Convert volumetric flow rate to linear velocity for column scale-up.
mL/min
cm
Please enter valid positive numbers for both fields.
Linear Flow Rate (Velocity):
0cm/h
Cross-Sectional Area:
0cm²
Residence Time (assuming 20cm bed):
0min
Understanding Linear Flow Rate in Bioprocessing
In chromatography and bioprocessing, correctly calculating the Linear Flow Rate (also known as linear velocity) is crucial for scaling up purification processes. While volumetric flow rate (mL/min) tells you how much volume moves through the system, linear flow rate (cm/h) describes the speed at which the mobile phase travels through the column bed, independent of column diameter.
This calculator functions similarly to tools provided by suppliers like Cytiva, allowing process engineers to maintain consistent residence times when moving from lab-scale (small diameter) to pilot or manufacturing-scale (large diameter) columns.
Why Convert Volumetric Flow to Linear Flow?
When scaling up a chromatography process, the goal is usually to keep the Linear Flow Rate constant. This ensures that the interaction time between the protein and the resin (residence time) remains the same, preserving the separation resolution and dynamic binding capacity.
Volumetric Flow Rate (Q): Measured in mL/min or L/min. Dependent on column size.
Linear Flow Rate (v): Measured in cm/h. Independent of column diameter, making it the standard metric for scale-up.
The Formula
To calculate linear flow rate from volumetric flow rate, you first need the cross-sectional area of the column.
Area (A) = π × (Diameter / 2)²
Linear Flow Rate (cm/h) = (Volumetric Flow × 60) / Area
Where:
Volumetric Flow is in mL/min.
Diameter is in cm.
Area is calculated in cm².
The factor 60 converts minutes to hours.
Example Calculation
Imagine you are running a purification on a lab column and want to verify your flow parameters:
Column Diameter: 1.6 cm (Radius = 0.8 cm)
Volumetric Flow Rate: 5 mL/min
Step 1: Calculate Area
A = π × 0.8² ≈ 2.01 cm²
Step 2: Calculate Linear Flow
v = (5 × 60) / 2.01 ≈ 149.25 cm/h
Common Column Diameters in Chromatography
Standard columns from manufacturers like Cytiva often come in specific diameters. This calculator handles any custom size, but common values include:
Lab Scale: 0.5 cm, 1.0 cm, 1.6 cm, 2.6 cm, 5.0 cm
Pilot/Process Scale: 10 cm, 20 cm, 30 cm, 45 cm, 60 cm+
Maintaining Residence Time
Another critical factor displayed in this calculator is Residence Time. This is the average time a molecule spends in the column bed. The generic calculation often assumes a standard bed height (e.g., 20 cm), though in practice:
Residence Time (min) = (Bed Height [cm] / Linear Flow Rate [cm/h]) × 60
By keeping linear velocity constant during scale-up, residence time remains constant (assuming bed height is unchanged), ensuring your purification results scale predictably.
function calculateFlowParams() {
// Get input elements by ID
var flowInput = document.getElementById('volumetricFlow');
var diamInput = document.getElementById('columnDiameter');
var errorBox = document.getElementById('errorDisplay');
var resultBox = document.getElementById('resultsDisplay');
// Parse values
var flowRate = parseFloat(flowInput.value);
var diameter = parseFloat(diamInput.value);
// Validation logic
if (isNaN(flowRate) || isNaN(diameter) || flowRate <= 0 || diameter <= 0) {
errorBox.style.display = 'block';
resultBox.style.display = 'none';
return;
}
// Hide error if valid
errorBox.style.display = 'none';
// 1. Calculate Radius (cm)
var radius = diameter / 2;
// 2. Calculate Cross-sectional Area (cm^2) = pi * r^2
var area = Math.PI * Math.pow(radius, 2);
// 3. Calculate Linear Flow Rate (cm/h)
// Formula: (Volumetric Flow [mL/min] * 60 min/h) / Area [cm^2]
// Note: 1 mL = 1 cm^3, so units cancel to cm/h
var linearFlow = (flowRate * 60) / area;
// 4. Calculate Approximate Residence Time (assuming standard 20cm bed height)
// Formula: (Bed Height [cm] / Linear Flow [cm/h]) * 60 min/h
// This is an estimation for context
var bedHeight = 20;
var residenceTime = (bedHeight / linearFlow) * 60;
// Update UI with Results (limiting to 2 decimal places)
document.getElementById('resLinearFlow').innerText = linearFlow.toFixed(1);
document.getElementById('resArea').innerText = area.toFixed(2);
document.getElementById('resResidence').innerText = residenceTime.toFixed(2);
// Show results container
resultBox.style.display = 'block';
}
function resetCalculator() {
document.getElementById('volumetricFlow').value = '';
document.getElementById('columnDiameter').value = '';
document.getElementById('resultsDisplay').style.display = 'none';
document.getElementById('errorDisplay').style.display = 'none';
}