Explanation Write the expression for the rate of flow of blood through the aorta. Q = V t (I) Here, Q is the rate of flow of blood, V is the volume, and t is the time period. Write the expression for the volume of the aorta. V = A d (II) Here, A is the area of the aorta and d is the distance of the wall of the aorta. Write the expression for the speed of the flow of blood. v 1 = d t (III) Here, v 1 is the speed of the flow of blood through aorta. Substitute the equation (II) and (III) in equation (I) to rewrite for v 1 . Q = A d t = A v 1 v 1 = Q A = Q π r 1 2 (IV) Here, r 1 is the radius of the aorta. According to the equation of continuity, A 1 v 1 = A 2 v 2 Here, A 1 is the area of the aorta, A 2 is the radius of the aortic aneurysm, and v 2 is the speed of the blood through aortic aneurysm. Rewrite the above relation for v 2 . v 2 = A 1 v 1 A 2 = π r 1 2 v 1 π r 2 2 = r 1 2 v 1 r 2 2 (V) According to the Bernoulli’s equation the change in pressure of the aortic aneurysm system, Δ P = 1 2 ρ ( v 1 2 − v 2 2 ) (VI) Here, Δ P is the average blood pressure inside the aneurysm and ρ is the density of the blood. Conclusion: Substitute 120 cm 3 / s for Q and 1

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Chapter 7, Problem 98P

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Chapter 7, Problem 97P

Chapter 7, Problem 99P

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