Poiseuille\'s Law for blood flow says that the volume following through an arter

Question

Poiseuille's Law for blood flow says that the volume following through an artery is proportional to the fourth power of the radius, that is V=k*r^4 for some positive constant k.

a) Calculate the differential dV from this equation

b) Use the differential to estimate the (absolute) increase in the volume of blood flow if the radius changes from .12cm to .15 cm. You may assume that the units are cubic cenitmeters per minute.

c) Use the differential to estimate the (relative) percentage by which the radius must be increased in order to cause a 50% increase in the volume of blood flow.

Explanation / Answer

dV = 4*k*dr ......(equation 1)

For absolute change in radius of (.15 - .12)= .03 cm

Change in volume = 4*k*0.03 = 0.12*k

V = 4*k*r

Divide by equation 1 then we get,

dV/V = dr/r

So, relative(or, absolute) change in volume = relative(or, absolute) change in radius.

Hence, to cause 50% increase in volume...50% radius should be increased

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