Thought I had the right ans. but do not?

Question

Calculate the flow rate of blood (density = 1.15 g/cm^3) in an aorta with a cross-sectional area of 2.54 cm^2 if the flow speed is 48.9 cm/s (in g/s).

Assume the aorta branches to form a large number of capillaries with a combined cross-sectional area of 2720 cm^2, what is the flow speed in the capillaries (in cm/s)?

Answer 1

To get the volumetric flow rate, multiply the cross sectional area by the flow speed:

F_v = 2.54 cm^2 * 48.9 cm/s = 124.2 cm^3/s

To get the mass flow rate, multiply the volumetric flow rate by the density of the fluid:

F_m = 124.2 cm^3/s * 1.15 gm/cm^3 = 142.8 gm/s.


Assuming the fluid is incompressible, the volumetric flow rate in the artery must be equal to the volumetric flow rate through the combined capillaries. Again using the fact that the volumetric flow rate is given by the cross sectional area (this time the combined area of all the capillaries) times the flow speed, we have that:

2.54 cm^2 * 48.9 cm/s = 2720 cm^2 * v_capillary
v_capillary = 48.9 cm/s * (2.54/2720)
v_capillary = 9.338*10^-4 * 48.9 cm/s
v_capillary = 4.57 * 10^-2 cm/s