Calculate flow rate ($Q$) based on Volume/Time or Pipe Diameter/Velocity.
Volume & Time (Q = V / t)
Pipe Diameter & Velocity (Q = A × v)
Liters
Cubic Meters ($m^3$)
US Gallons
Seconds
Minutes
Hours
Millimeters (mm)
Inches (in)
Meters (m)
Meters per sec (m/s)
Feet per sec (ft/s)
Results
Cubic Meters per Hour:–
Liters per Minute (LPM):–
US Gallons per Minute (GPM):–
Cubic Meters per Second:–
Calculated Cross-Section Area:–
function toggleVfrInputs() {
var mode = document.getElementById('vfr_calc_mode').value;
var volTimeDiv = document.getElementById('vfr_inputs_vol_time');
var diaVelDiv = document.getElementById('vfr_inputs_dia_vel');
if (mode === 'vol_time') {
volTimeDiv.style.display = 'block';
diaVelDiv.style.display = 'none';
} else {
volTimeDiv.style.display = 'none';
diaVelDiv.style.display = 'block';
}
document.getElementById('vfr_result').style.display = 'none';
}
function calculateFlowRate() {
var mode = document.getElementById('vfr_calc_mode').value;
var flowRateM3S = 0; // Base unit: Cubic meters per second
var isValid = true;
var areaM2 = 0;
if (mode === 'vol_time') {
var volume = parseFloat(document.getElementById('vfr_volume').value);
var volUnit = document.getElementById('vfr_volume_unit').value;
var time = parseFloat(document.getElementById('vfr_time').value);
var timeUnit = document.getElementById('vfr_time_unit').value;
if (isNaN(volume) || isNaN(time) || time 0).");
return;
}
// Convert Volume to m3
var volM3 = 0;
if (volUnit === 'liters') volM3 = volume / 1000;
else if (volUnit === 'm3') volM3 = volume;
else if (volUnit === 'gal') volM3 = volume * 0.00378541;
// Convert Time to seconds
var timeSec = 0;
if (timeUnit === 'sec') timeSec = time;
else if (timeUnit === 'min') timeSec = time * 60;
else if (timeUnit === 'hr') timeSec = time * 3600;
flowRateM3S = volM3 / timeSec;
document.getElementById('vfr_area_display').style.display = 'none';
} else {
var diameter = parseFloat(document.getElementById('vfr_diameter').value);
var diaUnit = document.getElementById('vfr_diameter_unit').value;
var velocity = parseFloat(document.getElementById('vfr_velocity').value);
var velUnit = document.getElementById('vfr_velocity_unit').value;
if (isNaN(diameter) || isNaN(velocity) || diameter <= 0) {
alert("Please enter valid diameter and velocity.");
return;
}
// Convert Diameter to meters
var diaM = 0;
if (diaUnit === 'mm') diaM = diameter / 1000;
else if (diaUnit === 'inch') diaM = diameter * 0.0254;
else if (diaUnit === 'm') diaM = diameter;
// Calculate Area (A = pi * r^2 = pi * (d/2)^2)
var radius = diaM / 2;
areaM2 = Math.PI * Math.pow(radius, 2);
// Convert Velocity to m/s
var velMPS = 0;
if (velUnit === 'mps') velMPS = velocity;
else if (velUnit === 'fps') velMPS = velocity * 0.3048;
// Q = A * v
flowRateM3S = areaM2 * velMPS;
// Show Area in result
document.getElementById('vfr_area_display').style.display = 'flex';
document.getElementById('res_area').innerHTML = areaM2.toFixed(6) + " m²";
}
// Calculate Outputs
var resM3H = flowRateM3S * 3600;
var resLPM = flowRateM3S * 1000 * 60;
var resGPM = flowRateM3S * 15850.32; // 1 m3/s approx 15850.32 GPM
// Update DOM
document.getElementById('res_m3h').innerHTML = resM3H.toFixed(2) + " m³/h";
document.getElementById('res_lpm').innerHTML = resLPM.toFixed(2) + " L/min";
document.getElementById('res_gpm').innerHTML = resGPM.toFixed(2) + " GPM";
document.getElementById('res_m3s').innerHTML = flowRateM3S.toFixed(5) + " m³/s";
document.getElementById('vfr_result').style.display = 'block';
}
Understanding the Volume Flow Rate Calculation Formula
Whether you are designing an HVAC system, managing water treatment facilities, or simply calculating water discharge from a pipe, understanding the volume flow rate is essential. In fluid dynamics, volumetric flow rate represents the volume of fluid which passes per unit of time.
What is Volume Flow Rate?
Volume flow rate, commonly denoted by the symbol $Q$, defines how much fluid (liquid or gas) is moving through a given cross-section within a specific timeframe. It is most commonly measured in cubic meters per second ($m^3/s$), liters per minute (LPM), or Gallons Per Minute (GPM).
The Core Formulas
There are two primary ways to calculate volume flow rate, depending on the data you have available:
1. The Volume over Time Method
If you know the total volume of liquid collected and the time it took to collect it, use this simple formula:
$$Q = \frac{V}{t}$$
$Q$ = Flow Rate
$V$ = Volume (e.g., Liters or cubic meters)
$t$ = Time (e.g., Seconds or minutes)
2. The Velocity and Area Method (Continuity Equation)
This is the most common method used in engineering for pipes and ducts. If you know the size of the pipe and the speed of the fluid, you can calculate the flow rate:
$$Q = A \times v$$
$Q$ = Flow Rate ($m^3/s$)
$A$ = Cross-sectional Area of the pipe ($m^2$)
$v$ = Average Flow Velocity ($m/s$)
Note: To find the area ($A$) of a round pipe using its diameter ($d$), use the formula: $A = \pi \times (\frac{d}{2})^2$.
Calculation Example
Let's say you have a water pipe with a diameter of 100mm (0.1 meters) and the water is flowing at a velocity of 2.0 meters per second.
Convert: To get Liters per Minute, multiply by 60,000 (since $1 m^3 = 1000 L$ and $1 min = 60s$). Result $\approx 942$ Liters per Minute.
Why is Flow Rate Important?
Pump Sizing: Selecting the correct pump requires knowing the required GPM and head pressure.
Irrigation: Ensuring crops receive the correct volume of water over a specific duration.
HVAC: Airflow rates (often in CFM) determine heating and cooling efficiency.
Frequently Asked Questions
Is Mass Flow Rate the same as Volume Flow Rate?
No. Volume flow rate measures space ($m^3/s$), while Mass flow rate measures mass ($kg/s$). They are related by the fluid's density ($\rho$): $\dot{m} = \rho \times Q$.
How do I convert GPM to Liters per Minute?
Multiply US Gallons per Minute (GPM) by approximately 3.785 to get Liters per Minute (LPM).