The viscosity of blood makes it neccessary to have a pressure difference between the ends of the blood vessel for blood to flow. The volume rate of flow is equal to [pie r^4(P1-P2)/8*coefficient of viscosity*length of tube]. The r in this formula is the radius of the vessel. The buildup of cholesterol causes the radius to decrease. Even a decrease of 25% in the radius will cause the equation to have a completely different answer. If cholesterol buildsup in the vessel the radius of the vessel will be significantly smaller and this smaller radius will cause the ends of the vessel to pump quicker (increased blood pressure) to pump the viscose blood through the smaller vessel.
The equation involved is Poiseuille's equation. Cholesterol builds up around the artery walls, reducing their radius. The radius is in the denominator of the equation when deltaP [...] is raised to the fourth power. Therefore, changing the radius by 1/4 will cause the pressure to be (.25r)^4 x higher. This causes the heart to work harder, and blood pressure to rise.
The basic fluid dynamics principles involved in blood flow are the radius of the vessels, the pressure at each end of the blood vessels, the length of the blood vessels, and the viscosity of the blood. These are combined to form Poiseuille's equation: Q = pi * r^4 * (P1 - P2) / 8nL. Blood pressure is so sensitive to cholesterol buildup because it reduces the radius of the vessels. As the equations shows, the r^4 means that the pressure is greatly reduced by even a small buildup, causing the heart to need to greatly increase pressure to keep up.
Blood pressure is so sensitive to cholesterol buildup because it makes the heart work harder than it has to. You see, in basic fluid dynamics, if a liquid is flowing through a tube, an artery here, and something blocks the flow, then the source of liquid feels more stress, the heart in this case. The basic equation involved in all of this is Poiseuille's. It states that the rate of flow depends on the radius of the tube and when it gets smaller the pressure must increase to keep the same flow rate. Here the body needs a certain amount of oxygen from the blood, so when the artery gets clogged the pressure becomes greater.
when the radius of an artery is reduced by even the smallest amount, the effects of that small decrease decreases flow by four times that of a normal artery.
