Fluid flow/pressure in a pipe going uphill

[j3dwards]

Homework Statement

Water is flowing along a pipe. Points B and C in the pipe are at the same height but point A is at a higher elevation.The pipe has the same cross-sectional area at points A and B but is wider at point C. Rank in order from largest to smallest, the pressures at the three points A, B, C. Briefly explain your reasoning.

Homework Equations

Bernoulli''s equation?

The Attempt at a Solution

Largest to smallest in order: A, B, C

Pressure highest at A because A is uphill, then B because it has a smaller cross sectional area than C, and then C because greatest cross sectional area.

But I'm not sure if pressure is higher at C because it's pushing fluid uphill?

 

[billy_joule]

If the water were not flowing what would your answer be?
Are you familiar with Pascals law?

 

[SteamKing]

Homework Statement

Water is flowing along a pipe. Points B and C in the pipe are at the same height but point A is at a higher elevation.The pipe has the same cross-sectional area at points A and B but is wider at point C. Rank in order from largest to smallest, the pressures at the three points A, B, C. Briefly explain your reasoning.

Homework Equations

Bernoulli''s equation?

The Attempt at a Solution

Largest to smallest in order: A, B, C

Pressure highest at A because A is uphill, then B because it has a smaller cross sectional area than C, and then C because greatest cross sectional area.

But I'm not sure if pressure is higher at C because it's pushing fluid uphill?

Is the pressure at A higher because it's uphill? What's the pressure at B relative to the pressure at A? Did you apply Bernoulli's equation to see if your reasoning is valid?

 

[j3dwards]

Is the pressure at A higher because it's uphill? What's the pressure at B relative to the pressure at A? Did you apply Bernoulli's equation to see if your reasoning is valid?

P_A + ρgy_A + 0.5ρv_A² = P_B + ρgy_B + 0.5ρv_B²

So y_A > y_B and I think the velocities are the same? So does that make the pressure higher at B?

 

[billy_joule]

correct on both counts.

 

[j3dwards]

If the water were not flowing what would your answer be?
Are you familiar with Pascals law?

P_B = P_A + ρgh

Again making pressure higher B than A!

 

[j3dwards]

correct on both counts.

But what about C? Is the pressure at C the same as the pressure at B?

 

[billy_joule]

No, not the same, apply Bernoulli's equation again.