How to Calculate Gas Flow Rate from Pressure and Diameter

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Gas Flow Rate Calculator

The inside diameter of the pipeline.
Natural Gas is typically ~0.6
Inlet gauge pressure.
Outlet gauge pressure.

Calculation Results

Daily Flow Rate (SCFD) –
Daily Flow Rate (MSCFD) –
Hourly Flow Rate (SCFH) –
Pressure Drop –

How to Calculate Gas Flow Rate from Pressure and Diameter

Calculating the gas flow rate through a pipeline is a critical task in fluid dynamics and pipeline engineering. The flow rate is determined by the pressure difference between the inlet and outlet, the diameter of the pipe, the length of the pipe section, and the properties of the gas itself.

This calculator utilizes the Weymouth Equation, which is the industry standard for calculating high-pressure gas flow in long pipelines. It specifically addresses the relationship between the pipe's internal diameter and the pressure drop required to move the gas.

The Weymouth Formula

The calculation is based on the following physical relationship:

Q = 433.5 × E × (Tb/Pb) × [ (P1² – P2²) / (G × T × L × Z) ]^0.5 × D^2.667

Where:

  • Q: Flow rate in Standard Cubic Feet per Day (SCFD)
  • D: Pipe internal diameter (inches)
  • P1: Upstream pressure (psia)
  • P2: Downstream pressure (psia)
  • L: Length of pipe (miles)
  • G: Specific gravity of gas (0.6 for Natural Gas)
  • T: Average gas temperature (assumed 520°R / 60°F)

Key Factors Influencing Flow Rate

1. Pipe Diameter (The Power of 2.667)

The diameter is the most significant factor. In the formula, flow rate is proportional to the diameter raised to the power of 2.667. This means that doubling the pipe diameter doesn't just double the flow; it increases it by a factor of nearly 6.3, assuming pressure and length remain constant.

2. Pressure Differential

Gas moves from high pressure to low pressure. The driving force is not just the difference ($P_1 – P_2$), but the difference of their squares ($P_1^2 – P_2^2$). Higher upstream pressure significantly increases the density and energy available to push the gas through the line.

Example Calculation

Let's calculate the flow rate for a natural gas pipeline with the following parameters:

  • Diameter: 10 inches
  • Length: 25 miles
  • Inlet Pressure: 500 psig
  • Outlet Pressure: 400 psig

Using the Weymouth equation, this configuration would yield a flow rate of approximately 38.5 Million SCFD. If you were to increase the diameter to 12 inches, the flow would jump significantly, demonstrating the sensitivity of gas flow to pipe diameter.

function calculateGasFlow() { // 1. Get Input Values var diameter = parseFloat(document.getElementById('gasDiameter').value); var length = parseFloat(document.getElementById('gasLength').value); var sg = parseFloat(document.getElementById('gasSpecificGravity').value); var p1_gauge = parseFloat(document.getElementById('upstreamPressure').value); var p2_gauge = parseFloat(document.getElementById('downstreamPressure').value); // 2. Validation if (isNaN(diameter) || isNaN(length) || isNaN(sg) || isNaN(p1_gauge) || isNaN(p2_gauge)) { alert("Please enter valid numbers for all fields."); return; } if (diameter <= 0 || length <= 0 || sg = p1_gauge) { alert("Upstream Pressure (P1) must be greater than Downstream Pressure (P2) to generate flow."); return; } // 3. Convert Units & Constants // Convert psig to psia (Absolute Pressure) var atmosphericPressure = 14.7; var p1_abs = p1_gauge + atmosphericPressure; var p2_abs = p2_gauge + atmosphericPressure; // Constants for Weymouth Equation var T_base = 520; // Base Temp (Rankine) var P_base = 14.73; // Base Pressure (psia) var T_flow = 520; // Flow Temp (Rankine) – Assumed 60F var Z = 0.9; // Compressibility Factor (Average for Natural Gas) var Efficiency = 0.92; // Pipeline Efficiency factor // 4. Calculate // Formula Term 1: Constant Block // Q = 433.5 * E * (Tb/Pb) var term1 = 433.5 * Efficiency * (T_base / P_base); // Formula Term 2: Pressure Term // (P1^2 – P2^2) var pressureDiffSquared = (p1_abs * p1_abs) – (p2_abs * p2_abs); // Formula Term 3: Denominator inside Sqrt // (G * T * L * Z) var denom = sg * T_flow * length * Z; // Formula Term 4: Sqrt Component var sqrtComponent = Math.sqrt(pressureDiffSquared / denom); // Formula Term 5: Diameter Component // D^2.667 var diamComponent = Math.pow(diameter, 2.667); // Total Flow (SCFD) var flowRateSCFD = term1 * sqrtComponent * diamComponent; // Derived Units var flowRateMSCFD = flowRateSCFD / 1000; // Thousand SCFD var flowRateSCFH = flowRateSCFD / 24; // Standard Cubic Feet per Hour var pressureDrop = p1_gauge – p2_gauge; // 5. Display Results document.getElementById('resSCFD').innerText = flowRateSCFD.toLocaleString('en-US', {maximumFractionDigits: 0}); document.getElementById('resMSCFD').innerText = flowRateMSCFD.toLocaleString('en-US', {maximumFractionDigits: 2}); document.getElementById('resSCFH').innerText = flowRateSCFH.toLocaleString('en-US', {maximumFractionDigits: 0}); document.getElementById('resDrop').innerText = pressureDrop.toFixed(1) + " psi"; // Show result container document.getElementById('gasResults').className = 'gas-results visible'; }

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