body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-wrapper {
background-color: #f0f7ff;
border: 1px solid #cce4ff;
border-radius: 8px;
padding: 25px;
margin-bottom: 30px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-header {
text-align: center;
margin-bottom: 20px;
color: #0056b3;
}
.input-group {
margin-bottom: 15px;
}
.input-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
color: #2c3e50;
}
.input-row {
display: flex;
gap: 10px;
}
input[type="number"], select {
width: 100%;
padding: 10px;
border: 1px solid #ddd;
border-radius: 4px;
font-size: 16px;
}
button.calc-btn {
background-color: #007bff;
color: white;
border: none;
padding: 12px 20px;
font-size: 16px;
font-weight: bold;
border-radius: 4px;
cursor: pointer;
width: 100%;
margin-top: 10px;
transition: background-color 0.2s;
}
button.calc-btn:hover {
background-color: #0056b3;
}
#result-container {
margin-top: 25px;
display: none;
background-color: white;
padding: 20px;
border-radius: 4px;
border-left: 5px solid #007bff;
}
.result-item {
display: flex;
justify-content: space-between;
border-bottom: 1px solid #eee;
padding: 10px 0;
}
.result-item:last-child {
border-bottom: none;
}
.result-label {
color: #666;
}
.result-value {
font-weight: bold;
color: #333;
}
.calculation-breakdown {
margin-top: 20px;
padding: 15px;
background-color: #fafafa;
border: 1px dashed #ccc;
font-family: monospace;
font-size: 14px;
}
h2 { margin-top: 40px; border-bottom: 2px solid #eee; padding-bottom: 10px; }
h3 { margin-top: 25px; color: #444; }
.formula-box {
background: #f9f9f9;
padding: 15px;
border-left: 4px solid #666;
margin: 15px 0;
font-style: italic;
}
.example-block {
background-color: #fff8e1;
padding: 15px;
border: 1px solid #ffe0b2;
border-radius: 5px;
}
function calculateFlowRate() {
// Get Inputs
var diameterInput = document.getElementById('pipeDiameter').value;
var velocityInput = document.getElementById('flowVelocity').value;
var diameterUnit = document.getElementById('diameterUnit').value;
var velocityUnit = document.getElementById('velocityUnit').value;
// Validation
if (diameterInput === "" || velocityInput === "" || isNaN(diameterInput) || isNaN(velocityInput)) {
alert("Please enter valid numbers for diameter and velocity.");
return;
}
var d = parseFloat(diameterInput);
var v = parseFloat(velocityInput);
if (d <= 0 || v < 0) {
alert("Diameter must be positive and velocity cannot be negative.");
return;
}
// 1. Convert Diameter to Meters
var diameterInMeters = 0;
var unitText = "";
if (diameterUnit === 'mm') {
diameterInMeters = d / 1000;
unitText = "mm";
} else if (diameterUnit === 'cm') {
diameterInMeters = d / 100;
unitText = "cm";
} else if (diameterUnit === 'inch') {
diameterInMeters = d * 0.0254;
unitText = "inches";
} else {
diameterInMeters = d;
unitText = "m";
}
// 2. Convert Velocity to m/s
var velocityInMS = 0;
if (velocityUnit === 'ft_s') {
velocityInMS = v * 0.3048;
} else {
velocityInMS = v;
}
// 3. Calculate Area (A = pi * r^2 = pi * (d/2)^2)
var radius = diameterInMeters / 2;
var area = Math.PI * Math.pow(radius, 2);
// 4. Calculate Flow Rate Q = A * v (Result in m^3/s)
var flowRateM3S = area * velocityInMS;
// 5. Conversions
var flowRateLPM = flowRateM3S * 60000; // m3/s to L/min
var flowRateM3H = flowRateM3S * 3600; // m3/s to m3/h
var flowRateGPM = flowRateLPM / 3.78541; // L/min to US Gallons/min
// Display Results
document.getElementById('result-container').style.display = 'block';
document.getElementById('res_m3s').innerHTML = flowRateM3S.toExponential(4) + " m³/s";
document.getElementById('res_lpm').innerHTML = flowRateLPM.toFixed(2) + " L/min";
document.getElementById('res_m3h').innerHTML = flowRateM3H.toFixed(2) + " m³/h";
document.getElementById('res_gpm').innerHTML = flowRateGPM.toFixed(2) + " GPM";
// Show Steps
var stepsHtml = "
";
stepsHtml += "1. Convert Diameter to Meters:";
stepsHtml += " D = " + d + " " + unitText + " = " + diameterInMeters.toFixed(4) + " m";
stepsHtml += "2. Calculate Cross-Sectional Area (A = π × (D/2)²):";
stepsHtml += " A = π × (" + (diameterInMeters/2).toFixed(4) + ")²";
stepsHtml += " A ≈ " + area.toExponential(4) + " m²";
stepsHtml += "3. Calculate Flow Rate (Q = A × v):";
stepsHtml += " Q = " + area.toExponential(4) + " m² × " + velocityInMS.toFixed(2) + " m/s";
stepsHtml += "
Understanding Flow Rate Calculations
Volumetric flow rate is a fundamental concept in fluid dynamics, engineering, and water management. It quantifies the volume of fluid that passes through a specific cross-sectional area per unit of time. Understanding how to calculate this is essential for sizing pipes, selecting pumps, and managing irrigation or HVAC systems.
The Core Formula
The most common method to calculate flow rate inside a pipe relies on the relationship between the pipe's area and the velocity of the fluid.
Calculating the Area (A)
Since most pipes are cylindrical, the cross-sectional area is a circle. To find the area, you need the internal diameter of the pipe.
The formula for the area of a circle is: A = π × r² or A = π × (d/2)².
- r = radius (diameter divided by 2)
- d = internal diameter
- π (Pi) ≈ 3.14159
Example of Flow Rate Calculation
Let's look at a realistic engineering scenario to understand the math better.
Scenario:
Water is flowing through a pipe with an internal diameter of 4 inches at a velocity of 2.5 meters per second. What is the flow rate in Liters per Minute?
Step 1: Unit Conversion
First, we must convert the diameter to meters (SI units) to be consistent with the velocity.
4 inches × 0.0254 = 0.1016 meters.
Step 2: Calculate Area
Calculate the radius: r = 0.1016 / 2 = 0.0508 m.
A = π × (0.0508)² ≈ 0.008107 m².
Step 3: Calculate Flow Rate (Q)
Q = 0.008107 m² × 2.5 m/s = 0.02027 m³/s.
Step 4: Final Unit Conversion
To get Liters per Minute (L/min):
1 m³ = 1,000 Liters.
0.02027 m³/s × 1,000 = 20.27 Liters/second.
20.27 L/s × 60 seconds = 1,216.2 L/min.
Why is Flow Velocity Important?
In the example above, flow rate depends directly on velocity. If you cannot measure the flow rate directly, you can estimate it by measuring the velocity. Velocity is often limited in engineering applications to prevent issues:
- Erosion: Extremely high velocities can erode pipe materials over time.
- Water Hammer: Sudden stops in high-velocity fluids can cause damaging pressure surges.
- Sedimentation: Low velocities may allow solids to settle and clog the pipe.
Common Unit Conversions
Flow rate is expressed in many different units depending on the industry:
- GPM (Gallons Per Minute): Common in the US for plumbing and pumps. (1 GPM ≈ 3.785 L/min)
- CFM (Cubic Feet per Minute): Often used for air flow in HVAC.
- m³/h (Cubic Meters per Hour): Standard in industrial processing and large-scale water treatment.
Use the calculator at the top of this page to quickly convert between these metrics and solve for specific pipe scenarios.