Compressible Pipe Flow Calculator

Compressible Flow Equation:

\[ Q = A \times \sqrt{\frac{2 \times \Delta P \times \gamma}{\rho \times (\gamma - 1)} \times \left(1 - \left(\frac{P2}{P1}\right)^{\frac{\gamma - 1}{\gamma}}\right)} \]

Cross-sectional Area (A):

m²

Pressure Difference (ΔP):

Specific Heat Ratio (γ):

Density (ρ):

kg/m³

Inlet Pressure (P1):

Outlet Pressure (P2):

Flow Rate (Q):

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1. What is Compressible Pipe Flow?

The compressible pipe flow equation calculates the mass flow rate of a compressible fluid through a pipe under isentropic conditions. It accounts for changes in density and pressure along the pipe length.

2. How Does the Calculator Work?

The calculator uses the isentropic flow equation:

\[ Q = A \times \sqrt{\frac{2 \times \Delta P \times \gamma}{\rho \times (\gamma - 1)} \times \left(1 - \left(\frac{P2}{P1}\right)^{\frac{\gamma - 1}{\gamma}}\right)} \]

Where:

\( Q \) — Volumetric flow rate (m³/s)
\( A \) — Cross-sectional area (m²)
\( \Delta P \) — Pressure difference (Pa)
\( \gamma \) — Specific heat ratio (dimensionless)
\( \rho \) — Density (kg/m³)
\( P1 \) — Inlet pressure (Pa)
\( P2 \) — Outlet pressure (Pa)

Explanation: The equation accounts for the compressibility of gases and the relationship between pressure, density, and flow area.

3. Importance of Compressible Flow Calculation

Details: Accurate flow rate calculation is crucial for designing piping systems, sizing valves, and ensuring proper operation of compressible fluid systems.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Ensure P2 is less than P1 for meaningful results. Typical γ values: 1.4 for air, 1.3 for natural gas.

5. Frequently Asked Questions (FAQ)

Q1: What is isentropic flow?
A: Isentropic flow is a reversible adiabatic flow where entropy remains constant - no heat transfer and no friction losses.

Q2: When is this equation valid?
A: For steady, one-dimensional, isentropic flow of an ideal gas through a constant-area duct with negligible potential energy changes.

Q3: What if the flow is choked?
A: This equation doesn't account for choked flow conditions (Mach = 1 at exit). Different equations apply in that case.

Q4: How does temperature affect the result?
A: Temperature is accounted for indirectly through the density (ρ) and specific heat ratio (γ) parameters.

Q5: What are typical applications?
A: Gas pipelines, pneumatic systems, HVAC ductwork, and any system where gas compressibility significantly affects flow.