Calculate the required volumetric flow rate (pumping speed) to evacuate a chamber.
1.0 (Ideal Conditions)
1.3 (Standard – Includes Pipe Loss)
1.5 (Conservative – High Outgassing)
Logarithmic Pressure Drop Ratio:–
Required Flow Rate (m³/h):0.00 m³/h
Required Flow Rate (CFM):0.00 CFM
Required Flow Rate (L/s):0.00 L/s
*Calculated using the logarithmic decay formula including the selected safety factor.
Understanding Vacuum Flow Rate
In vacuum engineering, calculating the appropriate flow rate—often referred to as Pumping Speed (S)—is critical for sizing vacuum pumps correctly. Unlike liquid pumps which maintain constant pressure, vacuum pumps must deal with expanding gases where the pressure drops exponentially over time.
The Calculation Formula
The required effective pumping speed ($S_{eff}$) to evacuate a vessel from an initial pressure to a target pressure within a specific timeframe is calculated using the following logarithmic formula:
S = (V / t) × ln(P_start / P_end) × SF
Where:
S = Pumping Speed (Volumetric Flow Rate)
V = Volume of the vacuum chamber
t = Time to pump down
ln = Natural Logarithm
P_start = Initial Pressure (usually atmospheric)
P_end = Target Vacuum Pressure
SF = Safety Factor (to account for conductance losses and outgassing)
Interpreting the Results
Metric (m³/h): Cubic meters per hour is the standard unit for industrial vacuum pumps in Europe and Asia. Imperial (CFM): Cubic Feet per Minute is commonly used in North America. Scientific (L/s): Liters per second is often used for high-vacuum applications and scientific instrumentation.
Factors Affecting Pump Sizing
Conductance: The connecting pipes between the chamber and the pump reduce the effective speed. Longer and narrower pipes restrict flow more significantly. The calculator's safety factor option helps estimate this loss. Outgassing: Materials inside the vacuum chamber release gas as pressure drops (outgassing). If your process involves wet surfaces, plastics, or porous materials, choose a higher safety factor (1.5 or greater).
Example Calculation
Imagine you have a 500 Liter chamber. You need to pump it down from atmospheric pressure (1013 mbar) to 1 mbar in 10 minutes.
Using the formula (ignoring safety factor for simplicity):
1. Volume (V) = 500 L
2. Time (t) = 10 min = 600 seconds
3. Ratio = ln(1013 / 1) ≈ 6.92
4. S (L/s) = (500 / 600) × 6.92 ≈ 5.77 L/s
5. Convert to m³/h: 5.77 × 3.6 ≈ 20.77 m³/h.
Using this calculator allows you to quickly adjust the safety factor to ensure your pump has enough overhead to meet the deadline.
function calculateVacuumFlow() {
// 1. Get input values
var volLiters = document.getElementById('chamberVolume').value;
var pStart = document.getElementById('initialPressure').value;
var pEnd = document.getElementById('targetPressure').value;
var timeMin = document.getElementById('pumpDownTime').value;
var safetyFactor = document.getElementById('safetyFactor').value;
// Elements for display
var resultArea = document.getElementById('results-area');
var errorMsg = document.getElementById('error-message');
var resRatio = document.getElementById('res-ratio');
var resM3h = document.getElementById('res-m3h');
var resCfm = document.getElementById('res-cfm');
var resLs = document.getElementById('res-ls');
// Reset display
errorMsg.style.display = 'none';
resultArea.style.display = 'none';
// 2. Validate Inputs
if (!volLiters || !pStart || !pEnd || !timeMin) {
errorMsg.innerText = "Please fill in all fields.";
errorMsg.style.display = 'block';
return;
}
volLiters = parseFloat(volLiters);
pStart = parseFloat(pStart);
pEnd = parseFloat(pEnd);
timeMin = parseFloat(timeMin);
safetyFactor = parseFloat(safetyFactor);
if (volLiters <= 0 || timeMin <= 0 || pStart <= 0 || pEnd = pStart) {
errorMsg.innerText = "Target pressure must be lower than initial pressure.";
errorMsg.style.display = 'block';
return;
}
// 3. Calculation Logic
// Formula: S (L/min) = (V / t) * ln(P1/P2) * SafetyFactor
// Logarithmic pressure ratio
var lnRatio = Math.log(pStart / pEnd);
// Base pumping speed required in Liters per Minute
var speedLitersPerMin = (volLiters / timeMin) * lnRatio * safetyFactor;
// 4. Convert Units
// Convert to Liters per Second (L/s)
var speedLs = speedLitersPerMin / 60;
// Convert to Cubic Meters per Hour (m³/h)
// 1 L/min = 0.06 m³/h
var speedM3h = speedLitersPerMin * 0.06;
// Convert to Cubic Feet per Minute (CFM)
// 1 m³/h = 0.588578 CFM
var speedCfm = speedM3h * 0.588578;
// 5. Display Results
resRatio.innerText = lnRatio.toFixed(3);
resM3h.innerText = speedM3h.toFixed(2) + " m³/h";
resCfm.innerText = speedCfm.toFixed(2) + " CFM";
resLs.innerText = speedLs.toFixed(2) + " L/s";
resultArea.style.display = 'block';
}