Question

A major artery with a cross sectional area of 1.00cm^2 branches into 18 smaller arteries, each with an average cross sectional area of 0.400cm^2. By what factor is the average velocity of the blood reduced when it passes into these branches

Answer 1

Here we can say that rate of flow must be constant

so here we will have

$A_1v_1 = 18 A_2v_2$

now we know that

$A_1 = 1 cm^2$

$A_2 = 0.4 cm^2$

now from above equation

$1 cm^2 v_1 = 18(0.400 cm^2)v_2$

$\frac{v_2}{v_1} = \frac{1}{18\times 0.4}$

$\frac{v_2}{v_1} = 0.14$

so velocity will reduce by factor 0.14