A medical technician is trying to determine what percentage of a patient’s arter

grasaladae5

grasaladae5

Answered question

2021-11-09

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 1.20×104Pa , while in the region of blockage it is 1.15×104Pa.. Furthermore, she knows that blood flowing through the normal artery just before the point of blockage is traveling at 30.0 cm/s, and the specific gravity of this patient’s blood is 1.06. What percentage of the cross-sectional area of the patient’s artery is blocked by the plaque?

Answer & Explanation

Novembruuo

Novembruuo

Beginner2021-11-10Added 26 answers

Step 1
The plaque presence will cause the speed to change because of the changing in the cross-sectional area of the artery. To grasp the change we employ the Bernoulli's equation
p1+ρgy1+12ρv12=p2+ρgy2+12ρv22
and we will combine it with the continuity equation v1A1=v2A2 from which we get
A1A2=v2v1
Step 2
Since two points are close to each other y1y2 we can rewrite Bernoulli's equation as
Step 3
Now, we can express the velocity when the plaque is present, v2 as follows
12ρv22=p1p2+12ρv12
v22=2p12p2+ρv12ρ
After inserting the given values we get that
v22=2×1.2×1042×1.15×104+1.06×103×0.321.06×103=1(ms)2
v2=1ms
Step 4
Now, we recall the continuity equation and use A1A2=v2v1 to write
A2=0.3A1
So we get that the 70% of the artery is vlovked by the plaque

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