Arterioles bifurcate (i.e., split into) capillaries in the circulatory system. B

Question

Arterioles bifurcate (i.e., split into) capillaries in the circulatory system. Blood flows at a velocity of 20cm/s through an arteriole with a diameter of 0.20cm. This vessel bifurcates into two vessels: one with a diameter of 0.17cm and a blood flow velocity of 18 cm/s, and one with a diameter of 0.15cm. Each of these two vessels splits again. The 0.15cm diameter vessels split into two vessels, each with a diameter of 0.12cm. The 0.17cm diameter vessel splits into two vessels, each with a diameter of 0.15cm. Determine the mass flow rate and velocity of blood in each of the four vessels at the end of the arteriole bifurcations. You may need to set up several systems, each with a different system boundary, in order to solve this problem.

Explanation / Answer

First of all consider the density of blood as, p =1.056g/mL

Now -

Mass flow rate of blood = AVp , Where

A= area of cross section

V = velocity

Now, calculate the velocity of unknown arterole from known arteriole using formula -

A1V1= A2V2

Here we are given velocity for only arteriole having 0.17 diameter . Using that we can calculate for 0.20 and 0.15 arterioles .

i.e., 0.17* 18= 0.20* V2 = 15.3 cm/s

Similarly for 0.15 diameter arteriole we get velocity = 20.4 cm/s

Calculating mass flow rate using AVp formula we get 3.23g/s for all 3 arterioles ie 0.20,0.17 and 0.15.

So, Velocity of 1st generation arteriole .

A1V1= A2v2

0.17 *18 = 0.15* V2

=> V2 = 20.4 cm/s

Again, mass flow rate for 2nd generation arteriole.

A1V1 = A2V2

0.15* 20.4 = 0.12* V2

=> V2 = 25.5 cm/s

Mass flow rate can be calculated using AVp

0.12*25.5*1.056 = Rate = 3.23 g/s

I think you understand the solutions. In-case of any difficulties please write me.

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