Question

A major artery with a 1.6 cm2 cross-sectional area branches into 18 smaller arteries, each with an average cross-sectional area of 0.7 cm2. By what factor is the average velocity of the blood reduced when it passes into these branches?

Answer 1

To solve this problem it is necessary to apply the continuity equations for which it is defined that the proportion of Area in the initial section is equal to the final section. In other words,

$A_1 v_1 = A_2 v_2$

Where,

$A_i =$ Cross sectional area at each section

$v_i =$Velocities of fluid at each section

The total area of the branch is eighteen times of area of smaller artery. The average cross-sectional area of each artery is $0.7cm^2.$

Therefore the Cross-sectional area at the end is

$A_2= 18*0.7cm^2$

$A_2 = 12.6cm^2$

Applying the previous equation we have then

$A_1 v_1 = A_2 v_2$

$(1.7cm^2) v_1 = (12.6cm^2)v_2$

The ratio of the velocities then is

$\frac{v_1}{v_2} = \frac{1.7}{12.6}$

$\frac{v_1}{v_2} = 0.135$

Therefore the factor by which the velocity of blood will reduce when it enters the smaller arteries is 0.1349