Narrowing the tube through which a viscous fluid flows to a third of its original radius will reduce the flow rate by a factor of 81.

Question

Quizplus · Accepted Answer

According to the Hagen-Poiseuille equation, the flow rate (Q) of a viscous fluid through a cylindrical tube is inversely proportional to the fourth power of the radius of the tube (r), i.e., Q ∝ 1/r^4. Therefore, if the radius is reduced to a third (r/3), the flow rate will be reduced by a factor of (3^4) = 81.

Narrowing the Tube Through Which a Viscous Fluid Flows to a Third