Fluid pressure in a U-shaped tube

In summary, the addition of a stopper in a tube filled with water does not affect the pressure at any point or the difference in pressure between points D and E. The pressure in a liquid is equal in all directions and remains the same even with the addition of the stopper.
  • #1
osker246
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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.

IMG_20101212_113834.jpg


"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 PDE, 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.
 
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  • #2
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.
 

Related to Fluid pressure in a U-shaped tube

1. What is fluid pressure in a U-shaped tube?

Fluid pressure in a U-shaped tube is a measure of the force exerted by a fluid on the walls of the tube. It is caused by the weight of the fluid above and the force exerted by the fluid molecules on each other.

2. How is fluid pressure calculated in a U-shaped tube?

Fluid pressure in a U-shaped tube is calculated using the equation P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height difference between the two arms of the tube.

3. What factors affect fluid pressure in a U-shaped tube?

The factors that affect fluid pressure in a U-shaped tube include the density of the fluid, the height difference between the two arms of the tube, and the acceleration due to gravity. The shape and diameter of the tube can also have an impact on the fluid pressure.

4. How does fluid pressure change as the height of the tube increases?

As the height of the tube increases, the fluid pressure also increases. This is because there is more fluid above, which exerts a greater force on the walls of the tube. The increase in pressure is directly proportional to the height difference between the two arms of the U-shaped tube.

5. What is the practical application of understanding fluid pressure in a U-shaped tube?

Understanding fluid pressure in a U-shaped tube is important in many industries, such as hydraulic engineering and fluid mechanics. It is also used in medical devices, such as blood pressure cuffs, to measure the pressure of fluids in the body. Additionally, it is essential in understanding the movement of fluids in natural systems, such as oceans and rivers.

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