The flow rate of blood through a 2.00 ? 10-6 m radius capillary is 3.80 ? 10-9 cm3/s.

Question

(a) What is the blood velocity? (This small velocity allows time for diffusion of materials to and from the blood.)

(b) Assuming all the blood in the body passes through capillaries, how many of them must there be to carry a total flow of 84.0 cm3/s? (The large number obtained is an overestimate, but it is still reasonable.)

Answer 1

 

(a) flow rate = velocity x cross section

Make sure units are consistant. If radius is in meters than flow rate should be in m^3 per second. Assuming units are consistant

3.8 x10^-9 = v x 2x10^-6

v = 1.9 x 10^-3 m/s make sure you check the units.

(b) Total blood flow = number of capillaries(n) x flow rate of one capillary

84 = n x 3.8 x 10^-9

n = 84/(3.8 x 10^-9) = 22 x 10^9

 

Answer 2

Hey Sarah -- velocity is flow rate (Q) / cross-section area for a 2 micrometer radius

... a circle is about 75% of a square => Area ~ 3E-12 sq.m or 3E-8 sq.cm ...

a) velocity = Q/A ~ 0.13 cm/s or about 1.3 mm/s

 

b) no. of caps = 84/(4E-9) ~ about 21 or 22 billion of 'em ... Best wishes, ma'am :)