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Chapter 15: Problem 81

If the artery has circular cross section even at the stenosis, but the diameter at the stenosis is half that in the surrounding artery, the blood flow speed in the stenosis will be a. one-fourth that in the surrounding artery. b. one-half that in the surrounding artery. c. the same as in the surrounding artery. d. \(\sqrt{2}\) times that in the surrounding artery. e. four times that in the surrounding artery.

Short Answer

Expert verified
The correct answer to the problem is e. The blood flow speed in the stenosis will be four times that in the surrounding artery.

Step by step solution

01

Identify Given Values

The diameter at the stenosis is half that in the surrounding artery. Therefore, the radius (which is half the diameter) is also reduced by half. This will affect the cross-sectional area since area, \(A = \pi r^{2}\). Because the radius is halved, the area at the stenosis will be one-fourth the area of the surrounding artery.
02

Apply the Continuity Equation

The Continuity Equation is given by \( A_{1}V_{1} = A_{2}V_{2}\). We know that \(A_{2}\) is one-fourth of \(A_{1}\), then the equation becomes \( V_{1} = \frac{A_{2}}{A_{1}} * V_{2} = \frac{1}{4} * V_{2}\). Solving for \(V_{2}\), the speed of blood in stenosis, gives \(V_{2} = 4 * V_{1}\).
03

Identify the Answer

Upon comparing our solution with the given options, we find that our computed result corresponds with option (e) which says the blood flow speed in the stenosis will be four times that of the surrounding artery.

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