Question

An artery with cross sectional area of 1 cm2 branches into 20 smaller arteries each with 0.5 cm2 cross sectional area. If the velocity of blood in the thicker artery is v, what is the velocity of the blood in the thinner arteries

Answer 1

Answer:

The velocity of the blood in the thinner arteries is 0.1 times that of the thicker artery.

Explanation:

To find the velocity of the blood we need to use the continuity equation:

$n_{1}A_{1}v_{1} = n_{2}A_{2}v_{2}$   (1)  

Where:

n: is the number of branches

A: is the cross-sectional area

v: is the velocity

For artery 1, we have:

n₁ = 1, A₁ = 1 cm², v₁ = v

For the 20 arteries (2), we have:

n₂ = 20, A₂ = 0.5 cm², v₂ =?

By using equation (1):

$n_{1}A_{1}v_{1} = n_{2}A_{2}v_{2}$

$1 cm^{2}*v = 20*0.5 cm^{2}*v_{2}$

$v_{2} = \frac{1 cm^{2}*v}{20*0.5 cm^{2}} = \frac{v}{10} = 0.1v$

Therefore, the velocity of the blood in the thinner arteries is 0.1 times that of the thicker artery.

I hope it helps you!