Poiseuille's Equation Calculator

Poiseuille's Equation, named after Jean Léonard Marie Poiseuille, is a fundamental principle in fluid mechanics that describes the flow of a viscous liquid in a long cylindrical pipe.

Historical Background

Poiseuille, a French physician, and physicist conducted extensive research in the 19th century on blood flow in the human body, leading to the formulation of this equation. It was derived from his experiments on the flow of fluids through tubes and is a pivotal equation in the field of fluid mechanics.

Calculation Formula

Poiseuille's Equation calculates the volume flow rate (\(Q\)) of a viscous fluid flowing through a pipe:

\[ Q = \frac{\pi r^4 (\Delta P)}{8 \mu L} \]

Where:

• \(r\) is the internal radius of the tube,
• \(\Delta P\) is the pressure difference between the two ends,
• \(\mu\) is the fluid's absolute viscosity,
• \(L\) is the total length of the tube.

Example Calculation

Consider a tube with:

• Pressure Difference (\(\Delta P\)): 100 mmHg,
• Internal Radius (\(r\)): 0.01 meters,
• Absolute Viscosity (\(\mu\)): 1 Centi-Poiseuille,
• Total Length (\(L\)): 2 meters.

The volume flow rate (\(Q\)) can be calculated as follows, ensuring units are consistent.

Importance and Usage Scenarios

Poiseuille's Equation is crucial in designing and analyzing systems involving the flow of liquids through pipes, such as in medical equipment (e.g., intravenous therapy), hydraulic systems, and chemical processing plants.

Common FAQs

1. Why is viscosity important in Poiseuille's Equation?

   • Viscosity is a measure of a fluid's resistance to flow. Higher viscosity means more resistance, affecting the flow rate.

2. How does tube radius affect the flow rate?

   • The flow rate increases with the fourth power of the radius, meaning small changes in the tube's radius can significantly affect the flow rate.

3. Can Poiseuille's Equation be used for gases?

   • While primarily for liquids due to viscosity's role, it can be adapted for gases under certain conditions, considering their compressibility and viscosity differences.