   Chapter 9, Problem 35P

Chapter
Section
Textbook Problem

(a) Calculate the mass flow rate (in grains per second) of blood (ρ= 1.0 g/cm3) in ail aorta with a cross-sectional area of 2.0 cm2 if 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 × 103 cm2. What is the flow speed in the capillaries?

(a)

To determine
The mass flow rate of blood in an aorta.

Explanation
The volume flow rate is V/t=Av and the volume of blood in aorta is V=m/ρ . Now the mass flow rate of blood becomes as m/t=ρAv .

Given info: Density of blood is 1.0g/cm3 , cross sectional area of aorta is 2.0cm2 , and the flow speed of blood in aorta is 40cm/s .

The formula for the mass flow rate of blood in an aorta is,

mt=ρAv

• ρ is density of blood.
• A is area of aorta.
• v is flow speed of blood in an aorta.

Substitute 1.0g/cm3 for ρ , 2

(b)

To determine
The flow speed in the capillaries.

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