1. What is Poiseuille's Law?

Poiseuille's Law describes the flow resistance of a fluid through a cylindrical pipe. It shows that resistance is directly proportional to the fluid's viscosity and pipe length, and inversely proportional to the fourth power of the pipe's radius.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law equation:

Where:

• \( R \) — Flow resistance (Pa s/m³)
• \( \mu \) — Dynamic viscosity of the fluid (Pa s)
• \( L \) — Length of the pipe (m)
• \( r \) — Inner radius of the pipe (m)

Explanation: The equation shows that small changes in pipe radius have dramatic effects on flow resistance due to the r⁴ relationship.

3. Importance of Flow Resistance Calculation

Details: Calculating flow resistance is essential for designing piping systems, predicting fluid flow rates, and determining pump requirements in engineering applications.

4. Using the Calculator

Tips: Enter viscosity in Pa s, length and radius in meters. All values must be positive numbers. The radius should be the inner radius of the pipe.

5. Frequently Asked Questions (FAQ)

Q1: What are typical viscosity values?
A: Water at 20°C has μ≈0.001 Pa s, while honey might be μ≈10 Pa s. Viscosity decreases with temperature for liquids.

Q2: Why is radius to the fourth power?
A: The r⁴ relationship comes from the parabolic velocity profile of laminar flow in pipes - smaller radii dramatically increase resistance.

Q3: When is Poiseuille's Law not applicable?
A: For turbulent flow (Re>2000), non-Newtonian fluids, very short pipes, or when temperature changes affect viscosity significantly.

Q4: How does pipe material affect resistance?
A: Material affects roughness which impacts turbulent flow, but for laminar flow (where Poiseuille applies), roughness has minimal effect.

Q5: What's the difference between R and pressure drop?
A: R is resistance (Pa s/m³). Pressure drop (ΔP) = R × flow rate (Q). R describes the pipe, ΔP depends on flow.