A medical technician is trying to determine what percentage of a patient\'s arte

Question

A medical technician is trying to determine what percentage of a patient's artery is blocked by plaque. To do this, she measures the blood pressure just before the region of blockage and finds that it is 1.20×104 Pa , while in the region of blockage it is 1.15×104 Pa . Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 27.5 cm/s , and the specific gravity of this patient's blood is 1.06.

What % of the cross sectional area is covered by plaque?

Explanation / Answer

P1 = 1.20 * 10^4 Pa
V1 = 27.5 m/s

P2 = 1.15 * 10^4 Pa
V2 = ?

v2 = sqrt[ 2*(P1 - P2)/w + v1^2 ]
v2 = sqrt[ 2*(1.20 * 10^4 - 1.15 * 10^4) / (1060)   + 0.275^2]
v2 = 1.0095 m/s

A1 * v1 = A2 * v2
A2/A1 = v1/v2 = 0.275/1.0095
A2/A1 = 0.272

% of Artery blocked = 72.8%

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