Blood flowing in a Vessel
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
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.