Poiseuillé’s law for rate of fluid flow: A consequence of Poiseuillé’s law for fluid velocities is Poiseuillé’s law for rate of flow of a fluid through a tube. As earlier, this law only applies to...

Poiseuillé’s law for rate of fluid flow: A consequence of Poiseuillé’s law for fluid velocities is Poiseuillé’s law for rate of flow of a fluid through a tube. As earlier, this law only applies to laminar flows. The law for rate of flow is a fourth-order polynomial that is also a power function:

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 -inch pipe compared with that through a 1 2 -inch pipe?

c. Suppose that an artery supplying blood to the heart muscle (see Figure 5.125) is partially blocked and is only half its normal radius. What percentage of the usual blood flow will flow through the partially blocked artery?