1. What is a Gas Flow Rate (Weymouth Formula) Calculator?

Definition: This calculator computes the flow rate (\( Q \)) of natural gas in commercial-industrial piping systems for pipes with a diameter of 3 inches or larger, using the Weymouth formula.

Purpose: It is used in commercial and industrial gas system design to determine the gas flow rate, aiding in pipe sizing, system efficiency, and ensuring adequate gas supply for large-scale applications.

2. How Does the Calculator Work?

The calculator uses the following formula for gas flow rate:

Gas Flow Rate: \[ Q = 28 d^{2.667} \sqrt[3]{\left( \frac{(P_1^2 - P_2^2) 520}{G L T} \right)} \]

Where:

• \( Q \): Flow rate (ft³/hr, m³/s)
• \( d \): Internal diameter of pipe (in., m)
• \( P_1 \): Initial absolute pressure (psia, Pa)
• \( P_2 \): Terminal absolute pressure (psia, Pa)
• \( G \): Specific gravity of gas (dimensionless, typically 0.60 for natural gas)
• \( L \): Length of pipe (miles, km)
• \( T \): Absolute temperature of the flowing gas (°R, K)

Unit Conversions:

• Internal Diameter (\( d \)): in., m (1 m = 39.3701 in.)
• Initial and Terminal Pressure (\( P_1 \), \( P_2 \)): psia, Pa (1 Pa = 0.000145038 psia)
• Pipe Length (\( L \)): miles, km (1 km = 0.621371 miles)
• Absolute Temperature (\( T \)): °R, K (1 K = 1.8 °R)
• Flow Rate (\( Q \)): ft³/hr, m³/s (1 ft³/hr = 7.86579e-6 m³/s)

Steps:

• Enter the internal diameter (\( d \)), initial absolute pressure (\( P_1 \)), terminal absolute pressure (\( P_2 \)), specific gravity (\( G \)), pipe length (\( L \)), and absolute temperature (\( T \)), and select their units.
• Convert \( d \), \( P_1 \), \( P_2 \), \( L \), and \( T \) to in., psia, psia, miles, and °R, respectively.
• Calculate the flow rate using the formula.
• Convert the result to the selected unit (ft³/hr or m³/s).
• Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Gas Flow Rate Calculation

Calculating the gas flow rate using the Weymouth formula is crucial for:

• Commercial-Industrial Gas System Design: Ensures pipes are sized to deliver sufficient gas for large-scale applications like manufacturing or heating.
• Safety and Efficiency: Prevents pressure drops that could impair system performance or safety in industrial settings.
• System Optimization: Balances pipe size, cost, and gas delivery requirements for efficient operation.

4. Using the Calculator

Examples:

• Example 1: For \( d = 6 \, \text{in.} \), \( P_1 = 24.7 \, \text{psia} \), \( P_2 = 23.7 \, \text{psia} \), \( G = 0.60 \), \( L = 0.1894 \, \text{miles} \), \( T = 520 \, \text{°R} \), flow rate in ft³/hr:
  • \( Q = 28 \times 6^{2.667} \times \sqrt[3]{\left( \frac{(24.7^2 - 23.7^2) \times 520}{0.60 \times 0.1894 \times 520} \right)} \approx 28 \times 81.631 \times \sqrt[3]{\frac{(610.09 - 561.69) \times 520}{0.60 \times 0.1894 \times 520}} \approx 28 \times 81.631 \times \sqrt[3]{\frac{25164.8}{59.1048}} \approx 28 \times 81.631 \times \sqrt[3]{425.92} \approx 28 \times 81.631 \times 7.523 \approx 20214 \)
  • Since 20214 > 10000, display in scientific notation: \( 2.02140 \times 10^4 \)
• Example 2: For \( d = 0.1524 \, \text{m} \), \( P_1 = 170000 \, \text{Pa} \), \( P_2 = 163000 \, \text{Pa} \), \( G = 0.60 \), \( L = 0.3048 \, \text{km} \), \( T = 288.89 \, \text{K} \), flow rate in m³/s:
  • Convert: \( d = 0.1524 \times 39.3701 \approx 6 \, \text{in.} \)
  • \( P_1 = 170000 \times 0.000145038 \approx 24.656 \, \text{psia} \)
  • \( P_2 = 163000 \times 0.000145038 \approx 23.641 \, \text{psia} \)
  • \( L = 0.3048 \times 0.621371 \approx 0.1894 \, \text{miles} \)
  • \( T = 288.89 \times 1.8 \approx 520 \, \text{°R} \)
  • \( Q = 28 \times 6^{2.667} \times \sqrt[3]{\left( \frac{(24.656^2 - 23.641^2) \times 520}{0.60 \times 0.1894 \times 520} \right)} \approx 28 \times 81.631 \times \sqrt[3]{\frac{(607.92 - 558.90) \times 520}{59.1048}} \approx 28 \times 81.631 \times \sqrt[3]{\frac{25487.2}{59.1048}} \approx 28 \times 81.631 \times \sqrt[3]{431.25} \approx 28 \times 81.631 \times 7.555 \approx 20214 \, \text{ft³/hr} \)
  • Convert to m³/s: \( 20214 \times 7.86579e-6 \approx 0.15897 \)
  • Since 0.15897 < 10000 and > 0.00001, display with 5 decimal places: \( 0.15897 \)
• Example 3: For \( d = 4 \, \text{in.} \), \( P_1 = 30 \, \text{psia} \), \( P_2 = 28 \, \text{psia} \), \( G = 0.60 \), \( L = 0.5 \, \text{miles} \), \( T = 530 \, \text{°R} \), flow rate in ft³/hr:
  • \( Q = 28 \times 4^{2.667} \times \sqrt[3]{\left( \frac{(30^2 - 28^2) \times 520}{0.60 \times 0.5 \times 530} \right)} \approx 28 \times 36.758 \times \sqrt[3]{\frac{(900 - 784) \times 520}{0.60 \times 0.5 \times 530}} \approx 28 \times 36.758 \times \sqrt[3]{\frac{60320}{159}} \approx 28 \times 36.758 \times \sqrt[3]{379.37} \approx 28 \times 36.758 \times 7.239 \approx 7451.7 \)
  • Since 7451.7 < 10000 and > 0.00001, display with 5 decimal places: \( 7451.70000 \)

5. Frequently Asked Questions (FAQ)

Q: What does gas flow rate in the Weymouth formula represent?
A: Gas flow rate (\( Q \)) quantifies the volume of natural gas delivered per unit time in commercial-industrial piping systems, critical for meeting large-scale demand.

Q: How can I determine the input parameters?
A: Internal diameter (\( d \)) is obtained from pipe specifications (must be ≥3 in.). Initial and terminal absolute pressures (\( P_1 \), \( P_2 \)) are measured or designed for the system. Specific gravity (\( G \)) is typically 0.60 for natural gas. Pipe length (\( L \)) is measured in miles or kilometers. Absolute temperature (\( T \)) is the gas temperature in °R (°F + 460) or K.

Q: Why is gas flow rate important in commercial-industrial gas system design?
A: It ensures pipes are sized to deliver sufficient gas for safe and efficient operation, optimizing system performance and cost for industrial applications.

Gas Flow Rate (Weymouth Formula) Calculator© - All Rights Reserved 2025