a valid pipe length (greater than 0)."; return; } if (isNaN(pressureDropPsi) || pressureDropPsi < 0) { resultElement.innerHTML = "Please enter a valid pressure drop (0 or greater)."; return; } if (isNaN(roughnessC) || roughnessC <= 0) { resultElement.innerHTML = "Please enter a valid Hazen-Williams C-factor (greater than 0)."; return; } // Constants for unit conversions var psiToPsf = 144; // 1 psi = 144 psf var feetPerSecondToGpm = 448.831; // Conversion factor for ft/s to GPM // Convert units for Hazen-Williams formula var diameterFeet = diameterInches / 12; // Diameter in feet var areaSqFeet = Math.PI * Math.pow(diameterFeet / 2, 2); // Cross-sectional area in sq ft var pressureDropPsf = pressureDropPsi * psiToPsf; // Pressure drop in psf // Hazen-Williams formula for velocity (v) in ft/s // v = 1.318 * C * R^0.63 * S^0.54 // Where: // C = Hazen-Williams roughness coefficient // R = Hydraulic radius (Area / Wetted Perimeter) = (pi * D^2 / 4) / (pi * D) = D / 4 // S = Slope of the hydraulic grade line = Pressure Drop (psf) / Length (ft) var hydraulicRadiusFeet = diameterFeet / 4; var slope = pressureDropPsf / lengthFeet; var velocityFps = 1.318 * roughnessC * Math.pow(hydraulicRadiusFeet, 0.63) * Math.pow(slope, 0.54); // Calculate flow rate (Q) in GPM // Q = Velocity (ft/s) * Area (sq ft) * Conversion Factor (GPM / (ft/s * sq ft)) var flowRateGpm = velocityFps * areaSqFeet * feetPerSecondToGpm; resultElement.innerHTML = "Flow Rate: " + flowRateGpm.toFixed(2) + " GPM"; }

Understanding the Flow Rate Calculator (Hazen-Williams Formula)

This calculator helps determine the flow rate of a fluid through a pipe system based on its physical characteristics. It utilizes the widely accepted Hazen-Williams formula, a semi-empirical formula commonly used in the design of water distribution systems.

What is Flow Rate?

Flow rate, often measured in gallons per minute (GPM) or liters per second (LPS), represents the volume of fluid that passes through a given point in a pipe system per unit of time. It's a crucial parameter for understanding system capacity, pressure requirements, and potential performance issues.

The Hazen-Williams Formula

The Hazen-Williams formula is specifically designed for the turbulent flow of water in pipes and is expressed as:

v = 1.318 * C * R^0.63 * S^0.54

Where:

  • v is the average velocity of the fluid in feet per second (ft/s).
  • C is the Hazen-Williams roughness coefficient. This value depends on the pipe material and its condition. Higher values indicate smoother pipes (e.g., 130 for new steel, 100 for old, pitted cast iron).
  • R is the hydraulic radius of the pipe, calculated as the cross-sectional area of the flow divided by the wetted perimeter of the pipe. For a full circular pipe, R = D/4, where D is the pipe diameter.
  • S is the slope of the hydraulic grade line, representing the energy loss per unit length of the pipe. It is calculated as the total pressure drop divided by the pipe length.

The calculator then converts this velocity into a flow rate (Q) using the formula:

Q = v * A

Where A is the cross-sectional area of the pipe.

Inputs Explained:

  • Pipe Diameter (inches): The internal diameter of the pipe.
  • Pipe Length (feet): The total length of the pipe segment through which the pressure drop is measured.
  • Pressure Drop (psi): The difference in pressure between the start and end of the pipe segment. This pressure drop is what drives the flow.
  • Hazen-Williams C-Factor: A coefficient representing the internal smoothness of the pipe. Common values are provided as examples in the input label.

How to Use the Calculator:

Enter the values for pipe diameter, pipe length, pressure drop, and the appropriate Hazen-Williams C-factor for your pipe material. Click "Calculate Flow Rate" to see the estimated flow in gallons per minute (GPM).

Example:

Consider a 4-inch diameter pipe that is 100 feet long. There is a pressure drop of 10 psi over this length, and the pipe is made of new steel with a C-factor of 130. Plugging these values into the calculator:

  • Pipe Diameter: 4 inches
  • Pipe Length: 100 feet
  • Pressure Drop: 10 psi
  • Hazen-Williams C-Factor: 130

The calculator would output an estimated flow rate. For these values, the result is approximately 346.99 GPM.

Important Considerations:

  • The Hazen-Williams formula is most accurate for water. For other fluids, different formulas may be more appropriate.
  • The C-factor can change over time as pipes age and accumulate scale or corrosion.
  • This calculation assumes a full, steady-state flow.
  • Minor losses due to fittings, valves, and bends are not accounted for in this simplified model.

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