2. You are a medical professional attempting to explore the problem of blood pre

Question

2. You are a medical professional attempting to explore the problem of blood pressure drops in diseased, narrowed arteries. The arteries have approximately circular cross-section. In a section of an artery, the diameter d1 is 0.0050 m and the speed v1 of the blood is 0.500 m/s. The section narrows into another segment of artery with diameter d2 = 0.0022 m . The height relative to the laboratory floor does not change (y1 = y2) . The density of blood is 1.06x103 kg/m3. NOTE: The diagram below shows dimensions and arrows qualitatively and may not be exactly at scale. (a) What is the circular cross-sectional area A1 of the first section of artery? (b) What is the circular cross-sectional area A2 of the second section ? (c) What is the speed v2 in the narrow section of artery? (d) What is the pressure difference P1 ? P2 between the two sections? (e) Short answer in sentence form or math form; just clearly explain your work: It was mentioned in class a drop in pressure could lead to the collapse of the narrow section of artery. Explain. What would be one major consequence of such a collapse?

Explanation / Answer

(a) A1 = r2 = (0.0025m)2 = 1.964 * 10-5 m2

(b) A2 = r2 = (0.0011m)2 = 3.801 * 10-6 m2

(c) v2 = v1(A1/A2) = 2.583 m/s

(d) v12/2 + gy1 + p1 = v22/2 + gy2 + p2 from Bernoulli's principle but since we know y1 = y2 we get

v12/2 + p1 = v22/2 + p2 so

p1 - p2 = /2(v22 - v12) = (1.06 * 103 kg/m3)/2 * ([2.583 m/s]2 - [0.50 m/s]2)

= 3.403 * 103 Pa

(e) Artery could collapse because external pressure remains the same in surrounding tissue, but internal pressure of the narrower artery decreases due to faster flow of blood and Bernoulli's Principle. Consequence could be a blocked artery.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.