I would appreciate detailed explanations to help me understand the concepts bett

Question

I would appreciate detailed explanations to help me understand the concepts better. Below are my approaches to a solution.

My attempt at a solution: For part A, I assumed that the pressure gradient is favorable, toward the direction of flow. Under this assumption, fluid pressure would decrease in the direction of flow. I feel like I am missing something though. I would appreciate a more detailed explanation.

For part B: My approach to a solution: I know that the question asks where the pressure is greatest. I started out by identifying where I think pressure is lowest, which might be at point C. I think point C might have the lowest pressure and highest fluid velocity in the pipe. My guess for region of highest pressure is point B because it is a corner, and I think water would push more against pipe walls in sections like this one.

A. Given a fluid flowing through a pipe in the direction indicated, what difference in parameters exists between points A and B?

B. If the liquid is flowing in the direction indicated, at what point is the pressure greatest?

Explanation / Answer

for A your explanation is correct, since the water flows from A to B, Pressure at A > Pressure at B

for B

clearly Pb > Pd, since both have same area so same velocity and at same height, so till now B is the winner

now at point C, we have Pb + 1/2 D * Vb2 + Dgh = Pc + 1/2 DVc2 + Dgh

here Dgh gets cancelled, and clearly Vc > Vb (since AcVc = AbVb) so to remain at eq, Pb >Pc

Pb still is the winner

NOw for point A

we have considering A's height 0 and B's height H,

Pa + 1/2 D Va2 = Pb + 1/2 D * Vb2 + Dgh , here since area are same, so Va = Vb

so we have Pa = Pb + Dgh

here we clearly see that Pa >Pb

now Pa is the winner

so contest goes for A and E

everything is same and since water flows all the way from A to E

it is quite natural that Pa >Pe

so Pressure at A is highest

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