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 1.20×10^4 Pa, while in the region of blockage it is 1.15×10^4 Pa. 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?

Question

I know that I have to convert the velocity to 0.300 m/s, then specific gravity is equal to the density of the blood in relation to the density of water, so the density of blood is 1060 kg/m^3. I have no idea where to go from here. I would try putting it into the equation:

P1 + (density * gravity * y1) + (.5 * density * (velocity1)^2) = P2 + (density * gravity * y2) + (.5 * density * (velocity2)^2)

But that doesn't seem to work. How do you figure out what the blockage amount is? I don't want an answer, I just want to know how.

Answer 1

y1=y2, so the equation goes to

P1+.5density*V1^2 =P2+.5density*V2^2
solve for v2.

then, use the law of mass continuity

Area1*velocity1=area2*velocity2
and solve for area2/area1, which will be a decimal number (then convert it to percent). That subtracted from 100 will the blocked area.