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The flow of blood around the circulatory system is modulated by numerous interacting factors, he science dedicated to understanding this flow is called hemodynamics.
Velocity vs Flow
A key first understanding is the difference between velocity and flow. Velocity refers to the distance an object moves over time, for example in blood this measurement is often given as cm/sec. Flow refers to the movement of a volume of a liquid or gas over time, for example in blood this measurement is often given as mL/sec
At its simplest, imaging a perfect rigid tube with no resistance and with a homogenous liquid flowing through perpendicularly, flow can be calculated using the following formula:
$F=v \cdot a$
Where F = flow, v = velocity and a = cross-sectional area.
The above example refers to, "a perfect rigid tube with no resistance and with a homogenous liquid flowing through perpendicularly". In real world terms this is not the case and there are numerous factors that will influence the calculation.
Velocity and Pressure
Movement of blood throughout the circulatory system is created by differences in pressure generated by the pumping of the heart. Pressure is greatest immediately after exiting the heart and drops as it circulates around the body, particularly through the arterioles and capillary networks. A greater difference in pressure results in a greater velocity, assuming all else remains equal, and so when increased blood flow is required the heart can pump more quickly and also in larger volume.
Velocity and Resistance
Resistance is the force which must be overcome by pressure in order for flow to occur and is a factor of vessel length, diameter and surface composition and the viscosity of the liquid flowing through. As resistance increases the difference in pressure which influences velocity decreases which in turn reduces flow. It is for this reason that the narrow arterioles rapidly reduce local blood pressure and slow the flow of blood through the capillaries, a beneficial effect allowing for efficient transfer of chemicals and nutrients. However, pathological changes in blood vessels which result in their narrowing or an increase in surface resistance can lead to a reduction in pressure, velocity and thus flow which can lead to tissue damage.
Velocity and Viscosity
Blood is a complex liquid formed from plasma and containing numerous cell types. As such its viscosity is relatively changeable depending on osmotic balance and cell load. Increases in viscosity, for example by reducing water content, lead to increases in resistance and thus reduction in flow.
Blood vessels are capable of vasodilation and vasoconstriction to alter their diameter. Assuming all else remains equal a reduction in diameter results in a reduction in flow, whereas an increase in vessel diameter results in an increase in flow.
These individual elements are tightly regulated by the body to maintain sufficient flow to the bodies organs and tissues