A pipe of diameter four cm is replaced by one of the same length but of diameter twelve 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) 3
B) 9
C) 27
D) 81
E) 243

Question

A pipe of diameter four cm is replaced by one of the same length but of diameter twelve 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) 3
B) 9
C) 27
D) 81
E) ​243

Quizplus · Accepted Answer

The rate of flow of a viscous liquid through a pipe is proportional to the fourth power of the diameter (Poiseuille's Law). If the diameter increases from 4 cm to 12 cm, the factor change in flow rate is (12/4)^4 = 3^4 = 81.

A Pipe of Diameter Four Cm Is Replaced by One