Question

In: Physics

A medical technician is trying to determine what percentage of a patient's artery is blocked by...

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.

Part A: What percentage of the cross-sectional area of the patient's artery is blocked by the plaque?

Solutions

Expert Solution

Specific gravity of blood = 1.06

Density of blood = = 1.06 x 1000 kg/m3 = 1060 kg/m3

Pressure of the blood in the unblocked area = P1 = 1.2 x 104 Pa

Speed of flow of blood in the unblocked area = V1 = 27.5 cm/s = 0.275 m/s

Cross-sectional area of the artery in the unblocked area = A1

Pressure of the blood in the blocked area = P2 = 1.15 x 104 Pa

Speed of flow of blood in the blocked area = V2

Cross-sectional area of the artery in the blocked area = A2

Assuming the artery is horizontal.

By bernoulli's equation,

V2 = 1.01 m/s

By continuity equation,

A1V1 = A2V2

A1(0.275) = A2(1.01)

A2 = 0.2722A1

The cross-sectional area of the artery in the blocked area is 27.22% of the unblocked area, therefore the plaque blocks 72.78% of the cross-sectional area.

A) Percentage of the cross-sectional area of the artery blocked by plaque = 72.78%


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