Question

The buildup of plaque on the walls of an artery may decrease its diameter from 1.2 cm to 0.75 cm . The speed of blood flow was 15 cm/s before reaching the region of plaque buildup. Find the speed of blood flow within the plaque region. Find the pressure drop within the plaque region.

Answer 1

here,

initial diameter , di = 1.2 cm

final diameter , df = 0.75 cm

the initial speed , vi = 15 cm/s

let the final speed be vf

using equation of continuity

Area * speed = volume flow rate

pi * (di/2)^2 * vi = pi *( df/2)^2 * vf

(1.2/2)^2 * 15 = (0.75/2)^2 * vf

solving for vf

vf = 38.4 cm/s

the speed of blood flow within the plaque region is 38.4 cm/s

b)

Bernoulli's equation:

p1 + 0.5 * p * v1^2 + p * gh1 = p2 + 0.5 p * v2^2 + p * gh2

Assuming the "h" terms cancel,

p1 + 0.5 * 1060 * (0.15 m/s)^2 = p2 + 0.5 * 1060 * (0.384 m/s)^2

p1 + 11.92 Pa = p2 + 78.15 Pa

p1 - p2 = 66.2 Pa