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Viscous blood is flowing through an artery partially clogged by cholesterol. A surgeon wants to remove enough of the cholesterol to double the flow rate of blood through this artery.

If the original diameter of the artery is D , what should be the new diameter (in terms of D ) to accomplish this for the same pressure gradient?

  • Physics -

    dV/dt = L/(R^4) for a constant pressure gradient

    dV/dt = L/(1/2*D)^4 = 16L/(D^4)

    2dV/dt = 16L/Dnew = 2*16L/(D^4)

    Dnew = 4th root{(2*D^4)}

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