1. What is the Hagen-Poiseuille Equation?

The Hagen-Poiseuille equation describes the volumetric flow rate of a fluid through a cylindrical pipe under laminar flow conditions. It's particularly important for calculating flow rates in heat pump systems and other fluid dynamics applications.

2. How Does the Calculator Work?

The calculator uses the Hagen-Poiseuille equation:

Where:

• \( Flow \) — Volumetric flow rate (m³/s)
• \( d \) — Internal diameter of the pipe (m)
• \( \Delta P \) — Pressure difference (Pa)
• \( \mu \) — Dynamic viscosity (Pa·s)
• \( L \) — Length of the pipe (m)

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

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing heat pump systems, determining pump requirements, and ensuring efficient heat transfer in HVAC applications.

4. Using the Calculator

Tips: Enter all values in SI units (meters for length/diameter, Pascals for pressure). Ensure viscosity is for the correct temperature as it varies significantly with temperature.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of the Hagen-Poiseuille equation?
A: It assumes laminar flow, Newtonian fluid, no-slip condition, constant viscosity, and a long cylindrical pipe with constant circular cross-section.

Q2: How does pipe diameter affect flow rate?
A: Flow rate increases with the fourth power of diameter - doubling diameter increases flow rate by 16 times (2^4).

Q3: What is typical viscosity for water in heat pump systems?
A: At 20°C, water viscosity is about 0.001002 Pa·s. It decreases with increasing temperature (≈0.000282 Pa·s at 100°C).

Q4: When is this equation not applicable?
A: For turbulent flow (Re > 2100), non-Newtonian fluids, short pipes, or non-circular cross-sections.

Q5: How does this relate to heat pump efficiency?
A: Proper flow rate ensures optimal heat transfer. Too low reduces efficiency; too high increases pump power requirements.