A pipe of diameter 4 cm is replaced by one of the same length but of diameter 5 cm.If the pressure difference between the ends of the pipe remains the same,by what factor is the rate of flow of a viscous liquid through it changed?
A) 5.1
B) 3.4
C) 2.4
D) 1.5

Question

Quizplus · Accepted Answer

According to Poiseuille's Law, the rate of flow through a pipe is directly proportional to the fourth power of its radius. Therefore, if the radius increases by a factor of 1.25 (from 2 to 2.5 cm), the flow rate will increase by a factor of (1.25)^4 = 2.4414. Rounded to the nearest tenth, this is 2.4. Therefore, the answer is C.

A Pipe of Diameter 4 Cm Is Replaced by One