BMS1031 Wk2WS

Week Two Overview

• Continuation from Week One: Fluids and Pressure

• Focus on two main concepts:

  • Dynamics of Flow

    • Laminar Flow

    • Turbulent Flow

  • Key Equations

    • Continuity of Flow Equation

    • Bernoulli's Equation

Activity 1: Continuity of Flow

• Continuity of Flow Equation

  • States that fluid velocity adjusts with changing cross-sectional area of a tube to maintain a constant flow rate.

  • Formula: A1V1 = A2V2

    • A = cross-sectional area, V = fluid velocity

  • Intuition Example: Covering a garden hose increases water speed.

Problem Solving

• Units Check

  • Volume Flow Rate: liters per second (L/s) to cubic meters per second (m³/s)

  • Example for Volume Flow:

    • 1 L = 0.001 m³

• Key Concept Questions:

  1. Impact of Tube Size Change:

     • If area increases (A1 < A2), velocity decreases (V1 > V2).

     • If area decreases, velocity increases to maintain flow.

  2. Flow Rate Conservation:

     • Example with arteries:

     • Larger artery (A1) branches into two smaller arteries (A2).

     • Q = A1V1 = 2A2V2

     • Answer: Two smaller arteries must have equal flow rates to the larger artery, reinforcing continuity.

  3. Radius and Flow Speed:

     • Larger artery radius (r1) to smaller arteries (r2).

  • Area is calculated using A = πr².

  • Both A2 need combined area equal to A1 to maintain flow.

  4. Blood Velocity in Aorta:

     • Given flow rate: Q = 0.1 L/s

     • Cross-sectional area: A = 1 x 10^-4 m²

     • Convert flow rate to m³/s and calculate velocity:

     • V = Q/A = (1 x 10^-4)/(1 x 10^-4) = 1 m/s.

  5. Capillary Subdivision:

     • Example of an artery and capillaries, apply continuity to find out the number of capillaries:

     • Q = A x V for both artery and capillaries to set up an equation.

     • Shows critical understanding of flow rates and continuity!

Activity 2: Bernoulli's Equation

• Bernoulli's Equation Overview

  • Relates pressure to fluid velocity in tubes of varying size

  • As velocity increases (tube narrows), pressure decreases.

Real-world Application

• Flight Dynamics:

  • Airplane wings:

  • Curved upper wing increases airspeed, resulting in lower pressure above the wing.

  • Pressure difference creates lift, showing application relevance beyond blood flow.

Changes with Height

• Effect of Height on Pressure and Flow:

  • Incorporates potential energy aspects of fluids in varying heights across the system. Bernoulli's equation shows how static pressure, dynamic pressure, and hydrostatic pressure relate.

Activity 3: Laminar vs Turbulent Flow

• Viscous Flow Considerations:

  • Laminar Flow: smooth, orderly, and occurs in lower velocity fluids.

    • Example: Honey vs Water

    • Poucille’s equation outlines how viscous forces affect flow dynamics.

  • Turbulent Flow: chaotic, irregular, occurs with high velocities.

    • Caused by sharp changes in velocity or tube narrowing.

Key Concepts and Equations

• Discuss Poiseuille's equation to calculate flow rate in tubes with laminar flow.

• Understand how viscosity affects flow and be able to calculate flow through tiny vessels like capillaries using given equations and values.

Problem Solving with Poiseuille’s Equation

• Manipulate equations for flow rates given stress on viscosity, radius, length, and pressure differences:

  • Relations between all variables presented in problems.

Example Scenarios for Problem Solving

• IV needle choices dictated by radius and length: maximize flow rate. Identify correct needle fitting considering flow dynamics.

• Kidney Filtration: calculate needed pores based on flow for effective filtration rates.

• Blood transfusion dynamics: assess pressure required due to viscosity and flow across various tube diameters.

End Notes

• Final problems on conversions between units, charts, and calculations of pressure discrepancies.

• Emphasis on understanding flow rates in practical applications.

• Recommended practicing conceptual questions from the worksheet independently.