1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the pressure drop in an incompressible and Newtonian fluid in laminar flow through a long cylindrical pipe of constant cross section. It is fundamental in fluid dynamics for analyzing pipe flow systems.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

Where:

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

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

3. Importance of Pressure Flow Calculation

Details: Accurate pressure drop calculation is crucial for designing piping systems, selecting pumps, and ensuring proper fluid flow in various engineering applications.

4. Using the Calculator

Tips: Enter all values in SI units. Ensure viscosity > 0, length > 0, flow rate > 0, and radius > 0. The calculator assumes laminar flow conditions.

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow?
A: Laminar flow occurs when fluid flows in parallel layers with no disruption between them, typically at Reynolds numbers below 2300.

Q2: Can this equation be used for turbulent flow?
A: No, the Hagen-Poiseuille equation is only valid for laminar flow. For turbulent flow, the Darcy-Weisbach equation should be used.

Q3: What are typical viscosity values?
A: Water at 20°C has μ ≈ 0.001 Pa·s, while honey might have μ ≈ 10 Pa·s. Viscosity varies significantly with temperature.

Q4: Why is radius to the fourth power?
A: The strong dependence on radius (r⁴) shows that small changes in pipe diameter dramatically affect pressure drop and flow rate.

Q5: What are practical applications?
A: Used in designing plumbing systems, medical devices (like IV lines), industrial piping, and microfluidic devices.