# Flow, pressure and resistance

## Basic definitions

The cardiovascular system is, from a physics standpoint, driven by pressure and flow and opposed by resistance. This page is an outline of certain relevant physics concepts.
In the International System of Units (or SI system, e.g. the modern metric system), length is defined as a metre (SI unit $m$). An area ($A$) is length squared, $m^2$, and a volume ($V$) is length cubed, $m^3$. Mass, in a physics sense, is an amount of matter. In SI units, mass is measured in kilograms (kg) and has the symbol $m$ (not to be confused with a metre). Acceleration ($\boldsymbol{a}$) is the rate of change of velocity ($\vec{\boldsymbol{v}}$), or meter per second ($\frac{m}{s}$) per second ($\frac{s}{1}$), which is $m \cdot s^{-2}$. Finally, a force ($\boldsymbol{F}$) is any influence that can change the motion (i.e. accelerate) a mass, so that a (net) force produces a proportional acceleration, given by the relationship $\boldsymbol{F} = m\boldsymbol{a}$ (Newton's second law of motion). Force has the SI units $\frac{kg \cdot m}{s^2}$.
All these tedious definitions help in defining pressure.

## Pressure and its measurement

Pressure ($P$) is a force perpendicular to a surface, or "force per area", defined as $P = \frac{F}{A}$. In SI units, $\frac{F}{A} = (\frac{kg \cdot m}{s^2}) \cdot \frac{m^2}{1} = \frac{kg \cdot m^3}{s^2}$. Force is also known as a Newton ($N$), so that $P = \frac{N}{A}$. Pressure is called Pascal in the SI system.
When there exists a difference in pressure between two points, fluids move from regions with high pressure to regions with low pressure. This is important for flow, discussed below. Traditionally, blood pressure was measured using a pressure measurement that was relative to ambient air pressure, a gauge pressure ("gauge" comes from Old North French's gauger, meaning "calibrate, measure", but the origin is unknown). Gauge pressure is done using a liquid column, where the ends of the column are exposed to different pressures. The fluid in the column moves until its weight (i.e. the gravitational force acting on the object) is in equilibrium with the pressure difference between the liquid column's ends. The hydrostatic pressure equation is $P = hg\rho$, where $P$ is pressure, $h$ is fluid column height, $g$ is gravitational acceleration (i.e. "gravity"), and $\rho$ (Greek letter rho) is fluid density (i.e. mass (fluid) per volume). "Hydrostatic" implies that a fluid is at rest.
Since the pressure applied at one end of the liquid column ($P_a$) must balance with the known reference pressure at the other end ($P_0$), the pressure difference ($P_a - P_0$) must be equal to the hydrostatic pressure exerted by the fluid column (which is $P$ in the hydrostatic pressure equation). This means that $P = hg\rho$ can be written $P_a - P_0 = hg\rho$. For a gauge pressure meter, $P_0$ is known, and for a known fluid $g$ and $\rho$ are known. This means that a reading of $h$ for a liquid column enables solving for $P_a$, which is the pressure of interest.
A liquid column gauge pressure meter is also known as a manometer, from Greek manos- meaning "thin" or "rare", and -metron meaning "measure", the word "manos" likely being used here in the sense of "rare and isolated", i.e. "(instrument) to isolate and measure the pressure in a fluid".
Traditionally, manometers used mercury (Hg) since the high density of Hg meant that the fluid column height was a reasonable size for pressure measurement; a water column would have a height more than ten times larger than that of Hg. Since the height of the column was measured in millimeters, the unknown pressure ($P_a$) could thus be expressed in "millimeters of mercury", or mmHg. This measurement is still used to today for cardiovascular applications, for blood pressure measurements, with a sphygmomanometer (the Greek sphygmos means "pulse"). Mercury is toxic and environmentally detrimental which is why mercury-containing products, including mercury sphygmomanometers, have been phased out. This is problematic because mercury sphygmomanometers are the "gold standard" for blood pressure measurements, and because there are concerns that newer, mercury-free sphygmomanometers are not as accurate as their mercury-laden counterparts.

## Resistance

In the context of blood flow, viscous resistance is essentially all properties that oppose the flow of blood.

## Flow

The motion of liquids and gases is called flow. In general, it can be said that a rate of flow is proportional to the driving force and inversely proportional to the resisting force. These principles of flow or movement of physical quantities can be summarized as transport phenomena, and equations for such phenomena are relevent to electricity, heat, and fluids.
In electricity, Ohm's law states that an electrical current $I$ (i.e. flow of charged particles) is proportional to the electrical potential difference (voltage, $V$) divided by the electrical resistance ($R$), so that $I = \frac{V}{R}$. In heat conduction, Fourier's law of heat conduction states that a heat ($Q$) creates a temperature difference ($\Delta T$ across a solid, where the properties of the solid's length ($L$), solid thermal conductivity ($k$) and cross-sectional area in the heat conduction's path ($A$) make up a resistance that is inversely proportional to the heat $Q$ can - analogously with Ohm's law - be written $Q = \frac{\Delta T}{I} \cdot \frac{k \cdot A}{L}$, where $\frac{k \cdot A}{L} = R$, so that $Q = \frac{\Delta T}{R}$. For fluids in a tube, Poiseuille's law states that the volume flowrate (F) is proportional to the pressure difference ($\Delta P$) and inversely proportional to viscous resistance ($R$), so that $F = \frac{\Delta P}{R}$.
The application of Poiseuille's law and resistance to blood flow is discussed further in the vascular physiology section.