A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the plaque decreases the diameter of the vessel by 74.0%. The blood approaching the blocked portion

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 74.0%. The blood approaching the blocked portion has speed 𝑣0. Just as the blood enters the blocked portion of the vessel, what is its speed 𝑣, expressed as a multiple of 𝑣0?

V=___x v0

Answer 1

This is a great question!

For this problem, we can use the continuity equation.

A1v1 = A2v2

where,

A = cross-sectional area

v = flow velocity

Now we need to rewrite A2 in relation to A1.

Since A2 is a 74% decrease of A1,

A2 = .26*A1

Now we solve for v2

v2 = A1*v1/A2

v2 = A1*v1(.26*A1)

v2 = v1/(.26)