00:01
Problem we have blood that's flowing through an aorta and the density of blood is given as one gram per centimeter cubed and the area of the aorta is given as two centimeters squared the speed of blood that's flowing through the aorta it's 40 centimeters per second and we want to calculate the mass flow rate which i'll just abbreviate as mfr and we want to to calculate this in units of grams per second.
00:38
So to do this we can use the equation for the mass flow rate, which is given as the density of blood times the area of the aorta, times the velocity of the blood that's flowing through the aorta.
00:52
And we can check the units just to make sure that this equation will give us the units of grams per second.
00:59
So for density, we'll have grams divided by centimeter cube times area where area here is centimeters squared times the speed to centimeters per second so we have three centimeters on the top we have centimeters squared and centimeters and all counts about centimeters cubed so we end up getting this grams per second so this equation will give us the correct units we're looking for so now we can just plug in our values so we have for the density of blood, 1 times the area of the aorta, 2 times the velocity of the blood, which 40.
01:43
So we end up getting 80 grams per second for the mass flow rate.
01:52
So that was part a.
01:54
Now in part b, this aorta will split into a bunch of capillaries.
02:00
And the total area of those capillaries is 3 times 10 to the 3 centimeters cubed.
02:09
And we want to calculate the speed, which we'll call v2, of the blood that's flowing inside of those capillaries...