The buildup of plaque on the walls of an artery may decreaseits diameter from 1.

Question

The buildup of plaque on the walls of an artery may decreaseits diameter from 1.1 cm to 0.71 cm. Thespeed of blood flow was 16 cm/s beforereaching the region of plaque buildup.
(a) Find the speed of blood flow within theplaque region.
1 cm/s

(b) Find the pressure drop within the plaque region. (Assume thatblood has the same density as water.)
2____________ Pa The first part is right but i can't get thesecond part. I'm convinced that you have to use Bernouli'sEquation but I'm stuck on how to use it, if that's even theequation to use. The buildup of plaque on the walls of an artery may decreaseits diameter from 1.1 cm to 0.71 cm. Thespeed of blood flow was 16 cm/s beforereaching the region of plaque buildup.
(a) Find the speed of blood flow within theplaque region.
1 cm/s

(b) Find the pressure drop within the plaque region. (Assume thatblood has the same density as water.)
2____________ Pa The first part is right but i can't get thesecond part. I'm convinced that you have to use Bernouli'sEquation but I'm stuck on how to use it, if that's even theequation to use.

Explanation / Answer

a) Since V1A1 =V2A2 we have V2= V1 (A1 /A2 )   = V1(r12 /r22)   = V2= 16 (1.1 / 0.71)2   =38 m/s b) since 0.5 V2 + gh + P/ = constant and h = 0 we have 0.5 V12 + P1/ = 0.5V22 + P2/ or Finally P = (P2 - P1) =0.5(V12 - V22) P = 0.5 x 1000 (0.162 - 0.38 2) P = -59 Pa

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