Gas Flow Pressure Drop Calculator

Pressure Drop Equation:

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

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

m³/s

Diameter (D):

Pressure Drop (ΔP):

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1. What is the Gas Flow Pressure Drop Equation?

The Hagen-Poiseuille equation calculates the pressure drop of a laminar flow in a cylindrical pipe. It's derived from the Navier-Stokes equations and assumes steady, incompressible, laminar flow through a constant circular cross-section.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

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

Where:

\( \Delta P \) — Pressure drop (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Length of pipe (m)
\( Q \) — Volumetric flow rate (m³/s)
\( D \) — Diameter of pipe (m)

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

3. Importance of Pressure Drop Calculation

Details: Calculating pressure drop is essential for designing piping systems, selecting appropriate pumps or compressors, and ensuring proper flow rates in industrial processes.

4. Using the Calculator

Tips: Enter all values in SI units (viscosity in Pa·s, length in meters, flow rate in m³/s, diameter in meters). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar flow (Reynolds number < 2100). For turbulent flow, use the Darcy-Weisbach equation.

Q2: How does pipe roughness affect the calculation?
A: Pipe roughness doesn't affect laminar flow calculations. For turbulent flow, roughness becomes significant.

Q3: What are typical viscosity values for common gases?
A: Air at 20°C: ~1.8×10⁻⁵ Pa·s; Water vapor: ~1.2×10⁻⁵ Pa·s; Natural gas: ~1.1×10⁻⁵ Pa·s.

Q4: Why is diameter raised to the 4th power?
A: This strong dependence shows that small changes in diameter dramatically affect pressure drop - halving diameter increases ΔP by 16 times.

Q5: Can this be used for compressible flow?
A: No, this equation assumes incompressible flow. For compressible gases at high pressure drops, more complex equations are needed.