H5-7

a. Calculate the mass flow rate (in grams per second) of blood ( = 1.0 g/cm³) in an aorta with a cross-sectional area of 2.0 cm²if the flow speed is 40 cm/s.

b. Assume that the aorta branches to form a large number of capillaries with a combined cross-sectional area of 3.0 10³cm².

What is the flow speed in the capillaries?

Given:

r= density of blood = 1.0 g/cm³

A = cross-sectional rea = 2.0 cm²

v = velocity = 40 cm/s

t = time

= mass flow rate

Q = volume flow rate

V = volume

Eqns:

r = m/V m =r V

Q = Av = constant

= m/t

Basically need to derive an equation that relates Volume flow rate to mass flow rate for part A

and for part B, the derivation comes straight from continuity... relating volume flow rate to flow speed.

thanks!