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 of constant cross-section. It relates the pressure difference to the flow rate, fluid viscosity, and pipe dimensions.

2. How Does the Calculator Work?

The calculator uses Poiseuille's Law:

Where:

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

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

3. Applications of Poiseuille's Law

Details: Poiseuille's Law is widely used in fluid dynamics, particularly in calculating pressure drops in piping systems, blood flow in arteries, and designing hydraulic systems.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, length in meters, flow rate in m³/s, and radius in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are the assumptions of Poiseuille's Law?
A: The fluid is incompressible and Newtonian, flow is laminar, the pipe is long with constant circular cross-section, and there's no slip at the pipe walls.

Q2: Why is radius raised to the fourth power?
A: This demonstrates the significant effect of pipe diameter on flow resistance. A small change in radius results in a large change in pressure required for the same flow.

Q3: What are typical viscosity values?
A: Water at 20°C has viscosity of about 0.001 Pa·s, while honey has viscosity around 10 Pa·s.

Q4: When is Poiseuille's Law not applicable?
A: It doesn't apply to turbulent flow, non-Newtonian fluids, short pipes, or pipes with varying cross-sections.

Q5: How does temperature affect the calculation?
A: Temperature primarily affects viscosity. For accurate calculations, use viscosity values at the appropriate temperature.