Question

A pump is used to circulate oil in an engine. If the diameter of the tube connecting the pump to the engine is increase by a factor of 2, the resulting pressure drop at the end of the tube changes by a factor of

O 1/32

O 1/16

O 1/8

O 1/2

O 1/4

Answer 1

Increasing the tube's diameter by a factor of 2 results in the pressure drop being 1/16 of its original value, as pressure drop is inversely proportional to the fourth power of the tube's radius.

Step-by-step explanation:

The question is concerned with the pressure drop in a tube when its diameter is increased. According to the principles of fluid dynamics, specifically the Hagen-Poiseuille equation, which describes laminar flow through a cylindrical pipe, the pressure drop (ΔP) is inversely proportional to the fourth power of the radius (r) of the tube.

If the diameter of the tube is doubled, the radius also doubles, and so the pressure drop changes by a factor of 1/24 or 1/16. Thus, the resulting pressure drop will be 1/16 of its original value, not 1/8 or 1/4 as suggested by the question.