Question

Blood flows in an aorta of radius 4.38mm at 32.5cm/s. a) Calculate the volume flow rate. b)Although the cross-sectional area of a capillary is much smaller than that of the aorta, there are many capillaries, so their total cross-sectional area is much larger. If all the blood from the aorta flows into the capillaries and the speed of flow through the capillaries is 1.10mm/s, calculate the total cross-sectional area of the capillaries.

Answer 1

part a )

volume flow rate = v*A

v = velcoty = 32.5 cm/s = .325 m/s

A = area = pi*r^2

r = 4.38 mm = 4.38 x 10^-3

A = 6.03 x 10^-5 m^2

Q = 1.959 x 10^-5 m^3/s

part b )

Q = v*A

A = Q/v

A = 1.959 x 10^-5 / 1.1x 10^-3 m/s = 0.0178 m^2