BIO Clogged Artery. 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?
Solution 49E Step 1: Diameter of the clogged Artery = D Diameter of the Artery after removing the cholesterol = D N Step 2: Consider a viscous blood of coefficient of viscosity () flowing through artery of radius (R). If dp is the pressure difference, then the Volume of the liquid flowing per second (Volumetric flow rate) through the artery is dV = dp R 4------------(1) (Poiseuille’s equation) dt l 8 Where is the coefficient of viscosity (in Ns m ) -2 dp l is the pressure gradient Step 3: Equation (1) is in the terms of radius, changing the radius as diameter, the equation becomes D 4 dV dp (2) dt = l 8 dV dp D 4 dt = l 8*2 4---------(2)