Question

A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the plaque decreases the diameter of the vessel by 73.0%. The blood approaching the blocked portion has speed ?0. Just as the blood enters the blocked portion of the vessel, what is its speed ?, expressed as a multiple of ?0?

Answer 1

Using Continuity equation:

A0*v0 = A1*v1

A1 = Area of vessel during the blocked portion = pi*d1^2/4

d1 = diameter in blocked portion = d0 - 73% of d0 = d0 - 0.73*d0 = 0.27*d0

So,

A1 = pi*d1^2/4 = pi*(0.27*d0)^2/4 = 0.27^2*A0

Now from continuity equation:

v1 = (A0/A1)*v0

v1 = (A0/(0.27^2*A0))*v0

v1 = (1/0.27^2)*v0

v1 = speed of blood when it enters in to blocked portion = 13.72*v0

Thanks have a nice day