Question

As an aid in working this problem, consult Concept Simulation 11.1. The volume flow rate in an artery supplying the brain is 3.50 10-6 m3/s.
(a) If the radius of the artery is 5.80 10-3 m, determine the average blood speed. m/s
(b) Find the average blood speed at a constriction in the artery if the constriction reduces the radius by a factor of 5. Assume that the volume flow rate is the same as that in part (a). m/s

Answer 1

Answer

given,

flow from the artery = 3.5 x 10⁻⁶ m³/s

Radius of artery = 5.80 x 10⁻³m

area = π R²

       = π x (5.8 x 10⁻³)²

       = 1.06 x 10⁻⁴ m²

$v = \dfrac{Q}{A}$

$v = \dfrac{3.5 \times 10^{-6}}{1.06 \times 10^{-4}}$

v = 0.033 m/s

b) new velocity of flow

Radius = R' = R/4

 A V = A' V'

 R² V = R'² V'

 R^2 V = (\dfrac{R}{4})^2 V'

 V' = 16 V

 V' = 16 x 0.033

  V' =0.528 m/s