Fluid pressure in a U-shaped tube

[osker246]

This really isn't a homework question, I just need help understanding some concepts. For my physics course, we have a section called "tutorial" where we work out of a book answering questions. Now I am not quite sure how to answer this one. Refer to the image below for the questions.

"The right end of the tube is now sealed with a stopper. The water levels on both sides remain the same, and there is no air between the stopper and water surface."

1. Do the pressures at points A and D increase, decrease, or remain the same? explain.

2. Is the pressure at point E greater than, less than, or equal to the pressure at point D? Does Delta P_DE, the difference in pressure between points D and E, change when the stopper is added?

3. Is the pressure at point F greater than, less than, or equal to atmospheric pressure? Is the force exerted by the stoppe on the water surface on the right greater than, less than, or equal to the force exerted by the atmosphere on the water surface on the left?


Now I understand the pressure in a liquid follows a linear relationship with depth (P=P₀ +rho*g*h), so point D would have a greater pressure than A if both ends were open. But how exactly does the addition of the cap affect the pressure? I want to say there is no change in pressure, but I can't explain why. If I can get a little help answering the first bit I may be able to work through this. Thanks.

 

[member 553083]

1. The pressures at both point A and D remain the same when the stopper is added. This is because the pressure in a liquid is equal in all directions, so when the stopper is added the pressure does not change. 2. The pressure at point E is equal to the pressure at point D, and Delta PDE does not change when the stopper is added. This is because the pressure in a liquid is equal in all directions, so when the stopper is added the pressure does not change. 3. The pressure at point F is equal to atmospheric pressure. The force exerted by the stopper on the water surface on the right is equal to the force exerted by the atmosphere on the water surface on the left. This is because the pressure in a liquid is equal in all directions, so when the stopper is added the pressure does not change.