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:
Impact of Tube Size Change:
If area increases (A1 < A2), velocity decreases (V1 > V2).
If area decreases, velocity increases to maintain flow.
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.
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.
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.
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.