In the condition known as atherosclerosis, a deposit or atheroma forms on the arteral wall and reduces the openin through which blood can flow. in the carotid artery in the neck, blood flows ten times faster through a partially blocked region than it does through an unobstructed region. determine the ratio of effective radii of the artery at the two places
Blood like most liquids, is incompressible, and the equation of continuity in the form of
A1v1 = A2v2 can be applied. We also have to use the fact that the area of a circle is πr2
unobstructed volume flow rate (πrU2)vU = (πrO2)vO obstructed volume flow rate
The ratio of radii then is given by: rU/rO = sqrt[vO/vU] = sqrt(3) = 1.7
