Fluid Dynamics: Velocity and Flow

Velocity, Flow, and Area

• Flow (Q) is the product of velocity (v) and cross-sectional area (A): Q = v × A.
• Velocity can be calculated from flow and area: v = Q/A.

Poiseuille’s Law and Resistance

• Poiseuille’s experiments demonstrated that blood flow is affected by pressure gradient (ΔP), length of the vessel (L), radius of the vessel (r), and fluid viscosity (η).
• Blood flow (Q) is proportional to the pressure gradient (ΔP) and the fourth power of radius (r^4), and inversely proportional to vessel length (L) and viscosity (η).
• Poiseuille’s Law is mathematically expressed as: Q = (ΔPr^4π) / (ηL8).

Total Resistance in the Cardiovascular System

• Total resistance is the cumulative effect of resistances in series and parallel configurations.
• Increasing the number of vessels in parallel decreases total resistance.

Laminar and Turbulent Flow

• Laminar flow occurs in layers, with the fastest flow in the center of the vessel; velocity profile resembles a parabolic shape.
• Turbulent flow occurs when lamina breakdown, resulting in decreased vascular conductance and increased resistance to flow.
• Reynold's Number (Re) indicates flow type: Re < 2000 suggests laminar flow, while Re > 2000 indicates turbulence.
• Turbulence may arise at vessel bends, branch points, or stenotic valves.

Blood Viscosity

• Blood is classified as a non-Newtonian fluid, exhibiting variable viscosity under different flow conditions.
• The Fahraeus-Lindqvist effect describes reduced apparent viscosity when vessel diameter is less than 0.2 mm due to axial accumulation of red blood cells (RBCs).

Learning Objectives

• Understand the differences in O2 content and saturation between arterial and venous blood, along with normal heart chamber pressures.
• Familiarize with normal hematocrit, hemoglobin levels, and plasma electrolyte values (K+, Na+, Ca²+).
• Recognize blood volume distribution in the cardiovascular system and estimate total blood volume based on body weight.
• Analyze the relationship between pressure, flow, and resistance and its implications on wall tension (law of Laplace).
• Distinguish between laminar and turbulent flow and factors influencing each type.
• Identify factors affecting blood viscosity and the implications of the Fahraeus-Lindqvist effect.

Cardiovascular System Overview

• The heart beats approximately 115,000 times daily, pumping about 7,230 liters of blood at rest.
• Blood pressure peaks at about one-sixth of an atmosphere, generating roughly two watts of mechanical power.
• The cardiovascular system functions as a closed-loop network supporting organ blood supply and performing essential roles like oxygen delivery, metabolic waste removal, hormone transport, immune response, temperature regulation, and fluid volume balance.

Key Hemodynamic Features

• Blood volume constitutes 7-8% of body weight; estimate it using: blood volume (L) = body weight (kg) × 0.08.
• Blood velocity decreases in capillaries where the cross-sectional area is maximized.

Relationships in Hemodynamics

• Pressure in the system correlates with flow and resistance: P = Q × R.
• Total intravascular pressure consists of static and dynamic components: P_total = P_static + P_dynamic.

Law of Laplace

• Transmural pressure (ΔP) represents the difference between internal and external pressures across a vessel wall.
• Wall tension (T) relates to radius and wall thickness, following the law of Laplace: T = ΔPr/h (for cylinders) and T = ΔPr/2h (for spheres).

Important Fluid Dynamics Concepts

• Increased vessel radius elevates tension on vessel walls, even if pressure remains constant.
• The presence of a cell-free layer at blood vessel walls enhances flow dynamics according to the Fahraeus-Lindqvist effect.
• Blood viscosity, affected by hematocrit levels, influences resistance; high hematocrit (polycythemia) raises viscosity and resistance, while low hematocrit (anemia) decreases both.

Explore the principles of fluid dynamics, focusing on velocity, flow, and cross-sectional area through the equation Q = v x A. Understand Poiseuille's law and its implications on resistance in blood vessels, considering factors like pressure gradient, tube length, radius, and fluid viscosity.