When Poiseuille's law is rearranged for pressure, what adjustment must be made in driving pressure to maintain the same flowrate when the radius of the tube is reduced by 50 percent?

Question

Quizplus · Accepted Answer

Poiseuille's law states that the flow rate through a cylindrical tube is directly proportional to the fourth power of the radius of the tube and the pressure difference across the tube, and inversely proportional to the viscosity and length of the tube. If the radius is reduced by 50% (i.e., to half its original size), the new radius to the fourth power would be (1/2)^4 = 1/16 of the original. To maintain the same flow rate, the pressure must be increased to 16 times the original pressure.

When Poiseuille's Law Is Rearranged for Pressure, What Adjustment Must