Suppose that there is a partial blockage of the aorta, which normally pumps about 5 L of blood per

Question

minute. If the diameter of the aorta were reduced by 30%, what increase in blood pressure gradient would
be needed to obtain the normal flow rate? (Assume that Poiseuille’s law applies.)

a. The pressure gradient would have to increase by a factor of 3.3.
b. The pressure gradient would have to increase by a factor of 1.4.
c. The pressure gradient would have to increase by a factor of 4.2.
d. The pressure gradient would have to increase by a factor of 123.
e. The pressure gradient would have to increase by a factor of 2.

Notes: I honestly don't even know where to start? Do I just take 30% off 5?

Answer 1

Q=π•P₁•r₁⁴/8•η• L = π•P₂•r₂⁴/8•η• L
P₂=(r₁/r₂)⁴P₁= (100%/70%)⁴• P₁=4.2• P₁.

c. The pressure gradient would have to increase by a factor of 4.2.