Calculating the flow rate of water through a pipe is a fundamental task in fluid dynamics, plumbing, and irrigation engineering. The flow rate depends primarily on the physical dimensions of the pipe (specifically the inner diameter) and the velocity at which the fluid is moving.
The core formula used in this calculator is:
Q = A × V
Where:
Q is the volumetric flow rate.
A is the cross-sectional area of the pipe.
V is the average velocity of the fluid.
Step-by-Step Calculation Logic
To perform this calculation manually, follow these steps:
Determine the Inner Diameter (ID): It is crucial to use the inner diameter of the pipe, not the outer diameter, as the wall thickness reduces the available area for flow.
Calculate the Cross-Sectional Area (A): For a circular pipe, the area is calculated as:
A = π × (Diameter / 2)² or A = (π × Diameter²) / 4.
Measure the Velocity (V): This is the speed at which the water travels through the pipe, typically measured in meters per second (m/s) or feet per second (ft/s).
Multiply Area by Velocity: The product gives you the flow rate.
Example Calculation
Let's say you have a pipe with an inner diameter of 2 inches and water flowing at a velocity of 5 feet per second.
First, convert units to a standard metric (or imperial) system. 2 inches ≈ 0.0508 meters.
Radius = 0.0254 meters.
Area (A) = 3.14159 × (0.0254)² ≈ 0.002027 m².
Velocity (V) = 5 ft/s ≈ 1.524 m/s.
Flow Rate (Q) = 0.002027 m² × 1.524 m/s ≈ 0.003089 m³/s.
Converting to Gallons Per Minute (GPM): ≈ 48.96 GPM.
Factors Affecting Flow Rate
While this geometric calculator provides the theoretical flow rate based on velocity and area, real-world systems are affected by:
Friction Loss: As water rubs against the pipe walls, pressure decreases, which can affect velocity.
Viscosity: Thicker fluids flow differently than water.
Pipe Roughness: Old, corroded pipes create more turbulence than smooth PVC or copper pipes.
function calculateWaterFlow() {
// 1. Get DOM elements
var diameterInput = document.getElementById('pipeDiameter');
var diameterUnitSelect = document.getElementById('diameterUnit');
var velocityInput = document.getElementById('flowVelocity');
var velocityUnitSelect = document.getElementById('velocityUnit');
var resultBox = document.getElementById('flowResult');
var areaDisplay = document.getElementById('areaResult');
var lpmDisplay = document.getElementById('resultLPM');
var gpmDisplay = document.getElementById('resultGPM');
var cmhDisplay = document.getElementById('resultCMH');
var cfsDisplay = document.getElementById('resultCFS');
// 2. Parse values
var diameter = parseFloat(diameterInput.value);
var velocity = parseFloat(velocityInput.value);
var diameterUnit = diameterUnitSelect.value;
var velocityUnit = velocityUnitSelect.value;
// 3. Validate Inputs
if (isNaN(diameter) || diameter <= 0) {
alert("Please enter a valid positive number for the Pipe Diameter.");
return;
}
if (isNaN(velocity) || velocity < 0) {
alert("Please enter a valid number for the Water Velocity.");
return;
}
// 4. Normalize to SI Units (Meters for distance, Meters/Second for velocity)
// Convert Diameter to Meters
var diameterInMeters = 0;
if (diameterUnit === 'mm') {
diameterInMeters = diameter / 1000;
} else if (diameterUnit === 'inch') {
diameterInMeters = diameter * 0.0254;
} else if (diameterUnit === 'ft') {
diameterInMeters = diameter * 0.3048;
} else {
// Default meters
diameterInMeters = diameter;
}
// Convert Velocity to Meters/Second
var velocityInMS = 0;
if (velocityUnit === 'fts') {
velocityInMS = velocity * 0.3048;
} else if (velocityUnit === 'mph') {
velocityInMS = velocity * 0.44704;
} else {
// Default m/s
velocityInMS = velocity;
}
// 5. Calculate Area (A = pi * r^2)
var radius = diameterInMeters / 2;
var areaM2 = Math.PI * Math.pow(radius, 2);
// 6. Calculate Flow Rate (Q = A * V) in Cubic Meters per Second (m^3/s)
var flowRateM3S = areaM2 * velocityInMS;
// 7. Convert Results to various units
// 1 m3/s = 60000 L/min
var flowLPM = flowRateM3S * 60000;
// 1 m3/s = 15850.32314 US GPM
var flowGPM = flowRateM3S * 15850.32314;
// 1 m3/s = 3600 m3/h
var flowCMH = flowRateM3S * 3600;
// 1 m3/s = 35.3146667 cubic feet per second
var flowCFS = flowRateM3S * 35.3146667;
// 8. Update Display
areaDisplay.innerHTML = areaM2.toFixed(6) + " m²";
lpmDisplay.innerHTML = flowLPM.toFixed(2) + " L/min";
gpmDisplay.innerHTML = flowGPM.toFixed(2) + " GPM";
cmhDisplay.innerHTML = flowCMH.toFixed(2) + " m³/h";
cfsDisplay.innerHTML = flowCFS.toFixed(4) + " cfs";
// Show result box
resultBox.style.display = "block";
}