A major artery with a 1.7 cm2 cross-sectional area branches into 18 smaller arteries, each with an average cross-sectional area of 0.4 cm2. By what factor is the average velocity of the blood reduced when it passes into these branches

0.14

Explanation:

Flow rate is the volume flowing through a point at a particular time, in calcuing flow rate we have

Q= v*t

it in terms of Area, we have Q= A*v

Where A= area

v= velocity.

Solving the question , flow rate is constant then

A*v= constant

A(i) v(i)= A(f) v(f)

Where A(i)= initial area= 1.00cm^2

A(f)= final area= 0.400cm^2

V(i) and V(f) are the initial and final velocity respectively and the ratio of the two will gives us the factor

Substitute the values into the equation we have

1 V(i)= 4 V(f)

But we were told that the cross sectional area of 1.00cm^2 branches into 18 smaller arteries.

Then

1 V(i)=0.4 V(f)*(18)

1 V(i)=7.2V(f)

Then if we find the ratio of the velocity, we will get the factor.

V(f)/V(i)= 1/7.2

V(f)/V(i)=0.14

Hence, the factor of the average velocity of the blood reduced when it passes into these branches is 0.14

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