How To Calculate Gas Flow Rate

Hagen-Poiseuille Equation:

\[ Q = \frac{\Delta P \times \pi \times r^4}{8 \times \mu \times L} \]

Pressure Difference (ΔP):

Radius (r):

Viscosity (μ):

Pa·s

Length (L):

Gas Flow Rate (Q):

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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 various engineering and scientific applications.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

\[ Q = \frac{\Delta P \times \pi \times r^4}{8 \times \mu \times L} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( \Delta P \) — Pressure difference between the two ends (Pa)
\( r \) — Internal radius of the pipe (m)
\( \mu \) — Dynamic viscosity of the fluid (Pa·s)
\( L \) — Length of the pipe (m)

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

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, ventilation systems, medical devices (like respiratory equipment), and many industrial processes involving gas transport.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length dimensions, Pascals for pressure). Ensure all values are positive and non-zero. The radius has the most significant impact on flow rate due to the r⁴ term.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of the Hagen-Poiseuille equation?
A: It assumes laminar flow, Newtonian fluid, steady state, no-slip conditions, and a long cylindrical pipe with constant circular cross-section.

Q2: How does temperature affect the calculation?
A: Temperature affects gas viscosity (μ). You must use the viscosity value appropriate for your gas at the operating temperature.

Q3: What's the difference between volumetric and mass flow rate?
A: Volumetric flow rate (Q) measures volume per time, while mass flow rate would multiply Q by the gas density (ρ).

Q4: How does pipe roughness affect the calculation?
A: The equation assumes smooth pipes. For rough pipes, especially with turbulent flow, other equations like Darcy-Weisbach would be more appropriate.

Q5: Can this be used for compressible gases?
A: The equation is strictly valid only for incompressible flow. For compressible gases with significant pressure drops, more complex equations are needed.