1. What is a Flow Through a Pipe Calculator?

Definition: This calculator determines the volumetric flow rate of a fluid through a cylindrical pipe using the Hagen-Poiseuille equation.

Purpose: It helps engineers, physicists, and students analyze fluid dynamics in pipe systems under laminar flow conditions.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

Where:

• \( Q \) — Volumetric flow rate (m³/s)
• \( r \) — Pipe radius (m)
• \( \Delta P \) — Pressure difference (Pa)
• \( \mu \) — Dynamic viscosity (Pa·s)
• \( L \) — Pipe length (m)

Explanation: The 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 calculations are essential for designing piping systems, predicting fluid behavior, and ensuring proper system operation in chemical, mechanical, and civil engineering applications.

4. Using the Calculator

Tips: Enter the pipe radius, pressure difference, fluid viscosity (default 0.001 Pa·s for water at 20°C), and pipe length (default 1 m). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this equation apply to?
A: The Hagen-Poiseuille equation applies only to laminar (not turbulent) flow with Reynolds number < 2100.

Q2: Why is radius to the fourth power?
A: The r⁴ relationship shows how dramatically pipe diameter affects flow rate - doubling the radius increases flow 16-fold.

Q3: What's a typical viscosity value for water?
A: Water at 20°C has μ ≈ 0.001 Pa·s. Honey might be ~10 Pa·s, while air is ~0.000018 Pa·s.

Q4: Can I use this for non-circular pipes?
A: No, this equation is specifically for circular cross-sections. For other shapes, use the hydraulic diameter method.

Q5: How does temperature affect the calculation?
A: Temperature primarily affects viscosity. Warmer fluids typically have lower viscosity, increasing flow rate.