All aneurism is an abnormal enlargement of a portion of a blood vessel (e.g., an

Question

All aneurism is an abnormal enlargement of a portion of a blood vessel (e.g., an artery). Suppose that, because of an aneurism, the cross-sectional area. A1, of a normal portional of a blood vessel increases to a value A2 = 1.7 A1. The speed of blood (density 1060 kg/m3) through the normal portion is 0.40 m/s. Assuming that the blood vessel is horizontal (the person is lying down), determine the amount by which the pressure in the enlarged region exceeds that in the normal region. (The excess pressure puts added stress on the already weakened tissue of the blood vessel wall, so the situation is unfortunately unstable.)

Explanation / Answer

Blood, like most fluids is an incompressible, and the equation of continuity in the form of A1V1 = A2V2 can be applied. We can also use the fact that the area of circle is pr2. (prU2) vU = unobstructed volume flow rate (prO2) vO = obstructed volume flow rate (prU2) vU = (prO2) vO The ratio of the radii is: rU = vU = v3 = 1.7 rO vO

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