Asked by Melissa
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?
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?
Answers
Answered by
Matt Daddy
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)}
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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