Precise control of the carrier gas flow rate is critical in Gas Chromatography (GC) for ensuring reproducible retention times, optimal separation efficiency, and detector performance. This calculator allows chromatographers to estimate the volumetric flow rate and linear velocity based on column dimensions and operating conditions using the Poiseuille equation for compressible fluids.
Key Parameters Explained
Column Length (L): The total length of the capillary column, typically 15m, 30m, or 60m. Longer columns provide better separation but require higher pressures or longer run times.
Internal Diameter (ID): The inner width of the column. Standard sizes include 0.18mm, 0.25mm, 0.32mm, and 0.53mm. Narrower columns offer higher efficiency but have lower sample capacity.
Inlet Pressure: The gauge pressure applied at the head of the column. This acts as the driving force for the mobile phase.
Carrier Gas Viscosity: The viscosity of the gas (Helium, Hydrogen, or Nitrogen) changes with temperature, significantly affecting flow rates during temperature-programmed runs.
The Physics of Flow Calculation
Unlike liquid chromatography, the mobile phase in GC is compressible. The flow rate is calculated using the Hagen-Poiseuille equation modified for gas compressibility. The relationship implies that flow is proportional to the square of the inlet pressure minus the square of the outlet pressure, inversely proportional to the column length and gas viscosity.
Note regarding optimization: To optimize separation efficiency (HETP), chromatographers often look at the Average Linear Velocity (u) rather than just volumetric flow. The optimal velocity depends on the carrier gas type (Van Deemter equation), with Hydrogen typically allowing for faster velocities without sacrificing resolution compared to Helium or Nitrogen.
Standard Operating Ranges
For a standard 30m x 0.25mm column:
Helium: Typically run at 20-40 cm/sec (~1.0 – 1.5 mL/min).
Hydrogen: Typically run at 30-60 cm/sec (~1.5 – 2.5 mL/min).
Nitrogen: Typically run at 10-20 cm/sec (~0.5 – 0.8 mL/min).
function calculateGCFlow() {
// 1. Get Input Values
var lengthM = parseFloat(document.getElementById('columnLength').value);
var idMm = parseFloat(document.getElementById('internalDiameter').value);
var pressureInPsig = parseFloat(document.getElementById('inletPressure').value);
var tempC = parseFloat(document.getElementById('columnTemp').value);
var gasType = document.getElementById('carrierGas').value;
var pressureOutPsig = parseFloat(document.getElementById('outletPressure').value);
// 2. Validation
if (isNaN(lengthM) || isNaN(idMm) || isNaN(pressureInPsig) || isNaN(tempC) || isNaN(pressureOutPsig)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (lengthM <= 0 || idMm dynes/cm^2)
// 1 psi = 68947.6 dynes/cm^2
var PSI_TO_DYNES = 68947.6;
var P_in_abs_psi = pressureInPsig + P_atm;
var P_out_abs_psi = pressureOutPsig + P_atm; // usually 0 gauge = 14.696 abs
// Convert pressures to dynes/cm^2
var Pi = P_in_abs_psi * PSI_TO_DYNES;
var Po = P_out_abs_psi * PSI_TO_DYNES;
// Convert Dimensions
var L_cm = lengthM * 100; // Meters to cm
var d_cm = idMm / 10; // mm to cm
var r_cm = d_cm / 2; // radius in cm
// 4. Calculate Viscosity (eta) in Poise based on Temperature
// Simple linear approximations for GC range (0-400C)
// Viscosity in Poise (1 Poise = 0.1 Pa*s)
// Values usually in microPoise, need conversion to Poise (1 uP = 1e-6 P)
var eta_uP = 0; // microPoise
if (gasType === 'He') {
// Helium approximation: ~198 + 0.44 * T(C) roughly
eta_uP = 186.0 + (0.47 * tempC);
} else if (gasType === 'H2') {
// Hydrogen approximation: ~84 + 0.20 * T(C) roughly
eta_uP = 84.0 + (0.19 * tempC);
} else if (gasType === 'N2') {
// Nitrogen approximation: ~167 + 0.43 * T(C) roughly
eta_uP = 167.0 + (0.43 * tempC);
}
var eta_Poise = eta_uP * 1e-6;
// 5. Calculate Flow Rate (F) at Outlet
// Formula: F_out = (Pi * r^4 * (Pi^2 – Po^2)) / (16 * eta * L * Po)
// Note: Standard formula for compressible flow (Poiseuille)
// F (mL/sec) = [Pi * r^4 * (Pi^2 – Po^2)] / [16 * eta * L * Po] * Conversion factors?
// Standard textbook formula for Volumetric Flow at outlet pressure:
// F_out = (Pi * r^4 * (Pi^2 – Po^2)) / (16 * eta * L * Po) No, that's complex
// Practical approximation for Velocity from Flow:
// u_avg (cm/s) = (Flow_mL_min / 60) / (CrossSectionArea) * j_factor
// Area = Pi * r^2
// Compressibility correction factor (j)
// j = (3/2) * [ (P^2 – 1) / (P^3 – 1) ] where P = Pi/Po
var P_ratio = Pi / Po;
var j_factor = 1.0;
if (P_ratio !== 1) {
j_factor = (3/2) * ( (Math.pow(P_ratio, 2) – 1) / (Math.pow(P_ratio, 3) – 1) );
}
var area_cm2 = Math.PI * Math.pow(r_cm, 2);
// Average linear velocity (cm/s)
// The flow calculated above is at Outlet Pressure (Expanded).
// Corrected Flow (average across column) = F_out * j_factor
// u_avg = F_corrected / Area
var flow_avg_cm3_sec = flow_cm3_sec * j_factor;
var velocity_avg_cm_sec = flow_avg_cm3_sec / area_cm2;
// 7. Calculate Dead Time (tM) in minutes
// L_cm / velocity_avg_cm_sec = seconds
var tM_sec = L_cm / velocity_avg_cm_sec;
var tM_min = tM_sec / 60;
// 8. Display Results
document.getElementById('flowRateVal').innerHTML = flow_mL_min.toFixed(2) + " mL/min";
document.getElementById('velocityVal').innerHTML = velocity_avg_cm_sec.toFixed(1) + " cm/sec";
document.getElementById('deadTimeVal').innerHTML = tM_min.toFixed(3) + " min";
document.getElementById('result').style.display = "block";
}