Question

The arterioles (small arteries) leading to an organ can constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 1.00% of its original value. For example, the circulatory system of penguins do this when they stand on ice to reduce the blood flow to their fect. A. By what factor can the radii of the arterioles constric? That is to say, if n is the initial radius and r is the constricted redius, what is r/n ?

r²/n=

Answer 1

The factor by which the radii of arterioles constrict when blood flow is reduced to 1.00% of the original value is about 0.177, which means the constricted radius is approximately 17.7% of the original radius.

Step-by-step explanation:

The process of arterioles constricting to decrease blood flow to an organ is an example of the body’s ability to regulate blood flow through vasoconstriction. When arterioles constrict to reduce blood flow to 1.00% of the organ's original flow, the radius of the arterioles changes to permit this drastic decrease.

To find the factor by which the radii of the arterioles constrict, we can use a principle from physics known as Poiseuille's law, which states that flow rate through a vessel is proportional to the fourth power of the radius of the vessel. If we let n represent the original radius and r represent the constricted radius, then according to the law, reducing the flow to 1.00% (or 0.01 in decimal form) of the original flow would mean that r4/n4 = 0.01.

Taking the fourth root, we find that r/n, the factor by which the radii constrict, is equal to the fourth root of 0.01, which is approximately 0.177. Hence, the constricted radius is about 17.7% of the original radius.