Question

The buildup of plaque on the walls of an artery may decrease its diameter from 1.1cm to 0.75 cm. If the speed of blood flow is 15 cm/s, before reaching the region of plaque buildup, find the speed (in cm/s) of the blood flow. [Express the answer in ONE decimal place]

Answer 1

v₂ = 32.4 cm/s

Step-by-step explanation:

From the continuity equation it is clear that:

Volume Flow Rate Before Plaque = Volume Flow Rate In Plaque

Q₁ = Q₂

A₁v₁ = A₂v₂

where,

A₁ = Area of artery before plaque build up = πd²/4 = π(1.1 cm)²/4 = 0.95 cm²

A₂ = Area of artery with plaque build up = πd²/4 = π(0.75 cm)²/4 = 0.44 cm²

v₁ = velocity of blood flow in artery before plaque region = 15 cm/s

v₂ = velocity of blood in artery in plaque region = ?

Therefore,

(0.95 cm²)(15 cm/s) = (0.44 cm²)(v₂)

v₂ = (14.25 cm³/s)/(0.44 cm²)

v₂ = 32.4 cm/s