Beware of the Cream Filling

Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Changes in the effective area of an artery can lead to large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel.

Consider an artery that is horizontal along some stretch. In the healthy portion of the artery the blood flow velocity is \(0.14~\mbox{m/s}\). If plaque closes off \(80\%\) of the area of the artery at one point, what is the magnitude of the pressure drop in Pascals?

Details and assumptions

  • The mass per unit volume of blood is \(\rho= 1050~\mbox{kg/m}^3\).
  • You may neglect the viscosity of blood.

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