Question

Plaque builds up on the walls of an artery decreasing its diameter from 1.16 cm to 0.60 cm. The flow speed is 11.5 cm/s before reaching the region of plaque buildup.

(a) Determine the speed at which blood is travelling through the plaque-constricted region.
cm/s

(b) Determine the pressure change within the plaque-constricted region. (Assume the density of blood is 1050 kg/m³. Be sure to include the appropriate sign with your answer.)
Pa

Answer 1

Given,

d1 = 1.16 cm ; d2 = 0.6 cm ; v1 = 11.5 cm/s ;

a)We know that

A1 v1 = A2 v2

pi d1^2/4 v1 = pi d2^2/4 v2

v2 = d1^2/d2^2 x v1

v2 = (1.16^2/0.6^2) x 11.5 = 42.98 cm/s

Hence, v2 = 42.98 cm/s

b)from Bernaulli's theorem

P1 + 1/2 rho v1^2 + rho g h = P2 + 1/2 rho v2^2 + rho g h2

since h1 = h2

P1 + 1/2 rho v1^2 = P2 + 1/2 rho v2^2 +

del-P = 1/2 rho (v2^2 - v1^2)

del-P = 0.5 x 1060 x (0.4298^2 - 0.115^2) = 91 Pa

Hence, del-P = 91 Pa