Understanding the flow rate of compressed air through a pipe is crucial for efficient system design and operation. This calculator helps you determine the volumetric flow rate of compressed air given key parameters like internal pipe diameter, pipe length, upstream and downstream pressures, and air temperature.
The calculation is based on principles of fluid dynamics, specifically considering pressure drops and flow characteristics within a pipe. Different formulas can be used depending on the flow regime (laminar vs. turbulent) and the specific assumptions made. This calculator employs a common engineering approach to estimate the flow rate.
Factors Affecting Flow Rate:
Internal Pipe Diameter: A larger diameter allows for more air to flow.
Pipe Length: Longer pipes generally lead to greater pressure drops and reduced flow rates.
Upstream Pressure: The pressure of the air before it enters the section of pipe being analyzed.
Downstream Pressure: The pressure of the air after it exits the section of pipe being analyzed.
Air Temperature: Temperature affects the density and viscosity of the air, influencing flow.
Pipe Roughness: The internal surface of the pipe can cause friction, impacting flow. (Simplified in this calculator).
function calculateFlowRate() {
var diameter_mm = parseFloat(document.getElementById("pipeDiameter").value);
var length_m = parseFloat(document.getElementById("pipeLength").value);
var p1_barg = parseFloat(document.getElementById("upstreamPressure").value);
var p2_barg = parseFloat(document.getElementById("downstreamPressure").value);
var temp_celsius = parseFloat(document.getElementById("airTemperature").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(diameter_mm) || isNaN(length_m) || isNaN(p1_barg) || isNaN(p2_barg) || isNaN(temp_celsius)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (diameter_mm <= 0 || length_m <= 0 || temp_celsius < -273.15) {
resultDiv.innerHTML = "Please enter positive values for diameter and length, and a valid temperature.";
return;
}
if (p1_barg < p2_barg) {
resultDiv.innerHTML = "Upstream pressure must be greater than or equal to downstream pressure.";
return;
}
// Constants
var rho_standard_kg_m3 = 1.225; // Density of air at sea level, 15°C (approx)
var specific_heat_ratio = 1.4; // For air
var gas_constant_air = 287.05; // J/(kg*K)
var viscosity_air_Pa_s = 1.81e-5; // Dynamic viscosity of air at 15°C (approx)
var pipe_roughness_m = 0.000045; // Typical roughness for smooth steel pipe
// Convert units
var diameter_m = diameter_mm / 1000;
var p1_pa = (p1_barg + 1.01325) * 100000; // Convert barg to Pa (absolute)
var p2_pa = (p2_barg + 1.01325) * 100000; // Convert barg to Pa (absolute)
var temp_kelvin = temp_celsius + 273.15;
// Calculate average density (simplified approach)
var avg_pressure_pa = (p1_pa + p2_pa) / 2;
var avg_density_kg_m3 = avg_pressure_pa / (gas_constant_air * temp_kelvin);
// Calculate average viscosity (approximate temperature dependence)
var viscosity_at_temp = viscosity_air_Pa_s * Math.pow((temp_kelvin / 288.15), 1.5); // Sutherland's Law approximation
var flow_rate_m3_s = 0;
// Use Darcy-Weisbach for pressure drop calculation to estimate flow
// This is an iterative process or can be simplified. For a direct calculation, we can use an approximation.
// A common simplified approach for flow rate estimation uses empirical formulas.
// Here, we'll use a method that approximates flow based on pressure difference and pipe characteristics.
// Calculate friction factor (Colebrook-White equation or Swamee-Jain for explicit solution)
// Swamee-Jain equation for friction factor (explicit)
var reynolds_number_approx = (avg_density_kg_m3 * Math.abs(p1_pa – p2_pa) * diameter_m) / (viscosity_at_temp * length_m); // A very rough initial guess
var friction_factor = 0;
var relative_roughness = pipe_roughness_m / diameter_m;
if (reynolds_number_approx < 2100) { // Laminar flow
friction_factor = 64 / reynolds_number_approx;
} else { // Turbulent flow – using Swamee-Jain for explicit calculation of friction factor
friction_factor = 0.25 / Math.pow(Math.log10((relative_roughness / 3.7) + (5.74 / Math.pow(reynolds_number_approx, 0.9))), 2);
}
// Calculate pressure drop using Darcy-Weisbach (delta P = f * (L/D) * (rho * v^2 / 2))
// We need to solve for velocity (v) or flow rate (Q = A*v)
// Rearranging: v = sqrt( (2 * delta_p * D) / (f * L * rho) )
var pressure_difference_pa = p1_pa – p2_pa;
if (pressure_difference_pa < 0) pressure_difference_pa = 0; // Ensure positive pressure difference
var velocity_m_s = Math.sqrt((2 * pressure_difference_pa * diameter_m) / (friction_factor * length_m * avg_density_kg_m3));
// Calculate volumetric flow rate in m^3/s
var area_m2 = Math.PI * Math.pow(diameter_m / 2, 2);
flow_rate_m3_s = velocity_m_s * area_m2;
// Convert to more common units (e.g., L/s, m³/h)
var flow_rate_ls = flow_rate_m3_s * 1000;
var flow_rate_m3h = flow_rate_m3_s * 3600;
resultDiv.innerHTML = "