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 28.0 cm/s, and the specific gravity of this patient's blood is 1.06.

Answer 1

To determine the reduction in radius of the artery caused by a blood clot, we can use the relationship between flow rate, pressure difference, and artery radius.

Step-by-step explanation:

To calculate the reduction in radius of the artery, we can use the fact that flow rate is inversely proportional to the fourth power of the radius. If the flow rate is reduced to 10.0% of its normal value, it means the radius must be reduced by a factor that is the fourth root of 10.0%. Let's call this factor A.

On the other hand, if the pressure difference has increased by 20.0%, it means the radius must be reduced by a factor that is the fourth root of 120.0%. Let's call this factor B.

To find the factor by which the clot reduced the radius of the artery, we need to find the ratio of A to B.