00:01
In this question we're told that the number of capillary vessels, n, is 10 to the 9th, and each vessel has a radius, r, of 4 micrometres, or 4 times 10 to the minus 6 metres.
00:16
Now the pumping rate, which is the volume flow rate, let's call it v dot, is 9 times 10 to the minus 5 metres cubed per second.
00:26
This is the total volume flow rate, and now we need to determine the average velocity of blood through each capillary vessel.
00:39
Well the volume flow rate is going to be the average velocity times the total area, but the total area is just the number of capillaries times the area of a capillary.
01:04
But the area of a capillary is pi times its radius squared, so then that means that the total area is pi times the number of capillaries times the radius of each capillary squared, and that tells us that the volume flow rate is the average velocity times pi times n times r squared.
01:30
Now rearranging we get that the average velocity is the volume flow rate divided by pi n r squared.
01:40
So that's 9 times 10 to the minus 5 divided by pi times 10 to the 9 times 4 times 10 to the minus 6 squared...