You are a medical professional attempting to explore the pro

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 d_1 is 0.0050 m and the speed V_1 of the blood is 0.500 m/s. The section narrows into another segment of artery with diameter d_2 = 0.0022 m . The height relative to the laboratory floor does not change (y_1 = y_2). The density of blood is 1.06 times 10^3 kg/m^3. The diagram below shows dimensions and arrows qualitatively and may not be exactly at scale. What is the circular cross-sectional area A_1 of the first section of artery? What is the circular cross-sectional area A_2 of the second section ? What is the speed v_2 in the narrow section of artery? What is the pressure difference P_1 - P_2 between the two sections? 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?

Solution

A)A1 =d₁²/4=19.625×10^-6m²

B)A2=d₂²/4=3.8×10^-6m²

C)A1V1=A2V2

V2=2.58 m/s

D)P1-P2=0.5p(V2²-V1²)

P1-P2=3395.39 kg/ms²

E)due to drop in pressure arteries collapse and internal bleeding occurs which can lead to death