Lecture Notes: Laminar Flow and Turbulence

Key Concepts

• Laminar Flow: Characterized by smooth, orderly layers of fluid that do not cross each other.
• Poiseuille's Law: Describes the volume of fluid flow per time through a pipe under laminar conditions.

Transition from Laminar to Turbulent Flow

• Laminar to Turbulent Transition: Occurs when layers of fluid start to cross, causing vortices and eddy currents.
• Predicting Turbulence:
  • Reynold's Number (R): A dimensionless number that predicts the transition from laminar to turbulent flow.
  • Critical Speed: The speed at which flow becomes chaotic if exceeded.

Reynold's Number

• Definition: A predictor of turbulence in fluid flow.
• Calculation:
  • Formula: [ R \times \text{viscosity (η)} \div (2 \times \text{density} \times \text{radius of the tube}) ]
  • Viscosity (η): The Greek letter eta is used to represent viscosity in the formula.

Application to Blood Flow

• Blood Flow in Aorta:
  • Reynold's Number for blood ≈ 2000.
  • Important in medical contexts to predict turbulence.

Importance of Reynold's Number

• Dimensionless: No units, as all units in the calculation cancel out.
• Predictive Tool: Determines where Poiseuille's Law may fail due to turbulence.

Challenges

• Complexity in Predicting Turbulence: Difficult to predict and describe behavior beyond the critical speed.
• Computational Approach: Often requires computer simulations for accurate modeling of turbulent flow.

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These notes provide a concise summary of how Reynold's Number is used to predict the transition from laminar to turbulent flow, specifically its application to blood flow and the limitations of analytical predictions.