Flow Rate to Pressure Calculator

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Understanding Flow Rate and Pressure

Pressure and flow rate are fundamental concepts in fluid dynamics. Pressure is the force exerted by a fluid per unit area, while flow rate is the volume of fluid that passes through a given point per unit time. These two quantities are intimately related, especially within a closed system where fluid is moving through pipes or conduits.

The relationship between flow rate and pressure drop in a pipe is governed by various physical principles, including Bernoulli's principle and the Hagen-Poiseuille equation (for laminar flow in pipes). For simpler calculations and common engineering applications, we often rely on empirical relationships and approximations.

In many practical scenarios, such as plumbing systems, industrial processes, or even biological systems, understanding how changing the flow rate will affect the pressure (or vice-versa) is crucial for system design, operation, and troubleshooting. For instance, a higher flow rate generally leads to a greater pressure drop due to increased friction and kinetic energy losses within the fluid as it moves through the system.

This calculator helps to estimate the pressure exerted by a fluid given its flow rate, along with other system parameters. By inputting the known values, you can gain insight into the expected pressure dynamics of your fluid system.

Flow Rate to Pressure Calculator

Gallons per Minute (GPM) Liters per Minute (LPM) Cubic Meters per Hour (m³/hr)
Inches Centimeters Millimeters
Feet Meters
Pounds per Cubic Foot (lb/ft³) Kilograms per Cubic Meter (kg/m³) Grams per Cubic Centimeter (g/cm³)
Centipoise (cP) Pascal-seconds (Pa·s) Poise
function calculatePressure() { var flowRate = parseFloat(document.getElementById("flowRate").value); var flowRateUnit = document.getElementById("flowRateUnit").value; var pipeDiameter = parseFloat(document.getElementById("pipeDiameter").value); var diameterUnit = document.getElementById("diameterUnit").value; var pipeLength = parseFloat(document.getElementById("pipeLength").value); var lengthUnit = document.getElementById("lengthUnit").value; var fluidDensity = parseFloat(document.getElementById("fluidDensity").value); var densityUnit = document.getElementById("densityUnit").value; var fluidViscosity = parseFloat(document.getElementById("fluidViscosity").value); var viscosityUnit = document.getElementById("viscosityUnit").value; var resultDiv = document.getElementById("result"); resultDiv.innerHTML = ""; // Clear previous results if (isNaN(flowRate) || isNaN(pipeDiameter) || isNaN(pipeLength) || isNaN(fluidDensity) || isNaN(fluidViscosity) || flowRate <= 0 || pipeDiameter <= 0 || pipeLength <= 0 || fluidDensity <= 0 || fluidViscosity <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for all fields."; return; } // — Unit Conversions to a consistent base (e.g., SI units for intermediate calculations) — // Flow Rate to m³/s var flowRate_m3_s; if (flowRateUnit === "gpm") { flowRate_m3_s = flowRate * 0.0000630902; // 1 GPM = 0.0000630902 m³/s } else if (flowRateUnit === "lpm") { flowRate_m3_s = flowRate * 0.0000166667; // 1 LPM = 0.0000166667 m³/s } else { // m3_hr flowRate_m3_s = flowRate / 3600; // 1 m³/hr = 1/3600 m³/s } // Diameter to meters var pipeDiameter_m; if (diameterUnit === "inches") { pipeDiameter_m = pipeDiameter * 0.0254; // 1 inch = 0.0254 m } else if (diameterUnit === "cm") { pipeDiameter_m = pipeDiameter * 0.01; // 1 cm = 0.01 m } else { // mm pipeDiameter_m = pipeDiameter * 0.001; // 1 mm = 0.001 m } // Length to meters var pipeLength_m; if (lengthUnit === "feet") { pipeLength_m = pipeLength * 0.3048; // 1 foot = 0.3048 m } else { // meters pipeLength_m = pipeLength; } // Density to kg/m³ var fluidDensity_kg_m3; if (densityUnit === "lb_ft3") { fluidDensity_kg_m3 = fluidDensity * 16.0185; // 1 lb/ft³ = 16.0185 kg/m³ } else if (densityUnit === "g_cm3") { fluidDensity_kg_m3 = fluidDensity * 1000; // 1 g/cm³ = 1000 kg/m³ } else { // kg_m3 fluidDensity_kg_m3 = fluidDensity; } // Viscosity to Pa·s var fluidViscosity_Pa_s; if (viscosityUnit === "cP") { fluidViscosity_Pa_s = fluidViscosity * 0.001; // 1 cP = 0.001 Pa·s } else if (viscosityUnit === "poise") { fluidViscosity_Pa_s = fluidViscosity * 0.1; // 1 Poise = 0.1 Pa·s } else { // Pa_s fluidViscosity_Pa_s = fluidViscosity; } // — Calculations — // Calculate cross-sectional area (A) var pipeRadius_m = pipeDiameter_m / 2; var pipeArea_m2 = Math.PI * Math.pow(pipeRadius_m, 2); // Calculate velocity (v) var velocity_m_s = flowRate_m3_s / pipeArea_m2; // Calculate Reynolds Number (Re) to determine flow regime (laminar vs. turbulent) var reynoldsNumber = (fluidDensity_kg_m3 * velocity_m_s * pipeDiameter_m) / fluidViscosity_Pa_s; var frictionFactor; var pressureDrop_Pa; // Pressure drop in Pascals // Use Darcy-Weisbach equation for pressure drop // First, determine friction factor (f) if (reynoldsNumber < 2300) { // Laminar Flow // For laminar flow, the Darcy friction factor is 64/Re frictionFactor = 64 / reynoldsNumber; } else { // Turbulent Flow (Simplified using Colebrook-White or Haaland approximation for demonstration) // Using Haaland approximation for simplicity as it's explicit for f // epsilon is roughness of the pipe. Assuming a smooth pipe (epsilon = 0) for simplicity here. // For a more accurate calculation, pipe roughness would be needed. var epsilon = 0; // Assume smooth pipe for this example var roughness = epsilon / pipeDiameter_m; // Haaland approximation for friction factor (f) var term1 = -1.8 * Math.log10((roughness / 3.7) + Math.pow(6.9 / reynoldsNumber, 1.11)); frictionFactor = Math.pow(1 / term1, 2); // Note: For a more rigorous approach, the Colebrook-White equation (implicit) or Moody chart would be used. // A common simplification for turbulent flow is to use a constant friction factor or a simpler empirical formula, // but Haaland provides a good explicit approximation. } // Calculate pressure drop (ΔP) using Darcy-Weisbach equation // ΔP = f * (L/D) * (ρ * v²/2) pressureDrop_Pa = frictionFactor * (pipeLength_m / pipeDiameter_m) * (fluidDensity_kg_m3 * Math.pow(velocity_m_s, 2) / 2); // Convert pressure drop to more common units (e.g., psi or kPa) var pressureDrop_psi = pressureDrop_Pa * 0.000145038; // 1 Pa = 0.000145038 psi var pressureDrop_kPa = pressureDrop_Pa / 1000; // 1 kPa = 1000 Pa // Display results var resultHTML = "

Calculation Results:

"; resultHTML += "Velocity: " + velocity_m_s.toFixed(3) + " m/s"; resultHTML += "Reynolds Number: " + reynoldsNumber.toFixed(2) + ""; resultHTML += "Friction Factor: " + frictionFactor.toFixed(4) + ""; resultHTML += "Pressure Drop: " + pressureDrop_psi.toFixed(3) + " PSI"; resultHTML += "Pressure Drop: " + pressureDrop_kPa.toFixed(3) + " kPa"; resultHTML += "Pressure Drop: " + pressureDrop_Pa.toFixed(2) + " Pa"; resultDiv.innerHTML = resultHTML; } .calculator-container { font-family: sans-serif; display: flex; flex-wrap: wrap; gap: 20px; margin-bottom: 20px; } .article-content { flex: 1; min-width: 300px; } .calculator-interface { flex: 1; min-width: 300px; border: 1px solid #ccc; padding: 20px; border-radius: 8px; background-color: #f9f9f9; } .calculator-interface h3 { margin-top: 0; color: #333; } .input-group { margin-bottom: 15px; display: flex; align-items: center; gap: 10px; } .input-group label { display: block; margin-bottom: 5px; font-weight: bold; flex: 1; min-width: 150px; /* Adjust as needed */ } .input-group input[type="number"] { padding: 8px; border: 1px solid #ccc; border-radius: 4px; width: 80px; /* Fixed width for number input */ } .input-group select { padding: 8px; border: 1px solid #ccc; border-radius: 4px; } .calculator-interface button { background-color: #4CAF50; color: white; padding: 10px 15px; border: none; border-radius: 4px; cursor: pointer; font-size: 16px; margin-top: 10px; } .calculator-interface button:hover { background-color: #45a049; } #result { margin-top: 20px; padding: 15px; border: 1px solid #ddd; border-radius: 4px; background-color: #fff; } #result h3 { margin-top: 0; color: #007bff; }

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