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March 29, 2017

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When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in an artery has been reduced to 30% of its normal value due to plaque formation, and the average pressure difference has increased by 40%, by what factor has the plaque reduced the radius of the artery?

% of its normal value

  • Physics - ,

    flow rate Q2 =
    v2 pi r2^2 = .3 v1 pi r1^2
    v2/v1 = .3 (r1/r2)^2

    .5 rho v2^2 =P2=1.4 P1=1.4*.5 rho v1^2
    v2^2/v1^2 = 1.4
    so
    v2/v1 = 1.18
    so
    1.18 = .3(r1/r2)^2
    r1/r2 = sqrt (1.18/.3)
    = 2
    so reduced to half the original radius

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