Blood flowing in a Vessel

Velocity of the Blood is a Function of r

Amanda works at a biomedical engineering lab. For a particular project, a sensor needs to be installed in a blood vessel at a location where the blood velocity has the same magnitude as the average velocity of the whole vessel cross-sectional area.

What is known:

• The vessel can be considered as a cylindrical tube with a radius of 0.08 mm and a length of 20 mm.
• The blood in the vessel is considered as a fully developed laminar flow with a velocity function as
  
  v(r) = [P / (4μl)] (R² - r²)
  
  where P is the pressure difference between the ends of the vessel, P = 400 Pa, μ is the viscosity of the blood, μ = 10x10^-3 kg/(m-s), R is the radius of the vessel, and l is the length of the vessel.

• Where does the blood velocity have the same magnitude as the average velocity of the whole cross-sectional area of the vessel?
• What is the average velocity of the whole vessel cross-sectional area?

Use the Mean Value Theorem for Integrals.