Gas Pipe Flow Rate Calculator

Hagen-Poiseuille Equation:

\[ \text{Flow Rate} = \frac{\pi \times \text{Diameter}^4 \times \Delta P}{128 \times \text{Viscosity} \times \text{Length}} \]

Diameter:

meters

Pressure Difference (ΔP):

Viscosity:

Pa·s

Length:

meters

Flow Rate:

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1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the volumetric flow rate of a fluid through a cylindrical pipe under laminar flow conditions. It's particularly useful for calculating gas flow rates in pipes with small diameters.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ \text{Flow Rate} = \frac{\pi \times \text{Diameter}^4 \times \Delta P}{128 \times \text{Viscosity} \times \text{Length}} \]

Where:

\( \pi \) — Mathematical constant (≈3.14159)
\( \text{Diameter} \) — Inner diameter of the pipe (meters)
\( \Delta P \) — Pressure difference between pipe ends (Pascals)
\( \text{Viscosity} \) — Dynamic viscosity of the gas (Pa·s)
\( \text{Length} \) — Length of the pipe (meters)

Explanation: The equation shows that flow rate is proportional to the fourth power of pipe diameter and directly proportional to pressure difference, while inversely proportional to viscosity and length.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing gas distribution systems, determining pipe sizing, and ensuring proper system operation.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length/diameter, Pascals for pressure, Pa·s for viscosity). Ensure all values are positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of this equation?
A: The equation assumes laminar flow, Newtonian fluid, constant viscosity, no-slip conditions, and a long straight pipe with constant circular cross-section.

Q2: How does temperature affect the calculation?
A: Temperature affects gas viscosity. Use viscosity values appropriate for your operating temperature.

Q3: Can this be used for turbulent flow?
A: No, this equation is only valid for laminar flow (typically Re < 2100). For turbulent flow, use the Darcy-Weisbach equation.

Q4: What's a typical viscosity value for natural gas?
A: At 20°C, natural gas viscosity is typically around 1.1 × 10⁻⁵ Pa·s, but varies with composition and temperature.

Q5: How accurate is this calculation?
A: Very accurate for ideal conditions, but real-world factors like pipe roughness, bends, and fittings will affect actual flow rates.