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2.5 Hydrostatics, Fluid Dynamics & Circulatory Hemodynamics
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1 MCAT Architecture, Test-Day Logistics & Scientific Inquiry Skills
1.1 MCAT Architecture, Test-Day Logistics & Scoring Scale (472–528) 1.2 Scientific Inquiry & Reasoning Skills (SIRS 1–4) & Experimental Design 1.3 Passage Navigation, Section Pacing & Strategic Guessing
2 Physics: Mechanics, Fluids & Periodic Motion
2.1 Translational Kinematics, Projectile Motion & Newton's Laws 2.2 Friction, Centripetal Force & Rotational Equilibrium in Biomechanics 2.3 Mechanical Work, Pressure-Volume Work & Forms of Energy 2.4 The Work-Energy Theorem, Power & Mechanical Advantage 2.5 Hydrostatics, Fluid Dynamics & Circulatory Hemodynamics 2.6 Periodic Motion, Wave Fundamentals, Superposition & Standing Waves 2.7 Sound Intensity, the Decibel Scale & the Doppler Effect
3 Physics: Electromagnetism, Optics & Atomic Physics
3.1 Coulomb's Law, Electric Fields & Electric Potential 3.2 Electric Dipoles, Membrane Potentials & the Nernst Equation 3.3 Electric Current, Resistance & Resistor Networks 3.4 Capacitance, Dielectrics & Axonal Cable Theory 3.5 Light, Refraction, Mirrors & Thin Lenses 3.6 The Optical System of the Eye & Corrective Lens Prescriptions 3.7 Nuclear Architecture, Binding Energy & Radioactive Decay Modes 3.8 Decay Kinetics, Half-Life & Medical Radiation Applications
4 General Chemistry: Atoms, Solutions & Thermodynamics
4.1 Quantum Numbers, Electron Configurations & Periodic Trends 4.2 Lewis Structures, Formal Charge, VSEPR Geometry & Molecular Polarity 4.3 States of Matter, Phase Diagrams, Heating Curves & Solvation 4.4 Concentration Units, Henry's Law & Colligative Properties 4.5 Thermodynamic Systems, the First Law, Enthalpy & Entropy 4.6 Gibbs Free Energy, Equilibrium & Bioenergetic Reaction Coupling 4.7 Collision Theory, Transition States & Empirical Rate Laws 4.8 Integrated Rate Laws, Half-Life, Arrhenius Behaviour & Catalysis
5 General Chemistry: Equilibrium, Acids, Bases & Electrochemistry
5.1 Chemical Equilibrium, Equilibrium Constants & Le Chatelier's Principle 5.2 Acid-Base Definitions, pH Scale, Titrations & Physiological Buffers 5.3 Electrochemical Cells, Reduction Potentials & the Nernst Equation
6 Organic Chemistry: Structure, Stereochemistry & Mechanisms
6.1 IUPAC Nomenclature, Functional Group Priority & Orbital Hybridisation 6.2 Resonance, Inductive Effects & Conformational Analysis 6.3 The Isomer Hierarchy, Chirality & CIP Priority Rules 6.4 Optical Activity, Diastereomers, Meso Compounds & Fischer Projections 6.5 Carbonyl Reactivity: Aldehydes, Ketones & Nucleophilic Additions 6.6 Carboxylic Acids & Derivatives: Nucleophilic Acyl Substitution
7 Bio-Organic Reactions, Laboratory Separations & Spectroscopy
7.1 Alcohol Physical Properties, Acidity, Leaving Groups & Protecting Groups 7.2 Carbon Oxidation States, Laboratory Oxidations & Biological Redox Cofactors 7.3 Extraction, Acid-Base Separation & Distillation 7.4 Analytical and Biomacromolecular Chromatography 7.5 Infrared and UV-Vis Spectroscopy 7.6 1H-NMR, 13C-NMR & Integrated Spectral Elucidation
8 Biochemistry: Amino Acids, Peptides & Enzymes
8.1 Amino Acid Stereochemistry & Side-Chain Classification 8.2 Zwitterions, Titration Curves, Isoelectric Points & the Peptide Bond 8.3 The Hierarchy of Protein Structure 8.4 Folding Thermodynamics, Haemoglobin Cooperativity & Denaturation 8.5 Catalytic Mechanisms, Enzyme Classification & Michaelis-Menten Kinetics 8.6 Enzyme Inhibition Modes & Allosteric Cooperativity
9 Biochemistry: Cellular Metabolism & Bioenergetics
9.1 Glycolysis: The Ten Steps, Regulation & Anaerobic Fermentation 9.2 Gluconeogenesis Bypass Enzymes & the Pentose Phosphate Pathway 9.3 The Pyruvate Dehydrogenase Complex & the Citric Acid (Krebs) Cycle 9.4 Mitochondrial Architecture & the Respiratory Complexes 9.5 Chemiosmotic Coupling, ATP Synthase, NADH Shuttles & Uncouplers 9.6 Fatty Acid Beta-Oxidation, Ketogenesis & Glycogen Dynamics
10 Molecular Biology: Nucleic Acids & Genetic Technologies
10.1 Nucleic Acid Chemistry, the Double Helix & Chromatin Organisation 10.2 DNA Replication: Replisome Enzymology & Fork Dynamics 10.3 DNA Damage & Cellular Repair Pathways 10.4 The Central Dogma, Strand Nomenclature & Transcription Machinery 10.5 Post-Transcriptional Processing of Eukaryotic Pre-mRNA 10.6 Regulation of Gene Expression: Operons, Enhancers & Epigenetics 10.7 The Genetic Code, Wobble & Mutation Taxonomy 10.8 tRNA Charging & the Stages of Ribosomal Translation 10.9 Translation Inhibitors & Post-Translational Processing 10.10 Restriction Enzymes, Cloning Vectors, cDNA Libraries & PCR 10.11 Blotting, Sequencing, Microarrays & CRISPR-Cas9
11 Cellular Biology & Microbiology
11.1 Eukaryotic Organelles, Membrane Transport & Cytoskeletal Dynamics 11.2 The Eukaryotic Cell Cycle, Mitosis, Checkpoints & Apoptosis 11.3 Cell Theory, Bacterial Morphology, Genetics & Sub-Viral Agents
12 Genetics, Evolution & Embryology
12.1 Mendel's Laws & the Cytology of Meiosis 12.2 Genetic Crosses, Non-Mendelian Inheritance, Linkage & Pedigree Analysis 12.3 The Hardy-Weinberg Principle, Assumptions & Clinical Calculations 12.4 Mechanisms of Evolution, Speciation & Macroevolutionary Patterns 12.5 Gametogenesis, Fertilisation, Cleavage & Implantation 12.6 Gastrulation, Germ Layer Derivatives, Stem Cell Potency & Neurulation
13 Human Physiology: Control & Transport Systems
13.1 Neuronal Anatomy, the Resting Potential & the Action Potential 13.2 Conduction Velocity, Synaptic Transmission & Postsynaptic Summation 13.3 Neurotransmitter Systems, CNS/PNS Organisation & Reflex Arcs 13.4 Hormone Classification & the Hypothalamus-Pituitary Axis 13.5 Negative Feedback Architecture, Endocrine Glands & Calcium Homeostasis 13.6 Cardiac Anatomy, Electrophysiology, the Cardiac Cycle & Cardiac Output 13.7 Vascular Hemodynamics, Starling Forces, Blood Components & Hemostasis 13.8 Respiratory Anatomy, Ventilation Mechanics & Pulmonary Surfactant 13.9 Spirometry, Dead Space, Gas Exchange & Haemoglobin Allostery 13.10 Carbon Dioxide Transport, the Chloride Shift & Acid-Base Control of Breathing
14 Human Physiology: Maintenance, Defense & Locomotion
14.1 Renal Anatomy, Glomerular Ultrafiltration & Tubular Transport 14.2 The Countercurrent Multiplier & Endocrine Regulation of Renal Function 14.3 GI Architecture, the Enteric Nervous System & Gastric Secretion 14.4 Pancreatic and Biliary Digestion & Intestinal Nutrient Absorption 14.5 Hepatic Processing, GI Endocrine Regulators & the Colon 14.6 Innate Immunity: Barriers, Complement & Cellular Effectors 14.7 Adaptive Humoral Immunity: B Cells & Immunoglobulins 14.8 Adaptive Cellular Immunity: T Cells, Thymic Selection & MHC Presentation 14.9 Muscle Types, Sarcomere Anatomy & Excitation-Contraction Coupling 14.10 Bone Architecture, Remodelling & the Integumentary System
15 CARS: Passage Analysis & Argument Mapping
15.1 CARS Architecture, Passage Genres (Humanities vs Social Sciences) & Mindset 15.2 Active Reading, Author's Central Thesis & Tone Analysis 15.3 Rhetorical Structure, Claim-Evidence Linkages & Argument Mapping
16 CARS: Question Types & Reasoning Strategies
16.1 Skill 1 Demands, Question Stems, Detail Retrieval & Paraphrase Recognition 16.2 Inferential Meaning, Distractor Taxonomy & a Worked Skill 1 Passage 16.3 Skill 2 Architecture, Question Stems, Unstated Assumptions & Evidence Strength 16.4 Rhetorical Mechanisms, Logical Fallacies & a Worked Skill 2 Passage 16.5 Skill 3 Architecture, Question Stems, Application & Analogy Mapping 16.6 Incorporating New Information, Calibrating Evidentiary Impact & a Worked Skill 3 Passage
17 Sensory Processing, Perception & Cognition
17.1 Sensation versus Perception & Sensory Receptor Classification 17.2 Psychophysical Thresholds, Weber's Law, Adaptation & Signal Detection Theory 17.3 Vision: Ocular Anatomy, Phototransduction & Central Visual Pathways 17.4 Audition & the Vestibular System 17.5 Somatosensation, Pain & Chemoreception 17.6 Models of Attention & Working Memory Architecture 17.7 Long-Term Memory Taxonomy, Encoding, Storage & Retrieval 17.8 Forgetting, Interference, Memory Distortion & Long-Term Potentiation 17.9 Problem Solving, Heuristics, Cognitive Biases & Language 17.10 Sleep Architecture, Circadian Neurobiology, Sleep Disorders & Psychoactive Drugs
18 Emotion, Stress, Motivation & Personality
18.1 Components of Emotion & Classical Theories of Emotion 18.2 The Limbic Circuit, Stress Appraisal & Selye's General Adaptation Syndrome 18.3 Intrinsic and Extrinsic Motivation, Drive-Reduction, Arousal & Incentive Theories 18.4 Cognitive and Humanistic Need Models & the Neuroendocrine Control of Hunger and Sex 18.5 The Psychoanalytic Perspective & Neo-Freudian Revisions 18.6 Humanistic, Trait & Social-Cognitive Perspectives on Personality 18.7 Biopsychosocial Etiology, Schizophrenia, Mood & Anxiety Disorders 18.8 Somatic, Dissociative, Personality & Neurodegenerative Disorders
19 Learning, Social Behavior & Identity
19.1 Non-Associative Learning & Classical Conditioning 19.2 Operant Conditioning, Reinforcement Schedules & Observational Learning 19.3 Self-Concept & Lifespan Developmental Theories 19.4 Kohlberg's Moral Development & Sociocultural Frameworks 19.5 Social Influence: Conformity, Obedience, Group Dynamics & Prosocial Behavior 19.6 Social Cognition, Attribution Theory, Prejudices, Stereotypes & Discrimination
20 Sociology, Demographics & Healthcare Disparities
20.1 Macro versus Micro Paradigms, Structural Functionalism & Conflict Theory 20.2 Symbolic Interactionism, Social Constructionism & Modern Paradigms 20.3 Major Social Institutions: Structure, Function & Dysfunction 20.4 Demographics, Population Pyramids, the Demographic Transition & Globalisation 20.5 Systems of Stratification, Socioeconomic Status & Social Mobility 20.6 Poverty, Spatial Inequality, the Socioeconomic Gradient & Health Inequities
2.5 Hydrostatics, Fluid Dynamics & Circulatory Hemodynamics
Key Takeaways Explain This Topic AI
Hydrostatic pressure scales linearly with fluid depth according to P = P0 + ρ g h; clinical blood pressure readings (e.g., 120/80 mmHg) measure gauge pressure (Pgauge = P - Patm), representing the pressure differential above atmospheric pressure.
Archimedes' principle states that the buoyant force on a submerged body equals the weight of displaced fluid (Fb = ρfluid Vsubmerged g); a floating object submerges to a volume fraction equal to the ratio of its density to fluid density (Vsubmerged / Vtotal = ρobject / ρfluid).
The continuity equation (A1 v1 = A2 v2) dictates that fluid velocity is inversely proportional to cross-sectional area; the enormous aggregate cross-sectional area of systemic capillary beds (~2500–3000 cm²) reduces blood velocity to <1 mm/s, maximizing time for transcapillary solute diffusion.
Poiseuille's law (Q = π ΔP r^4 / [8 η L]) demonstrates that laminar flow rate depends on the fourth power of vessel radius; a 20% reduction in arteriolar radius increases vascular resistance by approximately 2.44-fold (a 144% increase), establishing arterioles as the primary regulators of total peripheral resistance (TPR).
Bernoulli's principle and the Venturi effect state that fluid acceleration through a constricted lumen reduces static lateral pressure; in hypertrophic cardiomyopathy, high-velocity blood flow through a narrowed outflow tract creates negative pressure that pulls the anterior mitral valve leaflet toward the septum, exacerbating left ventricular outflow obstruction.
Last updated: September 2026
2.5 Hydrostatics, Fluid Dynamics & Circulatory Hemodynamics
The cardiovascular and respiratory systems are complex fluid-transport networks. The MCAT frequently tests fluid physics through physiological scenarios: hydrostatic pressures in upright patients, buoyant forces in bone densitometry, Venturi airflow in nebulizers, and Poiseuille flow across vasoconstricted arterioles. Distinguishing between ideal fluids (incompressible, non-viscous, laminar) and real fluids (viscous, subject to turbulent breakdown) is essential for predicting circulatory behavior.
- Fluid Statics: Density, Pressure & Buoyancy
- Density & Specific Gravity
- Density ( ρ \rho ρ ) is the mass per unit volume of a substance: ρ = m V \rho = \frac{m}{V} ρ = V m
For pure water at 4 ∘ C 4^\circ\text{C} 4 ∘ C , ρ water = 1000 kg/m 3 = 1.0 g/cm 3 = 1.0 g/mL \rho_{\text{water}} = 1000\text{ kg/m}^3 = 1.0\text{ g/cm}^3 = 1.0\text{ g/mL} ρ water = 1000 kg/m 3 = 1.0 g/cm 3 = 1.0 g/mL .
Specific Gravity ( S G SG SG ) is the dimensionless ratio of a substance's density to that of water: S G = ρ substance ρ water SG = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}} SG = ρ water ρ substance
In clinical medicine, urine specific gravity ( 1.002 − 1.030 1.002 - 1.030 1.002 − 1.030 ) evaluates renal concentrating ability and hydration status; elevated S G > 1.030 SG > 1.030 SG > 1.030 indicates dehydration, glycosuria, or SIADH.
Hydrostatic Pressure & Gauge Pressure
Hydrostatic pressure is the compressive force exerted by a static fluid per unit surface area. The absolute (total) hydrostatic pressure at a depth h h h below the surface of a fluid is: P = P 0 + ρ g h P = P_0 + \rho g h P = P 0 + ρ g h
where P 0 P_0 P 0 is the ambient pressure at the surface (typically atmospheric pressure, P atm P_{\text{atm}} P atm ).
Gauge Pressure ( P gauge P_{\text{gauge}} P gauge ) is the pressure relative to local atmospheric pressure: P gauge = P − P atm = ρ g h P_{\text{gauge}} = P - P_{\text{atm}} = \rho g h P gauge = P − P atm = ρ g h
Clinical sphygmomanometers measure gauge pressure. A blood pressure reading of 120 / 80 mmHg 120/80\text{ mmHg} 120/80 mmHg means that systolic and diastolic pressures exceed atmospheric pressure by 120 mmHg 120\text{ mmHg} 120 mmHg and 80 mmHg 80\text{ mmHg} 80 mmHg , respectively.
Unit Conversions for Pressure: 1 atm = 101 , 325 Pa ≈ 1.013 × 10 5 Pa = 760 mmHg = 760 Torr = 1033 cm H 2 O 1\text{ atm} = 101,325\text{ Pa} \approx 1.013 \times 10^5\text{ Pa} = 760\text{ mmHg} = 760\text{ Torr} = 1033\text{ cm H}_2\text{O} 1 atm = 101 , 325 Pa ≈ 1.013 × 1 0 5 Pa = 760 mmHg = 760 Torr = 1033 cm H 2 O
Pascal's Principle
A pressure change applied to an enclosed, incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel: Δ P = F 1 A 1 = F 2 A 2 ⟹ F 2 = F 1 ( A 2 A 1 ) \Delta P = \frac{F_1}{A_1} = \frac{F_2}{A_2} \implies F_2 = F_1 \left(\frac{A_2}{A_1}\right) Δ P = A 1 F 1 = A 2 F 2 ⟹ F 2 = F 1 ( A 1 A 2 )
Because liquid volume is conserved ( A 1 d 1 = A 2 d 2 A_1 d_1 = A_2 d_2 A 1 d 1 = A 2 d 2 ), mechanical work is conserved in an ideal hydraulic lift ( W = F 1 d 1 = F 2 d 2 W = F_1 d_1 = F_2 d_2 W = F 1 d 1 = F 2 d 2 ). A small force exerted over a large distance at a narrow piston produces a large force over a small distance at a broad piston.
Archimedes' Principle & Buoyant Force
Any object fully or partially submerged in a fluid experiences an upward buoyant force ( F b F_b F b ) equal in magnitude to the weight of the fluid displaced by the object: F b = m fluid g = ρ fluid V submerged g F_b = m_{\text{fluid}} g = \rho_{\text{fluid}} V_{\text{submerged}} g F b = m fluid g = ρ fluid V submerged g
Apparent Weight ( W apparent W_{\text{apparent}} W apparent ): For an object submerged in fluid: W apparent = W actual − F b = ( ρ object − ρ fluid ) V object g W_{\text{apparent}} = W_{\text{actual}} - F_b = (\rho_{\text{object}} - \rho_{\text{fluid}}) V_{\text{object}} g W apparent = W actual − F b = ( ρ object − ρ fluid ) V object g
Floating Objects: An object floats in static equilibrium if its weight is fully balanced by the buoyant force ( F b = W object F_b = W_{\text{object}} F b = W object ): ρ fluid V submerged g = ρ object V total g ⟹ V submerged V total = ρ object ρ fluid = S G \rho_{\text{fluid}} V_{\text{submerged}} g = \rho_{\text{object}} V_{\text{total}} g \implies \frac{V_{\text{submerged}}}{V_{\text{total}}} = \frac{\rho_{\text{object}}}{\rho_{\text{fluid}}} = SG ρ fluid V submerged g = ρ object V total g ⟹ V total V submerged = ρ fluid ρ object = SG For an iceberg or floating cell with S G = 0.90 SG = 0.90 SG = 0.90 , exactly 90 % 90\% 90% of its volume is submerged below the liquid surface.
Ideal Fluid Dynamics: Continuity & Bernoulli's Equations
An ideal fluid satisfies four foundational criteria:
Incompressible: Density ρ \rho ρ remains uniform throughout.
Non-viscous: Internal frictional resistance (viscosity η \eta η ) is zero.
Laminar (Streamline) Flow: Fluid particles follow smooth, non-intersecting streamlines without turbulence.
Irrotational: Fluid elements do not rotate about their centers of mass.
The Continuity Equation
Conservation of mass dictates that the mass flow rate ( d m d t = ρ A v \frac{dm}{dt} = \rho A v d t d m = ρ A v ) across any cross-section of a conduit is constant. For an incompressible fluid (constant ρ \rho ρ ): Q = A 1 v 1 = A 2 v 2 = constant Q = A_1 v_1 = A_2 v_2 = \text{constant} Q = A 1 v 1 = A 2 v 2 = constant
where Q Q Q is the volumetric flow rate ( m 3 / s \text{m}^3/\text{s} m 3 / s ), A A A is the cross-sectional area ( m 2 \text{m}^2 m 2 ), and v v v is the average flow velocity (m/s).
When a tube narrows, fluid velocity increases proportionately: v 2 = v 1 ( A 1 A 2 ) v_2 = v_1 \left(\frac{A_1}{A_2}\right) v 2 = v 1 ( A 2 A 1 ) . If a circular tube's radius is halved, its cross-sectional area decreases by a factor of 4 4 4 ( A = π r 2 A = \pi r^2 A = π r 2 ), forcing flow velocity to quadruple ( 4 × 4\times 4 × ).
Bernoulli's Equation
Bernoulli's equation is a statement of the conservation of mechanical energy for an ideal, flowing fluid along a streamline: P 1 + 1 2 ρ v 1 2 + ρ g y 1 = P 2 + 1 2 ρ v 2 2 + ρ g y 2 = constant P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2 = \text{constant} P 1 + 2 1 ρ v 1 2 + ρ g y 1 = P 2 + 2 1 ρ v 2 2 + ρ g y 2 = constant
where:
P P P : Static pressure exerted on the conduit walls (energy density, J/m 3 = N/m 2 = Pa \text{J/m}^3 = \text{N/m}^2 = \text{Pa} J/m 3 = N/m 2 = Pa ),
1 2 ρ v 2 \frac{1}{2} \rho v^2 2 1 ρ v 2 : Dynamic pressure (kinetic energy per unit volume),
ρ g y \rho g y ρ g y : Hydrostatic potential energy density associated with height y y y .
The Venturi Effect
For a horizontal conduit ( y 1 = y 2 y_1 = y_2 y 1 = y 2 ), Bernoulli's equation simplifies to: P 1 + 1 2 ρ v 1 2 = P 2 + 1 2 ρ v 2 2 P_1 + \frac{1}{2} \rho v_1^2 = P_2 + \frac{1}{2} \rho v_2^2 P 1 + 2 1 ρ v 1 2 = P 2 + 2 1 ρ v 2 2
As a fluid flows from a wider region into a constriction ( A 2 < A 1 A_2 < A_1 A 2 < A 1 ), the continuity equation requires velocity to increase ( v 2 > v 1 v_2 > v_1 v 2 > v 1 ). Because kinetic energy density ( 1 2 ρ v 2 \frac{1}{2} \rho v^2 2 1 ρ v 2 ) rises, static lateral pressure must decrease ( P 2 < P 1 P_2 < P_1 P 2 < P 1 ). This drop in lateral pressure within a constricted stream is the Venturi effect .
Clinical and Biological Venturi Manifestations
Venturi Oxygen Masks: High-velocity oxygen enters through a narrow nozzle, creating a localized drop in static pressure that entrains room air through calibrated side ports, delivering precise F i O 2 F_i\text{O}_2 F i O 2 mixtures to COPD patients.
Obstructive Hypertrophic Cardiomyopathy (HOCM): Asymmetrical septal hypertrophy narrows the left ventricular outflow tract (LVOT). During systole, blood accelerates through the narrowed LVOT; the resulting Venturi drop in lateral pressure pulls the anterior leaflet of the mitral valve toward the septum (Systolic Anterior Motion, SAM), worsening outflow obstruction.
Obstructive Sleep Apnea: When pharyngeal musculature relaxes during sleep, the airway narrows. Inhaled air accelerates through the constriction, dropping luminal pressure and causing soft tissue airway collapse.
Real Fluids: Viscosity, Poiseuille's Law & Turbulence
Real biological fluids (such as plasma and whole blood) possess viscosity ( η \eta η ), a measure of internal fluid friction arising from cohesive intermolecular forces and cellular collisions. The SI unit of viscosity is the Pa ⋅ s \text{Pa}\cdot\text{s} Pa ⋅ s ( 1 Pa ⋅ s = 1 kg / [ m ⋅ s ] = 10 Poise 1\text{ Pa}\cdot\text{s} = 1\text{ kg}/[\text{m}\cdot\text{s}] = 10\text{ Poise} 1 Pa ⋅ s = 1 kg / [ m ⋅ s ] = 10 Poise ). Normal blood viscosity at body temperature is ≈ 3.0 − 4.0 × 10 − 3 Pa ⋅ s \approx 3.0 - 4.0 \times 10^{-3}\text{ Pa}\cdot\text{s} ≈ 3.0 − 4.0 × 1 0 − 3 Pa ⋅ s ( 3 – 4 cP 3\text{–}4\text{ cP} 3 – 4 cP ).
Poiseuille's Law
Laminar flow of a viscous fluid through a rigid cylindrical pipe driven by a pressure gradient Δ P = P in − P out \Delta P = P_{\text{in}} - P_{\text{out}} Δ P = P in − P out is governed by Poiseuille's Law : Q = π Δ P r 4 8 η L Q = \frac{\pi \Delta P r^4}{8 \eta L} Q = 8 η L π Δ P r 4
Rearranging in analogy to Ohm's law ( Δ V = I R \Delta V = I R Δ V = I R ): Δ P = Q × R hydraulic \Delta P = Q \times R_{\text{hydraulic}} Δ P = Q × R hydraulic
where hydraulic vascular resistance ( R R R ) is: R = 8 η L π r 4 R = \frac{8 \eta L}{\pi r^4} R = π r 4 8 η L
The Fourth-Power Rule ( r 4 r^4 r 4 ): Flow rate depends on the fourth power of vessel radius ( r 4 r^4 r 4 ). A 16% reduction in radius cuts flow in half ( 0.84 4 ≈ 0.50 0.84^4 \approx 0.50 0.8 4 4 ≈ 0.50 ). Halving the vessel radius ( 0.5 r 0.5 r 0.5 r ) increases vascular resistance by 2 4 = 16 -fold 2^4 = 16\text{-fold} 2 4 = 16 -fold and decreases flow by 93.75 % 93.75\% 93.75% . Because arterioles are wrapped in smooth muscle sphincters capable of altering lumen diameter, arterioles account for > 60 % > 60\% > 60% of systemic vascular resistance (SVR/TPR).
Reynolds Number ( R e Re R e ) and Turbulent Flow
At high velocities, flow ceases to be laminar and becomes turbulent , characterized by vortices, eddies, and high energy dissipation. The onset of turbulence is predicted by the dimensionless Reynolds number ( R e Re R e ): R e = ρ v D η Re = \frac{\rho v D}{\eta} R e = η ρ v D
where ρ \rho ρ is density, v v v is mean velocity, D D D is conduit diameter ( 2 r 2r 2 r ), and η \eta η is viscosity.
R e < 2000 Re < 2000 R e < 2000 : Flow is predominantly laminar and silent.
R e > 3000 Re > 3000 R e > 3000 : Flow is turbulent, generating acoustic energy.
Turbulent blood flow generates murmurs, bruits (e.g., carotid stenosis), and Korotkoff sounds during sphygmomanometry as the compressed brachial artery allows intermittent high-velocity jets.
Systemic Circulatory Hemodynamics
The systemic circulation functions as a closed hydraulic loop driven by a pulsatile pump. Applying fluid dynamics principles clarifies vascular behavior:
1. Velocity Profile Across Vascular Beds
By the continuity equation, v = Q / A total v = Q / A_{\text{total}} v = Q / A total . Although individual capillaries are microscopic ( r ≈ 4 – 5 μ m r \approx 4\text{–}5\,\mu\text{m} r ≈ 4 – 5 μ m ), they branch in parallel to form an enormous aggregate network of approximately 10 billion vessels, providing a total cross-sectional area of ∑ A ≈ 2500 − 3000 cm 2 \sum A \approx 2500 - 3000\text{ cm}^2 ∑ A ≈ 2500 − 3000 cm 2 (compared to the aorta's A ≈ 3 − 5 cm 2 A \approx 3 - 5\text{ cm}^2 A ≈ 3 − 5 cm 2 ).
- Aortic velocity: v ≈ 30 − 40 cm/s v \approx 30 - 40\text{ cm/s} v ≈ 30 − 40 cm/s
- Capillary velocity: v < 0.05 cm/s v < 0.05\text{ cm/s} v < 0.05 cm/s ( < 1 mm/s < 1\text{ mm/s} < 1 mm/s )
This velocity nadir in capillaries provides the residence time required for diffusive gas, nutrient, and metabolite exchange across endothelial walls.
2. Arterial Blood Pressure & Mean Arterial Pressure (MAP)
Because the heart contracts pulsatilely, arterial pressure fluctuates between systolic blood pressure (SBP ≈ 120 mmHg \approx 120\text{ mmHg} ≈ 120 mmHg ) and diastolic blood pressure (DBP ≈ 80 mmHg \approx 80\text{ mmHg} ≈ 80 mmHg ). Because the heart spends approximately two-thirds of the resting cardiac cycle in diastole: MAP = DBP + 1 3 ( SBP − DBP ) = 1 3 SBP + 2 3 DBP \text{MAP} = \text{DBP} + \frac{1}{3}(\text{SBP} - \text{DBP}) = \frac{1}{3}\text{SBP} + \frac{2}{3}\text{DBP} MAP = DBP + 3 1 ( SBP − DBP ) = 3 1 SBP + 3 2 DBP MAP = CO × SVR \text{MAP} = \text{CO} \times \text{SVR} MAP = CO × SVR
Arterioles exhibit the steepest pressure drop across the entire circulatory tree (dropping from ≈ 85 mmHg \approx 85\text{ mmHg} ≈ 85 mmHg down to ≈ 35 mmHg \approx 35\text{ mmHg} ≈ 35 mmHg ), confirming their role as primary resistance vessels.
Hemodynamic Profiles Across Vascular Beds
Vascular Segment Aggregate Cross-Sectional Area ( cm 2 \text{cm}^2 cm 2 ) Mean Linear Velocity ( v v v , cm/s \text{cm/s} cm/s ) Mean Pressure ( mmHg \text{mmHg} mmHg ) Primary Physiological Function
Aorta 3 – 5 3\text{–}5 3 – 5 30 – 40 30\text{–}40 30 – 40 95 – 100 95\text{–}100 95 – 100 High-pressure conduit, Windkessel elastic damping
Conduit Arteries 10 – 20 10\text{–}20 10 – 20 15 – 25 15\text{–}25 15 – 25 90 – 95 90\text{–}95 90 – 95 Low-resistance delivery to organ systems
Arterioles 40 – 100 40\text{–}100 40 – 100 2 – 10 2\text{–}10 2 – 10 85 → 35 85 \to 35 85 → 35 (steep drop) Primary resistance vessels, regulation of TPR & capillary flow
Capillaries 2500 – 3000 2500\text{–}3000 2500 – 3000 (massive) < 0.05 <0.05 < 0.05 ( < 1 mm/s <1\text{ mm/s} < 1 mm/s ) 35 → 15 35 \to 15 35 → 15 Solute, gas, and fluid exchange via Starling forces
Venules 200 – 500 200\text{–}500 200 – 500 0.5 – 2 0.5\text{–}2 0.5 – 2 15 → 10 15 \to 10 15 → 10 Post-capillary exchange, leukocyte extravasation
Veins & Vena Cava 20 – 40 20\text{–}40 20 – 40 10 – 20 10\text{–}20 10 – 20 10 → 2 – 4 10 \to 2\text{–}4 10 → 2 – 4 Capacitance vessels (contain ~65% blood volume), preload return
Worked Numerical Example: Arteriolar Vasoconstriction
Problem: A patient experiences systemic sympathetic activation during an acute hemorrhage. Circulating norepinephrine induces arteriolar vasoconstriction that decreases mean arteriolar radius by 20 % 20\% 20% throughout a mesenteric vascular bed. Assuming blood viscosity and vessel length remain constant, calculate:
The fold-increase in hydraulic resistance ( R R R ) across this vascular bed.
If cardiac perfusion pressure ( Δ P \Delta P Δ P ) to this organ is maintained constant, what percentage of the original volumetric blood flow rate ( Q 0 Q_0 Q 0 ) continues to perfuse the tissue?
Step 1: Determine change in vessel radius A 20 % 20\% 20% reduction in radius means the new radius is: r 1 = 0.80 r 0 r_1 = 0.80 \, r_0 r 1 = 0.80 r 0
Step 2: Calculate hydraulic resistance change using Poiseuille's Law Resistance is inversely proportional to r 4 r^4 r 4 : R ∝ 1 r 4 R \propto \frac{1}{r^4} R ∝ r 4 1 R 1 R 0 = ( r 0 r 1 ) 4 = ( r 0 0.80 r 0 ) 4 = ( 1 0.80 ) 4 = ( 1.25 ) 4 ≈ 2.441 \frac{R_1}{R_0} = \left(\frac{r_0}{r_1}\right)^4 = \left(\frac{r_0}{0.80 \, r_0}\right)^4 = \left(\frac{1}{0.80}\right)^4 = (1.25)^4 \approx 2.441 R 0 R 1 = ( r 1 r 0 ) 4 = ( 0.80 r 0 r 0 ) 4 = ( 0.80 1 ) 4 = ( 1.25 ) 4 ≈ 2.441
Arteriolar vascular resistance increases by a factor of 2.44 2.44 2.44 (a 144 % 144\% 144% increase in resistance).
Step 3: Calculate the resulting volumetric flow rate ( Q Q Q ) Under constant perfusion pressure ( Δ P 1 = Δ P 0 \Delta P_1 = \Delta P_0 Δ P 1 = Δ P 0 ): Q = Δ P R ⟹ Q 1 Q 0 = R 0 R 1 = 1 2.441 ≈ 0.4096 = 41 % Q = \frac{\Delta P}{R} \implies \frac{Q_1}{Q_0} = \frac{R_0}{R_1} = \frac{1}{2.441} \approx 0.4096 = 41\% Q = R Δ P ⟹ Q 0 Q 1 = R 1 R 0 = 2.441 1 ≈ 0.4096 = 41%
Flow drops to approximately 41 % 41\% 41% of baseline , representing a 59 % 59\% 59% reduction in tissue perfusion. This illustrates how small changes in smooth muscle tone dramatically alter regional blood flow.