Question Detail
Question
The pulmonary artery which connects the heart to the lungs is 8.5 cm long and has a pressure difference over this length of 450 Pa. If the inside radius of the artery is 2.4 mm, what is the average speed of blood in the pulmonary artery? (coefficient of viscosity = 0.00272 N.s/m²)
Correct Answer
Option C is the correct answer.
Detailed Explanation
This problem involves fluid flow through a cylindrical tube, which can be solved using Poiseuille's law. The average velocity v = (ΔP × r²)/(8ηL), where ΔP = 450 Pa, r = 2.4 mm = 0.0024 m, η = 0.00272 N·s/m², and L = 8.5 cm = 0.085 m. Substituting: v = (450 × (0.0024)²)/(8 × 0.00272 × 0.085) = (450 × 0.00000576)/(0.0018496) = 0.002592/0.0018496 = 1.4 m/s.
Hint
Use Poiseuille's equation for laminar flow in a cylindrical tube. Convert all units to SI (meters, Pascals) before calculating.