Chapter 5.6, Problem 4E

Poiseuille's Law for Rate of Fluid Flow Poiseuille's law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function:

$F=c{R}^4$,

where $F$ is the flow rate (measured as a volume per unit time), $c$ is a constant, and $R$ is the radius of the tube.

a. Assume that $R$ increases by 10%. Explain why $F$ increases by 46.41%. (Hint: Consider $1.10$ raised to the fourth power.)

b. What is the flow rate through a $3/4-\text{inch}$ pipe compared with that through a $1/2-\text{inch}$ pipe?

c. Suppose that an artery supplying blood to the heart muscle (see Figure $5.86$) is partially blocked and is only half its normal radius. What percentage of the usual blood will flow through the partially blocked artery?