Physics

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

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  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.

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