Gas Flow Calculator Through Pipe

Poiseuille's Equation:

\[ Q = \frac{\pi d^4 \Delta P}{128 \mu L} \]

Diameter (d):

Pressure Difference (ΔP):

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

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1. What is Poiseuille's Equation?

Poiseuille's equation describes the flow rate of a fluid through a cylindrical pipe under laminar flow conditions. It's particularly useful for calculating gas flow through pipes in various engineering applications.

2. How Does the Calculator Work?

The calculator uses Poiseuille's equation:

\[ Q = \frac{\pi d^4 \Delta P}{128 \mu L} \]

Where:

\( Q \) — Flow rate (m³/s)
\( d \) — Pipe diameter (m)
\( \Delta P \) — Pressure difference (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Pipe length (m)

Explanation: The equation shows that flow rate is proportional to the fourth power of the pipe diameter, making diameter the most influential factor in flow calculations.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, determining pump requirements, and optimizing fluid transport in various industrial applications.

4. Using the Calculator

Tips: Enter all values in SI units. Ensure all inputs are positive values. The calculator assumes laminar flow conditions and Newtonian fluid behavior.

5. Frequently Asked Questions (FAQ)

Q1: What are the limitations of Poiseuille's equation?
A: It assumes laminar flow, constant viscosity, no slip at the pipe wall, and Newtonian fluid behavior. It's not accurate for turbulent flow or non-Newtonian fluids.

Q2: How does temperature affect the calculation?
A: Temperature affects viscosity significantly. For accurate results, use viscosity values at the appropriate temperature for your application.

Q3: Can this be used for both liquids and gases?
A: Yes, but the equation is more accurate for incompressible fluids (liquids). For gases, it works best with small pressure differences.

Q4: What is the Reynolds number range for laminar flow?
A: Typically, flow is laminar when Reynolds number is below 2300. For accurate results using this equation, ensure your flow conditions are laminar.

Q5: How does pipe roughness affect the calculation?
A: Poiseuille's equation assumes smooth pipes. Roughness increases flow resistance and would require different equations for accurate prediction.