Please enter valid positive numbers for both fields.
Volumetric Flow Rate:0.000 mL/min
Cross-Sectional Area:0.000 cm²
function calculateFlowRate() {
// Get input values
var idInput = document.getElementById('gcColumnId');
var velocityInput = document.getElementById('gcVelocity');
var resultBox = document.getElementById('gcResult');
var errorBox = document.getElementById('gcError');
var idMm = parseFloat(idInput.value);
var velocityCms = parseFloat(velocityInput.value);
// Reset display
resultBox.style.display = 'none';
errorBox.style.display = 'none';
// Validation
if (isNaN(idMm) || isNaN(velocityCms) || idMm <= 0 || velocityCms <= 0) {
errorBox.style.display = 'block';
return;
}
// Calculation Logic
// 1. Convert Diameter (mm) to Radius (cm)
// d (mm) / 10 = d (cm)
// r = d (cm) / 2
var radiusCm = (idMm / 10) / 2;
// 2. Calculate Cross-Sectional Area (cm^2)
// Area = pi * r^2
var areaCm2 = Math.PI * Math.pow(radiusCm, 2);
// 3. Calculate Flow Rate
// Flow (mL/min) = Area (cm^2) * Velocity (cm/s) * 60 (s/min)
// Note: 1 cm^3 = 1 mL
var flowRate = areaCm2 * velocityCms * 60;
// Display Results
document.getElementById('resultFlowRate').innerHTML = flowRate.toFixed(3) + " mL/min";
// Scientific notation for area if it's very small, otherwise fixed
var areaDisplay = areaCm2 < 0.001 ? areaCm2.toExponential(4) : areaCm2.toFixed(5);
document.getElementById('resultArea').innerHTML = areaDisplay + " cm²";
resultBox.style.display = 'block';
}
Understanding Gas Chromatography Flow Calculations
In Gas Chromatography (GC), precise control of the carrier gas flow is critical for maintaining separation efficiency and reproducibility of retention times. While modern electronic pressure control (EPC) systems often handle these calculations automatically, understanding the relationship between Linear Velocity and Volumetric Flow Rate is essential for method development, troubleshooting, and translating methods between different instruments.
Linear Velocity vs. Volumetric Flow Rate
These two terms describe the movement of the carrier gas through the column, but they measure different aspects:
Average Linear Velocity ($u$): Measured in cm/sec. This represents the speed at which the carrier gas (and the analyte) travels through the column. It is directly related to the column's efficiency (HETP) as described by the Van Deemter equation.
Volumetric Flow Rate ($F$): Measured in mL/min. This represents the volume of gas passing through the column per unit of time. This is what you physically measure at the detector outlet using a flow meter.
Why Convert Between Velocity and Flow Rate?
Chromatographers often optimize a method based on linear velocity to find the "sweet spot" for separation efficiency (typically 20-40 cm/s for Helium). However, hardware settings or bubble flow meters operate in volumetric flow (mL/min). This calculator allows you to quickly determine the required flow rate setting to achieve your desired linear velocity for a specific column geometry.
The Calculation Formula
To convert linear velocity to volumetric flow rate, we treat the column as a cylinder. The formula is derived from basic geometry:
$$ F = u \times A_c \times 60 $$
Where:
$F$ = Volumetric Flow Rate (mL/min)
$u$ = Average Linear Velocity (cm/sec)
$A_c$ = Cross-sectional Area of the column (cm²)
60 = Conversion factor from seconds to minutes
The cross-sectional area ($A_c$) is calculated from the column's internal diameter ($d$):
Note: The divisor is 20 because the diameter is typically given in millimeters (mm), but we need the radius in centimeters (cm) for the area calculation ($1 \text{ mm} = 0.1 \text{ cm}$).
Example Calculation
Let's say you are using a standard capillary column and want to calculate the flow rate:
Parameter
Value
Column Internal Diameter (ID)
0.25 mm
Desired Linear Velocity
36 cm/sec
Step 1: Calculate Radius in cm
$r = (0.25 \text{ mm} / 10) / 2 = 0.0125 \text{ cm}$