Challenge Problem: An aneurysm is an abnormal enlargement of a blood vessel such as the aorta. Because of an aneurysm, the cross-sectional area of the aorta increases by 1.7 times. The speed of the blood (ρ = 1060 kg/m3) through a normal portion of the aorta is 0.40 m/s. Assuming that the aorta is horizontal (the person is lying down), determine the amount by which the pressure P2 in the enlarged region exceeds the pressure P1 in the normal region.

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 The Equation of Continuity A1v1 = A2v2 can be rearranged to v2/v1 = A1/A2. Since we know v1 and that A2 is 1.7 times A1 we can solve for v2 = 0.4/1.7 = 0.235 m/s. Now we can rearrange Bernoulli's equation for horizontal flow: P2 + ½ρv22 = P1 + ½ρv12 P2 - P1 = ½ρ[v12 - v22] P2 - P1 = ½(1060)[0.42 - 0.2352] P2 - P1 = 55 Pa This positive answer indicates that P2 is greater than P1. The excess pressure puts added stress on the already weakened tissue of the arterial wall at the aneurysm.