Question

Consider a pipeline for which some sections of the pipeline are higher than other sections. Is it possible for the pressure in the fluid in the pipeline to be the same in the higher sections as it is in the lower sections in the pipeline? (You may assume that the pipeline is transporting an ideal incompressible fluid.)

No, the pressure cannot be the same everywhere in the pipeline.

Yes, the pressure can be the same in the higher sections as it is in the lower sections of the pipeline provided that the radius of the pipe is larger in the higher sections than in the lower sections.

Yes, the pressure can be the same in the higher sections as it is in the lower sections of the pipeline provided that the radius of the pipe is smaller in the higher sections than in the lower sections.

Answer 1

From Bernoulli equation

So when pressure remains same at higher section then

Here 'h' is higher hence velocity must be lower. Now using continuity equation

therefore for lower velocity, an area of the cross section must be higher. Therefore correct option will be

Yes, the pressure can be the same in the higher sections as it is in the lower sections of the pipeline provided that the radius of the pipe is larger in the higher sections than in the lower sections.