How Flow Rate, Bernoulli's Equation,and Poiseuilles Law Relates to Atherosclerosis
The flow rate of blood shows the P1v1A1= P2v2A2 and flow rate=A1v1=A2v2 because blood is a non compressible fluid. To maintain a constant flow rate in a clogged artery, the blood must travel faster than normal through the constriction. If the blood speed is high enough in the constricted region, the artery may collapse under external pressure, causing an interruption in this flow. From this principle it is seen that a sign of atherosclerosis is high blood pressure. This is due to the narrowing of the arteries which causing the blood to travel more quickly through them. Since blood is thick and the arteries are not as elastic as they once were, the pressure traveling through the plaque filled arteries is more than the artery wants to handle with the limited space for the blood to travel through and eventually a clot forms. Bernoulli's equation relates speed, height and pressure by P + ½pv² + pgy = constant. This equations acts as another way of stating the work energy theorem. Poiseuilles Law states dP*pi*r^4/8*theta*L=V/t. From this one can see how the radius relates to the volume of the artery. Since it is to the 4th power in causes the volume to increase or decrease by a factor of 16 so a blocked artery with a smaller radius for blood to travel through decreases the volume of blood that it can hold by a factor of 16. This shows how atherosclerosis causes a large problem, however their are ways to treat atherosclerosis and solve these problems.
posted by Matthew @ 12:10 PM
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