How to Calculate Flow Rate of Gas Through Pipe

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Gas Flow Rate Calculator (Weymouth Formula)

Calculation Results:

Standard Cubic Feet / Hour:

0.00

Standard Cubic Feet / Day:

0.00
function calculateGasFlow() { var p1 = parseFloat(document.getElementById("p1").value); var p2 = parseFloat(document.getElementById("p2").value); var d = parseFloat(document.getElementById("pipe_dia").value); var l_ft = parseFloat(document.getElementById("pipe_len").value); var sg = parseFloat(document.getElementById("gas_sg").value); var temp_f = parseFloat(document.getElementById("gas_temp").value); if (p1 <= p2) { alert("Inlet pressure must be higher than outlet pressure for flow to occur."); return; } if (p1 <= 0 || p2 <= 0 || d <= 0 || l_ft <= 0 || sg <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Weymouth Equation parameters // Q (SCFH) = 18.062 * sqrt( ((P1^2 – P2^2) * d^5.333) / (G * L_miles * T_Rankine) ) var l_miles = l_ft / 5280; var t_rankine = temp_f + 459.67; var pressure_diff = Math.pow(p1, 2) – Math.pow(p2, 2); var diameter_pow = Math.pow(d, 5.3333333); var denominator = sg * l_miles * t_rankine; var flow_scfh = 18.062 * Math.sqrt((pressure_diff * diameter_pow) / denominator); var flow_scfd = flow_scfh * 24; document.getElementById("scfh_res").innerText = flow_scfh.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + " SCFH"; document.getElementById("scfd_res").innerText = flow_scfd.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 0}) + " SCFD"; document.getElementById("gas-result-container").style.display = "block"; }

How to Calculate Gas Flow Rate Through a Pipe

Calculating the flow rate of gas through a pipeline is a fundamental task for mechanical engineers, HVAC technicians, and gas utility professionals. Unlike liquids, gases are compressible, meaning their volume changes significantly with pressure and temperature variations. To provide accurate results, specialized formulas like the Weymouth Equation are used.

The Weymouth Equation Formula

The Weymouth formula is one of the oldest and most widely used equations for calculating the flow of natural gas in high-pressure, long-distance transmission lines. The simplified form of the equation is:

Q = 18.062 * √[ (P1² – P2²) * d^5.333 / (G * L * T) ]
  • Q: Flow rate in Standard Cubic Feet per Hour (SCFH).
  • P1: Inlet Pressure (Absolute PSIA).
  • P2: Outlet Pressure (Absolute PSIA).
  • d: Internal diameter of the pipe (Inches).
  • G: Specific Gravity of the gas (Air = 1.0).
  • L: Length of the pipe (Miles).
  • T: Absolute temperature (Rankine = °F + 460).

Step-by-Step Calculation Guide

To calculate the gas flow rate manually, follow these steps:

  1. Determine Absolute Pressures: Ensure you are using PSIA (Pounds per Square Inch Absolute). If you have gauge pressure (PSIG), add atmospheric pressure (roughly 14.7) to your value.
  2. Calculate Pressure Squared Difference: Square the inlet and outlet pressures, then subtract the outlet from the inlet (P1² – P2²).
  3. Find the Inner Diameter: Use the actual internal diameter (ID) of the pipe, not the nominal size. For example, a 4-inch Schedule 40 pipe has an ID of 4.026 inches.
  4. Adjust for Specific Gravity: Most natural gas has a specific gravity of approximately 0.60 relative to air.
  5. Convert Units: The Weymouth formula typically uses miles for length and Rankine for temperature. Our calculator handles these conversions for you automatically from feet and Fahrenheit.

Practical Example

Imagine you are running natural gas (Specific Gravity 0.60) through a 4-inch ID pipe that is 1,000 feet long. The inlet pressure is 100 PSIA and the outlet pressure is 80 PSIA at a temperature of 60°F.

  • Pressure Difference: 100² – 80² = 10,000 – 6,400 = 3,600
  • Diameter Term: 4.026^5.333 ≈ 1,677
  • Temperature: 60°F + 460 = 520 Rankine
  • Length in Miles: 1,000 / 5,280 = 0.189 miles

Using the calculator above with these figures, you would find a flow rate of approximately 148,000 SCFH or 3.5 Million SCFD.

Key Factors Influencing Flow Rate

Several factors can dramatically change the volume of gas delivered through your piping system:

  • Pressure Drop: The greater the difference between P1 and P2, the higher the flow rate. However, excessive velocity can cause noise and pipe erosion.
  • Pipe Diameter: Flow capacity increases exponentially with diameter (to the power of 5.333 in the Weymouth formula). Doubling the pipe size results in much more than double the flow.
  • Temperature: As gas heats up, it expands and becomes less dense, which can impact the mass flow rate through the system.

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