*Calculated at standard reference conditions (ANR).
Understanding Pneumatic Flow Rate Calculations
Sizing pneumatic components correctly is critical for the efficiency and safety of air-driven systems. This calculator utilizes the methodology defined in ISO 6358 and JIS B 8390 standards, commonly referred to as the "SMC method" due to its widespread adoption by SMC Corporation for characterizing valves, regulators, and piping.
Key Parameters Explained
Unlike simple liquid flow, compressible gas flow depends heavily on the relationship between upstream and downstream pressures. To use this calculator effectively, you need to understand the following coefficients:
Sonic Conductance (C)
Measured in dm³/(s·bar), this represents the maximum flow capacity of a component when the air is moving at the speed of sound (sonic velocity). A higher "C" value indicates a larger internal passage and higher flow capability.
Critical Pressure Ratio (b)
This dimensionless value (between 0 and 1) defines the transition point between Subsonic Flow and Choked Flow. It represents the pressure characteristics of the flow path geometry.
Flow Regimes: Choked vs. Subsonic
The calculation logic changes based on the pressure differential:
Choked Flow (Sonic Flow): Occurs when the downstream pressure is low enough (below the critical ratio) that the air reaches sonic velocity. In this state, lowering the downstream pressure further does not increase the flow rate. The flow depends solely on the supply pressure.
Subsonic Flow: Occurs when the pressure drop is small. The air moves slower than the speed of sound, and the flow rate is influenced by both the supply and outlet pressures.
How to Use This Calculator
Input C: Find the Sonic Conductance value in the component's datasheet.
Input b: Enter the Critical Pressure Ratio from the datasheet.
Pressures: Enter the Supply (P1) and Outlet (P2) pressures in MPa (Gauge). The calculator automatically converts these to absolute pressure for the formula.
Temperature: Enter the fluid temperature (default is 20°C).
Formulas Used
The calculator applies the standard ISO 6358 formulas:
Note: Pressures must be converted to Absolute Bar for the calculation (Pabs = Pgauge + 0.1013 MPa).
If P2/P1 ≤ b (Choked): Q = 600 × C × P1abs × √[293 / (273 + t)]
If P2/P1 > b (Subsonic): Q = 600 × C × P1abs × √[1 – ((P2/P1 – b) / (1 – b))²] × √[293 / (273 + t)]
function calculateFlow() {
// 1. Get Input Values
var sonicC = parseFloat(document.getElementById('sonicConductance').value);
var criticalB = parseFloat(document.getElementById('criticalPressureRatio').value);
var p1GaugeMPa = parseFloat(document.getElementById('supplyPressure').value);
var p2GaugeMPa = parseFloat(document.getElementById('outletPressure').value);
var tempC = parseFloat(document.getElementById('temperature').value);
// 2. Validate Inputs
if (isNaN(sonicC) || isNaN(criticalB) || isNaN(p1GaugeMPa) || isNaN(p2GaugeMPa) || isNaN(tempC)) {
alert("Please enter valid numeric values for all fields.");
return;
}
if (sonicC < 0 || criticalB 1 || p1GaugeMPa < 0 || p2GaugeMPa = p1GaugeMPa) {
alert("Outlet pressure (P2) must be lower than Supply pressure (P1) to generate flow.");
return;
}
// 3. Convert Units
// Convert Gauge MPa to Absolute MPa (approx +0.1013)
// Then convert Absolute MPa to Absolute Bar because C is in dm3/(s·bar)
// 1 MPa = 10 Bar.
var atmPressureMPa = 0.101325;
var p1AbsMPa = p1GaugeMPa + atmPressureMPa;
var p2AbsMPa = p2GaugeMPa + atmPressureMPa;
var p1AbsBar = p1AbsMPa * 10;
var p2AbsBar = p2AbsMPa * 10;
// 4. Calculate Pressure Ratio
var pressureRatio = p2AbsBar / p1AbsBar;
// 5. Temperature Correction Coefficient
// Reference temp is 20°C (293K)
var tempCoeff = Math.sqrt(293 / (273 + tempC));
// 6. Calculate Flow (Q) in L/min (ANR)
var flowRate = 0;
var flowState = "";
var badgeColor = "";
if (pressureRatio <= criticalB) {
// Choked Flow
flowState = "Choked Flow";
badgeColor = "#d63384"; // Pink/Redish for limit reached
// Q = 600 * C * P1(abs) * Kt
flowRate = 600 * sonicC * p1AbsBar * tempCoeff;
} else {
// Subsonic Flow
flowState = "Subsonic Flow";
badgeColor = "#28a745"; // Green
// Q = 600 * C * P1(abs) * sqrt(1 – [(r – b) / (1 – b)]^2) * Kt
var term1 = (pressureRatio – criticalB) / (1 – criticalB);
var term2 = Math.pow(term1, 2);
var term3 = Math.sqrt(1 – term2);
flowRate = 600 * sonicC * p1AbsBar * term3 * tempCoeff;
}
// 7. Display Results
var resultBox = document.getElementById('resultBox');
var flowOutput = document.getElementById('flowResult');
var stateBadge = document.getElementById('flowStateBadge');
resultBox.style.display = "block";
flowOutput.innerHTML = flowRate.toFixed(2) + " L/min (ANR)";
stateBadge.innerHTML = flowState;
stateBadge.style.backgroundColor = badgeColor;
}