Question

The buildup of plaque on the walls of an artery may decrease its diameter from 1.1 cm to 0.90 cm. The speed of blood flow was 17 cm/s before reaching the region of plaque buildup.
A). Find the speed of blood flow within the plaque region. This was 25 cm/s.
B.) Find the pressure drop within the plaque region. I got 17.808 but says I'm wrong. Am I missing a step?

Answer 1

Answer

Initial radius of the artery is (1.1 cm) / 2 = 0.55 cm

final radius of the artery is (0.90 cm) / 2 = 0.45 cm

initial velocity of the blood is 17 cm/s

Using  equation of continuity is

                                      A₁v₁=A₂v₂

                                 π r₁² x v₁ = π r₂² x v₂

                                  r₁² x v₁ = r₂² x v₂

                                  0.55² x 17 =0.45² x v₂

                                        v₂=25.39 cm/s

Bernoulli's equation is

$P_1 - P_2 = \dfrac{1}{2}\rho (v_2^2-v_1^2)$

rho is the density of blood = 1060 kg/m^3

$P_1 - P_2 = \dfrac{1}{2}\times 1060 \times (0.254^2-0.17^2)$

$P_1 - P_2 =18.87\ Pa$