1. What is Poiseuille's Law?

Poiseuille's Law describes the pressure drop in an incompressible Newtonian fluid in laminar flow through a long cylindrical pipe. It is fundamental in fluid dynamics and hemodynamics.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law equation:

Where:

• \( \Delta P \) — Pressure drop (Pa)
• \( Q \) — Flow rate (m³/s)
• \( \mu \) — Dynamic viscosity (Pa·s)
• \( L \) — Length of pipe (m)
• \( r \) — Radius of pipe (m)
• \( \pi \) — Mathematical constant (3.1416)

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

3. Importance of Pressure Drop Calculation

Details: Calculating pressure drop is crucial for designing piping systems, understanding blood flow in vessels, optimizing industrial processes, and ensuring efficient fluid transport.

4. Using the Calculator

Tips: Enter flow rate in m³/s, viscosity in Pa·s, length in meters, and radius in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is laminar flow?
A: Laminar flow is characterized by fluid particles following smooth paths in layers, with minimal mixing between adjacent layers, typically at low Reynolds numbers.

Q2: When is Poiseuille's Law applicable?
A: The law applies to steady, laminar flow of incompressible Newtonian fluids in long, straight, cylindrical pipes with constant cross-section.

Q3: How does radius affect pressure drop?
A: Pressure drop is inversely proportional to the fourth power of radius. Doubling the radius reduces pressure drop by a factor of 16.

Q4: What are typical viscosity values?
A: Water at 20°C: 0.001 Pa·s; Blood: 0.003-0.004 Pa·s; Honey: 2-10 Pa·s; Air: 0.000018 Pa·s.

Q5: Can this be used for blood flow calculations?
A: Yes, but with limitations. Blood is non-Newtonian and vessels are elastic, so modifications are needed for accurate hemodynamic modeling.