Medical Physics - Fluid Mechanics, Hydrodynamics, and Rheology

A set of 100 vocabulary flashcards covering fluid mechanics, hydrodynamics, viscosity, blood pressure, rheology, and centrifugation in medical physics.

Medical Physics

The application of physics concepts in medicine, healthcare, and medical sciences.

Fluid

A substance that can flow, encompassing both liquids and gases.

Fluid Statics (Hydrostatics)

The branch of fluid mechanics that studies fluids at rest and the conditions under which fluids are at rest in stable equilibrium.

Fluid Dynamics

A subdiscipline of fluid mechanics that deals with fluid flow—the science of liquids and gases in motion.

Pressure ($p$)

A scalar quantity numerically equal to the normal force acting per unit area of a surface ($p = \frac{F_n}{S}$).

Pascal ($Pa$)

The SI unit of pressure, defined as one newton per square metre ($1\,Pa = 1\,N/m^2$).

Hectopascal ($hPa$)

A unit of atmospheric pressure measurement equal to $100\,Pa$ ($1\,hPa = 100\,Pa$).

Atmosphere ($atm$)

A unit of pressure where $1\,mmHg = 0.0013158\,atm$.

Bar

A unit of pressure equal to $10^5\,Pa$ ($1\,bar = 10^5\,Pa$).

Millimeter of Mercury ($mmHg$)

A common unit of pressure where $1\,mmHg = 133.322\,Pa$.

Meter ($m$)

The SI base unit for length.

Kilogram ($kg$)

The SI base unit for mass.

Second ($s$)

The SI base unit for time.

Ampere ($A$)

The SI base unit for electric current.

Kelvin ($K$)

The SI base unit for thermodynamic temperature.

Mole ($mole$)

The SI base unit for the amount of substance.

Candela ($cd$)

The SI base unit for luminous intensity.

Pascal's Law

States that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of its container.

Hydrostatic Pressure

The pressure exerted by a vertical column of fluid of density $\rho$ and height $h$, given by $p = \rho g h$.

Archimedean Force ($F_A$)

The vertically upward buoyant force acting on an object immersed in a fluid, applied at the center of gravity of the displaced fluid volume.

Archimedes' Law

States that the magnitude of the buoyant force ($F_A$) acting on an immersed body equals the weight of the fluid displaced by the object ($F_A = \rho g V$).

Ideal Fluid

A fluid model in which internal friction between its layers is neglected and the fluid is treated as incompressible.

Viscous Fluid (Real Fluid)

A fluid in which internal frictional forces arise between its individual layers during relative movement.

Mach's Number ($M$)

The ratio of the gas flow velocity ($v$) to the velocity of sound in that gas flow ($v_s$), given by $M = \frac{v}{v_s}$.

Aerodynamics

The branch of science that studies the compressibility and motion phenomena of gas media when the Mach number $M \ge 1$.

Euler's Method

A hydrodynamics method that examines the distribution of the velocity vector field across the space occupied by a fluid.

Velocity Vector Field

The set of velocity vectors for all points in a fluid.

Fluid Line (Streamline)

An imaginary line in a fluid at every point of which the velocity vectors lie on the tangent line.

Fluid Pipe

A tubular region formed by fluid lines surrounding a flow path.

Stationary Motion (Steady-State Assumption)

Fluid motion in which the velocity vector at any given point in the fluid does not change with time.

Equation of Continuity

An equation for incompressible fluids stating $S_1 v_1 = S_2 v_2$, meaning the volume of fluid passing through any section of a tube per second is constant.

Volumetric Flow Rate ($Q$)

The volume of fluid crossing a tube per unit time, calculated as $Q = S v$.

Bernoulli's Equation

The basic equation of hydrodynamics for ideal fluid flow: $p + \rho g h + \frac{1}{2}\rho v^2 = \text{const}$.

Static Pressure

The thermodynamic pressure term $p$ in Bernoulli's equation, which is minimal where fluid velocity is highest.

Dynamic Pressure

The pressure term $\frac{1}{2}\rho v^2$ in Bernoulli's equation caused by fluid flow velocity.

Hydrostatic Pressure Term (in Bernoulli's Equation)

The pressure term $\rho g h$ in Bernoulli's equation resulting from fluid elevation.

Tangential Forces of Internal Friction

Frictional forces that act between adjacent layers of a real fluid during relative movement.

Newton's Law of Viscosity

States that the tangential internal friction force between fluid layers is proportional to the velocity gradient and layer area: $F = \eta S \frac{du}{dy}$.

Velocity Gradient ($\frac{du}{dy}$)

The change in fluid velocity $u$ per unit distance in a direction transverse ($y$) to the movement.

Dynamic Viscosity ($\eta$)

The proportionality factor in Newton's law of viscosity, representing the internal friction of a fluid, with SI units of $Pa \cdot s$.

Pascal-second ($Pa \cdot s$)

The SI unit of dynamic viscosity ($1\,Pa \cdot s = 1\,N \cdot s \cdot m^{-2}$).

Superfluidity

The phenomenon discovered by Kapitsa where liquid helium exhibits zero dynamic viscosity ($\eta = 0$) near $0\,K$ at $T_C = 2.17\,K$.

Curie Temperature ($T_C = 2.17\,K$)

The critical temperature at which liquid helium exhibits superfluidity ($\eta = 0$).

Pyotr Kapitsa

The Russian physicist who discovered the phenomenon of superfluidity in liquid helium.

Laminar Motion

Slow fluid motion in which trajectories of adjacent fluid particles differ little from each other and flow in smooth parallel layers.

Turbulent Motion

Fluid motion characterized by intensive mixing of liquid layers and chaotic particle trajectories at higher velocities.

Kinematic Viscosity ($\nu$)

The ratio of dynamic viscosity to fluid density: $\nu = \frac{\eta}{\rho}$, with units of $m^2 \cdot s^{-1}$.

Reynolds Number ($Re$)

A dimensionless criterion for flow regime defined as $Re = \frac{\langle u \rangle l}{\nu} = \frac{\rho \langle u \rangle l}{\eta}$.

Stokes' Method

A method for measuring dynamic viscosity ($\eta > 0.1\,Pa \cdot s$) by measuring the parameters of small spherical bodies falling uniformly in a viscous fluid.

Stokes' Empirical Law

States that the force of internal friction acting on a sphere of radius $r$ moving at speed $v$ in a fluid is $F = 6 \pi \eta r v$.

Poiseuille's Method

A method for determining viscosity based on the laminar movement of fluids with lower viscosity through a thin capillary.

Poiseuille's Equation

An equation used to calculate volumetric blood flow or viscosity in a tube: $V = \frac{\pi \Delta p R^4 t}{8 \eta l}$.

Centipoise ($cP$)

A practical unit of dynamic viscosity equal to $1\,mPa \cdot s$ ($1\,cP = 1\,mPa \cdot s$).

Relative Viscosity ($\eta_0$ or $\eta_r$)

The dimensionless ratio of the dynamic viscosity of a fluid/blood to that of distilled water at the same temperature: $\eta_0 = \frac{\eta}{\eta_{\text{water}}}$.

Erythrocyte Sedimentation Rate (ESR)

The rate at which red blood cells settle out of blood plasma due to gravity, normally $11 \text{ to } 20\,mm/h$ ($3 \text{ to } 6\,\mu m/s$).

Systolic Pressure

The peak blood pressure exerted on arterial walls during the contraction of the heart's left ventricle.

Diastolic Pressure

The baseline pressure exerted on blood by elastic recoil of arteries during the pauses between heart contractions.

Pulse Wave (Pulse)

The elastic deformation of the aorta propagating along arterial walls.

Pulse Wave Frequency

The rate of pulse wave propagation, equal to the heart rate ($\nu_h = 1 \text{ to } 1.5\,Hz$).

Blood Velocity in Aorta

The highest blood flow velocity in the cardiovascular system, approximately $50\,cm \cdot s^{-1}$.

Blood Velocity in Capillaries

The lowest blood flow velocity in the cardiovascular system, approximately $0.5\,mm \cdot s^{-1}$, due to the high total cross-sectional area.

Blood Velocity in Veins

The speed of returning blood flow, increasing up to a maximum value of $30 \text{ to } 35\,cm \cdot s^{-1}$.

Speed of the Pulse Wave

The velocity of elastic wave propagation in vessel walls ($6 \text{ to } 8\,m \cdot s^{-1}$), which is significantly greater than blood flow velocity.

Sphygmomanometer

An indirect medical device used to measure arterial blood pressure using an inflatable cuff and manometer.

Blood Pressure (Medical Definition)

The difference between the pressure of blood in a specific blood vessel and ambient atmospheric pressure.

Brachial Artery

The standardized location in the middle of the upper left arm at heart height used for blood pressure measurement.

Korotkov Tones

Sounds perceived with a stethoscope caused by turbulent blood flow as cuff pressure falls below systolic pressure.

Riva-Rocci Method

The classic indirect blood pressure measurement method developed in 1896 using an inflatable arm cuff and mercury manometer.

Normal Blood Pressure ($RR\,120/80$)

Standard healthy blood pressure values in a young person: $120\,mmHg$ ($16\,kPa$) systolic and $80\,mmHg$ ($10.7\,kPa$) diastolic.

Central Venous Pressure Measurement

A direct method of measuring blood pressure using a catheter placed in a major vein near the heart.

Piezoelectric Pressure Converter

A transducer attached to a catheter tip that converts pressure changes into electrical signals based on resistance or voltage shifts.

Sedimentation

The phase separation process in heterogeneous systems where dispersed particles deposit at the bottom under gravity.

Centrifugation

A separation process that uses centripetal/centrifugal acceleration from rapid rotation to accelerate particle settling.

Rheology

The branch of mechanics that studies the flow of gases and liquids and the deformation of solid bodies under stress.

Eugene Bingham

The American physical chemist who proposed the term 'rheology' in 1929.

Newtonian Fluid

A fluid that obeys Newton's law of viscosity, maintaining a constant dynamic viscosity independent of velocity gradient/shear stress.

Non-Newtonian Fluid

A fluid whose viscosity changes depending on applied force or velocity gradient (e.g., blood, ketchup, starch suspensions).

Specific Viscosity ($\eta_{\text{specific}}$)

The fractional viscosity increase of a solution relative to its solvent: $\eta_{\text{specific}} = \frac{\eta - \eta_{\text{solvent}}}{\eta_{\text{solvent}}} = \eta_{\text{relative}} - 1$.

Reduced Viscosity

The ratio of specific viscosity to molar concentration of the impurity: $\frac{\eta_{\text{specific}}}{c}$.

Characteristic Viscosity ($[\eta]$)

The limiting value of reduced viscosity as concentration $c$ approaches zero: $[\eta] = \lim_{c \to 0} \frac{\eta_{\text{specific}}}{c}$.

Einstein's Equation for Suspension Viscosity

The formula $\eta_s = \eta (1 + k \Phi)$, describing the viscosity of a suspension based on particle shape factor ($k$) and volume fraction ($\Phi$).

Dilatant Movement

Fluid flow behavior in which dynamic viscosity increases as the velocity gradient increases.

Bingham Fluid (Plastic)

A viscoplastic material that behaves as a rigid solid at low shear stress but flows as a viscous fluid at high stress (e.g., mayonnaise).

Hematocrit ($\Phi$)

The ratio of the total volume of formed blood elements (mainly erythrocytes) to total blood volume, normally around $0.45$ ($45\%$).

Dynamic Viscosity of Blood

The dynamic viscosity coefficient $\eta_s$ of whole blood in a healthy person at normal hematocrit, equal to $3.6 \text{ to } 4.7\,mPa \cdot s$.

Dynamic Viscosity of Blood Plasma

The dynamic viscosity $\eta$ of blood plasma at $20^\circ C$, ranging between $1.7$ and $2.2\,mPa \cdot s$.

Relative Viscosity of Plasma

The viscosity of plasma relative to water at $37^\circ C$, equal to approximately $1.8$.

Relative Viscosity of Blood (at 40% Hematocrit)

The relative viscosity of whole blood compared to water at normal hematocrit, equal to approximately $4.0$.

Polycythemia

A condition characterized by an abnormal elevation in red blood cell hematocrit (e.g., to $60\%$), doubling relative blood viscosity from $4$ to $8$.

Anemia (Viscosity Effect)

A medical condition causing decreased hematocrit and lowering relative blood viscosity down to $1.7$.

Coin Pillars (Rouleaux)

Aggregates of individual erythrocytes forming coin-like stacks at low blood flow velocities, causing a sharp rise in blood viscosity.

Fibrillar Proteins in Plasma

Plasma proteins (fibrinogen and gamma-globulin) required for the formation of erythrocyte coin pillars.

Rotary Viscometer

An instrument for measuring viscosity of non-Newtonian fluids using a rotating inner rotor and measuring spiral spring bending angle ($\alpha$).

Uniform Circular Motion

Motion along a circular path at constant speed, characterized by constant angular frequency and radial acceleration.

Period of Rotation ($T$)

The time required for a rotating body to make one complete revolution ($\phi = 2\pi\,\text{rad}$).

Linear Frequency ($\nu$)

The number of complete revolutions executed per unit time, given by $\nu = \frac{1}{T}$.

Angular Frequency ($\omega$)

The rate of rotation in radians per second, calculated as $\omega = \frac{2\pi}{T} = 2\pi\nu$.

Centripetal Acceleration ($a_c$)

The radial acceleration directed toward the center of a circular path, calculated as $$a_c = \frac{v^2}{R} = \omega^2 R$.

Centripetal Force ($F_c$)

The force directed toward the center of rotation that maintains circular motion ($F_c = m a_c = m \omega^2 R$).

Centrifugal Force ($F_{cf}$)

An apparent inertial force in a non-inertial rotating reference frame directed outward from the center, equal and opposite to centripetal force ($F_{cf} = -F_c$).