Free MCAT study guide — Chemical and Physical Foundations of Biological Systems
Fluid mechanics is a high-yield MCAT physics topic with direct applications to cardiovascular physiology. You need to understand fluid statics (density, specific gravity, pressure, Pascal's law, hydrostatic pressure, buoyancy/Archimedes' principle) and fluid dynamics (continuity equation, Bernoulli's equation, Poiseuille's law, viscosity, laminar vs. turbulent flow, and Reynolds number). The MCAT bridges physics and biology by asking you to apply these principles to blood flow through vessels, the circulatory system, and clinical scenarios like atherosclerosis, aneurysms, and edema. Key equations include P = rho x g x h (hydrostatic pressure), A1v1 = A2v2 (continuity equation), P + 1/2 rho v^2 + rho g h = constant (Bernoulli's equation), and Q = (pi x delta P x r^4) / (8 x eta x L) (Poiseuille's law). Understanding how vessel radius, blood viscosity, and pressure gradients determine blood flow rate is essential. The interplay between Starling forces (hydrostatic and oncotic pressures) in capillary exchange is another important topic.
Pressure is force per unit area (P = F/A), measured in Pascals (Pa = N/m^2) or mmHg (1 atm = 101,325 Pa = 760 mmHg). Hydrostatic pressure increases with depth: P = P_atm + rho x g x h, where rho is fluid density, g is gravitational acceleration, and h is depth below the surface. Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions -- this is the principle behind hydraulic lifts and blood pressure measurement. Gauge pressure is the pressure above atmospheric: P_gauge = rho x g x h. Archimedes' principle states that the buoyant force on a submerged object equals the weight of the displaced fluid: F_b = rho_fluid x V_displaced x g. An object floats when its density is less than the fluid density (F_b > weight), sinks when denser, and is neutrally buoyant when densities are equal. Specific gravity is the ratio of a substance's density to water's density (1000 kg/m^3) and is dimensionless. These principles apply to understanding lung mechanics, IV fluid administration, and the behavior of gases in blood.
The continuity equation expresses conservation of mass for an incompressible fluid flowing through a pipe: A1v1 = A2v2, where A is cross-sectional area and v is flow velocity. When a pipe narrows, velocity increases; when it widens, velocity decreases. Volume flow rate Q = Av is constant throughout the system. In the circulatory system, blood velocity is fastest in the aorta (smallest total cross-sectional area) and slowest in the capillaries (largest total cross-sectional area, despite each capillary being very small). This slow capillary flow maximizes time for gas and nutrient exchange. The total cross-sectional area of all capillaries combined is approximately 600 times that of the aorta, so blood velocity in capillaries is approximately 1/600th of aortic velocity. When blood vessels branch, the total cross-sectional area increases, and velocity decreases. This is why the continuity equation must be applied using TOTAL cross-sectional area at each level of branching, not the area of a single vessel.
Bernoulli's equation describes the relationship between pressure, velocity, and height for an ideal (inviscid, incompressible, laminar) fluid: P + 1/2 rho v^2 + rho g h = constant. This equation represents conservation of energy per unit volume along a streamline. The three terms are static pressure, dynamic pressure (kinetic energy per volume), and gravitational potential energy per volume. Key consequence: where velocity increases (narrow section), pressure decreases, and vice versa. This Bernoulli effect explains the Venturi effect (fluid pressure drops in a constriction), airplane lift (faster air over curved wing top creates lower pressure), and the pathophysiology of atherosclerosis (plaque narrows the vessel, increasing velocity and decreasing lateral pressure, potentially causing vessel collapse during systole). In the cardiovascular system, Bernoulli's equation helps explain why aneurysms (dilated vessels) have high pressure and low velocity, promoting turbulent flow and further weakening the vessel wall. Note that Bernoulli's equation applies strictly to ideal fluids -- real blood flow requires corrections for viscosity (Poiseuille's law).
Poiseuille's law describes the volume flow rate of a viscous fluid through a cylindrical tube: Q = (pi x delta P x r^4) / (8 x eta x L), where delta P is the pressure difference, r is the radius, eta (eta) is dynamic viscosity, and L is tube length. The most critical insight is the fourth-power dependence on radius: halving the radius reduces flow by a factor of 16 (2^4). This explains why small changes in arteriolar radius have dramatic effects on blood flow and blood pressure. Resistance to flow is R = (8 x eta x L) / (pi x r^4), analogous to electrical resistance (Ohm's law: delta P = Q x R, like V = IR). Total peripheral resistance in the circulatory system is primarily determined by arteriolar radius. Viscosity of blood depends on hematocrit (higher hematocrit = higher viscosity), temperature (higher temp = lower viscosity), and vessel diameter (Fahraeus-Lindqvist effect: viscosity decreases in very small vessels as RBCs align in single file). Polycythemia (elevated hematocrit) increases blood viscosity and resistance, raising blood pressure.
Laminar flow is smooth, orderly flow in parallel layers (laminae), with the fastest flow at the center of the tube (parabolic velocity profile) and zero velocity at the walls (no-slip condition). Turbulent flow is chaotic, with eddies and mixing, and is associated with energy loss and audible sounds (murmurs, bruits). The Reynolds number (Re) predicts the flow regime: Re = (rho x v x D) / eta, where D is tube diameter. Re < 2000 indicates laminar flow; Re > 4000 indicates turbulent flow; 2000-4000 is the transition region. Turbulent flow is promoted by high velocity, large diameter, high fluid density, and low viscosity. In the circulatory system, turbulent flow normally occurs only in the aorta during peak systole (highest velocity). Pathological turbulence occurs in stenotic (narrowed) valves or vessels (increased velocity through the constriction) and in anemia (decreased viscosity due to lower hematocrit). Turbulent flow creates sounds detectable with a stethoscope: heart murmurs from valvular disease and Korotkoff sounds during blood pressure measurement.
Fluid movement across capillary walls is governed by Starling forces (not to be confused with the Frank-Starling law of the heart). Four pressures determine net fluid movement: capillary hydrostatic pressure (P_c, pushes fluid OUT, approximately 35 mmHg at arteriolar end, 15 mmHg at venular end), interstitial hydrostatic pressure (P_i, pushes fluid IN, approximately 0 mmHg), capillary oncotic pressure (pi_c, pulls fluid IN, approximately 25 mmHg, due to plasma proteins especially albumin), and interstitial oncotic pressure (pi_i, pulls fluid OUT, approximately 0-5 mmHg). Net filtration pressure = (P_c - P_i) - (pi_c - pi_i). At the arteriolar end, net pressure favors filtration (fluid leaves capillary). At the venular end, net pressure favors reabsorption (fluid returns). Edema (tissue swelling) results from increased capillary hydrostatic pressure (heart failure), decreased plasma oncotic pressure (liver failure, nephrotic syndrome, malnutrition), increased capillary permeability (inflammation), or lymphatic obstruction.
Hydrostatic pressure: P = rho x g x h. Pressure increases linearly with depth.
Buoyant force = rho_fluid x V_displaced x g. Object floats if rho_object < rho_fluid.
Continuity equation: A1v1 = A2v2. Smaller area = faster flow.
Bernoulli's equation: P + 1/2 rho v^2 + rho g h = constant. Higher velocity = lower pressure.
Poiseuille's law: Q proportional to r^4. Halving radius reduces flow by 16x.
Blood flows fastest in the aorta, slowest in capillaries (largest total cross-sectional area).
Resistance = (8 eta L) / (pi r^4). Arterioles are the primary resistance vessels.
Reynolds number > 4000 indicates turbulent flow. Promoted by high velocity, large diameter, low viscosity.
Starling forces: hydrostatic pressure pushes fluid out; oncotic pressure pulls fluid in.
Edema causes: increased hydrostatic pressure, decreased oncotic pressure, increased permeability, lymphatic blockage.
Viscosity of blood increases with hematocrit. Anemia decreases viscosity.
delta P = Q x R (flow analogy to Ohm's law: V = IR).
Applying Bernoulli's equation to viscous fluids without acknowledging its limitations -- real blood flow involves viscous losses.
Confusing velocity with flow rate: velocity decreases in capillaries, but total flow rate (Q) remains constant.
Forgetting the r^4 dependence in Poiseuille's law -- radius is by far the most important factor in determining flow resistance.
Using individual capillary cross-sectional area instead of TOTAL cross-sectional area when applying the continuity equation.
Confusing oncotic pressure (due to proteins, pulls water in) with osmotic pressure in other contexts.
Assuming Bernoulli's equation means high velocity causes low pressure -- it is conservation of energy, not causation.
Forgetting that turbulent flow increases energy loss compared to laminar flow for the same flow rate.
Practice applying Bernoulli's equation and Poiseuille's law to cardiovascular scenarios. If a vessel's radius is reduced by 50% due to atherosclerosis, what happens to resistance (increases 16x) and flow rate (decreases to 1/16th if pressure gradient stays constant)? What happens to velocity through the constriction (increases by the continuity equation)? These multi-step problems connecting physics to biology are common on the MCAT.
Work through Starling force calculations: given capillary hydrostatic pressure, interstitial pressure, and oncotic pressures, determine the direction of fluid movement and predict whether filtration or reabsorption predominates. Practice predicting the consequences of clinical scenarios: what happens to fluid balance in nephrotic syndrome (protein lost in urine, decreased plasma oncotic pressure, edema) or in heart failure (increased venous pressure, increased capillary hydrostatic pressure, pulmonary and peripheral edema)?
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