Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about $2.0 \textrm{ cm}^2$. Use the data of Example 10–12.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. This is the equation of continuity which says that the volume rate of flow in one part of the system has to equal the volume rate of flow in the other part. So we have area of the aorta times the speed of blood going through the aorta has to equal the area of these other major arteries times the speed that the blood's going through those arteries. So we have to solve for v arteries by dividing both sides by this and we get the speed in arteries then is A of the aorta times speed in the aorta divided by area of the arteries. So that's π times r squared for the aorta, the radius, and we get π times 1.2 centimeter squared times 40 centimeter per second divided by 2.0 centimeter squared for the area of the arteries and no need to convert the centimeters into meters because since we are using centimeters everywhere in this formula, they will end up, you know, working out nicely because the main thing is that your units are consistent within your formulas so we have centimeters cubed on top and centimeters squared on bottom which divides to make just centimeters on top and then we have this per seconds here. So we have 90 centimeters per second is the speed in the arteries.