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 69.0 %. The blood approaching the blocked portion has speed v 0 . Just as the blood enters the blocked portion of the vessel, what is its speed v , expressed as a multiple of v 0

Answer 1

Answer:10.4 times of initial velocity

Explanation:

Given

Diameter reduced by 69 %

it approaches with velocity $v_0$

suppose its velocity is v during blocked passage

suppose d is the initial diameter and $d_2$ diameter is

$d_2=d(1-0.69)$

$d_2=0.31 d$

$A_2=\frac{\pi d_2^2}{4}$

As flow is constant

$Q_1=Q_2$

$d^2v_0=d_2^2v$

$v=10.40 v_0$