CFR9_CVS3 Continuity Equation

Components of Blood

Plasma

  • Definition: Liquid component of blood, comprises over 50% of blood volume.

  • Composition: Mainly water, dissolved salts (electrolytes), and proteins.

Red Blood Cells (Erythrocytes)

  • Volume: Approximately 40% of blood's volume.

  • Function: Contains hemoglobin, which carries oxygen from the lungs to body tissues.

White Blood Cells (Leukocytes)

  • Ratio: About 1 white blood cell for every 660 red blood cells.

  • Function: Defends the body against infections.

Platelets (Thrombocytes)

  • Definition: Cell-like particles involved in blood coagulation.

  • Ratio: About 1 platelet to every 20 red blood cells.

  • Function: Clumping together at bleeding sites to form plugs and seal blood vessels.

Haematocrit

  • Definition: Volume ratio of red blood cells to total blood volume.

  • Measurement: Typically measured by centrifugation.

  • Significance: Determines blood viscosity; varies among tissues and body conditions.

  • Example: In a 70 kg male, approximately 5 liters of blood, heart pumps about 80 ml per contraction.

Heart Function as a Pump

  • Types of Pumps:

    1. Vacuum Pumps: Designed to reduce pressure.

    2. Forced Pumps: Increase pressure (e.g. heart).

  • Mechanics:

    • Chambers expand, causing volume increase and pressure decrease, leading to blood intake.

    • Contraction decreases volume, increasing pressure, forcing blood out.

Blood Circulation

  • Heart operates as two synchronous pumps:

    1. Systemic Circulation: Left side of the heart.

    2. Pulmonary Circulation: Right side of the heart.

  • Pressure Changes:

    • In systemic circulation, pressure drops due to viscous forces from ~120 mm Hg to ~4-5 mm Hg at right atrium.

    • Right heart boosts pressure to approximately 25-30 mm Hg before entering lungs.

Fluid Dynamics Principles

Types of Fluid Flow

  1. Streamline (Laminar) Flow:

    • Smooth path of fluid particles, causing minimal energy loss.

    • Commonly found in clean, smooth blood vessels.

  2. Turbulent Flow:

    • Chaotic and irregular, characterized by eddy currents.

    • Absorbs significant energy.

Continuity Equation

  • States that for incompressible fluids, flow into a channel equals flow out.

  • Formula: ( Q = A \cdot v )

    • ( Q ): flow rate, ( A ): cross-sectional area, ( v ): fluid velocity.

  • Application: Blood flow features and variations in velocity as cross-sectional area changes.

Blood Flow Patterns

  • Blood speed increases in narrowed arteries (due to plaque), contrary to common expectation of flow speed increases with smaller diameter.

  • Example: Aorta ~3 cm² cross-sectional area vs total capillary area ~900 cm² results in lower speed in capillaries (~1 mm/s) for efficient gas exchange.

Critical Flow Speed

  • Definition: The speed above which turbulence occurs.

  • Calculated using Reynold’s number: ( V_{crit} = (Constant) \cdot (Viscosity) \cdot (Density) \cdot (Vessel\ Radius) )

  • Typical value for blood: ( V_{crit} \approx 0.4\ m/s ).

Conclusion

  • Blood flow dynamics are critical for understanding cardiovascular function and health.

  • Understanding these principles aids in diagnosing and managing cardiovascular conditions.