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I need to answer the following question: assume you have two pipelines, one with diameter d...

I need to answer the following question: assume you have two pipelines, one with diameter d and another with diameter D (where d << D). In both flows the same fluid with the same average velocity, but, in one Bernoulli's principle holds much better than the other. Which pipeline is this one and why (with proof)? (Help: check the assumption of Bernoulli's theorem at a differential level).

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Answer #1

Bernoulli's equation will be more suitable for large diameter pipes.
Explanation:
We know that the loss due to friction which is major loss is inversely proportional to the diameter for a given average flow velocity. In Bernoulli's assumption losses are not considered so it should hold better for large pipe diameters.

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