Does Hydrostatic Pressure Follow the Same Rules for All Shapes of Containers?

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Discussion Overview

The discussion revolves around the principles of hydrostatic pressure in different shapes of containers, specifically comparing cylindrical and hourglass-shaped beakers. Participants explore the implications of these shapes on pressure calculations and scale readings, focusing on theoretical and conceptual aspects of hydrostatic pressure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that hydrostatic pressure is given by the formula pgh, applicable regardless of container shape, and provides calculations for both cylindrical and hourglass beakers.
  • Another participant challenges the measurement methods used, suggesting that the approach to calculating pressure and weight may be incorrect.
  • A participant reiterates the pressure formula and agrees with the initial assertion but emphasizes that the scale measures the weight of the beaker and water, noting that the pressure-area product only equals the weight under specific conditions (vertical walls).
  • It is pointed out that the pressure-area calculation for the hourglass does not account for the net force exerted by the water on the entire surface of the beaker.
  • A participant acknowledges a misunderstanding regarding the vertical components of pressure on the sides of the hourglass, indicating a refinement of their earlier logic.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the pressure calculations for different container shapes, with some agreeing on the hydrostatic pressure formula while others contest the measurement methods and implications of the results. The discussion remains unresolved regarding the correct interpretation of pressure in non-vertical containers.

Contextual Notes

Participants highlight the importance of considering vertical pressure components and the net forces acting on the beaker, indicating that assumptions about container shape and pressure distribution may affect calculations.

brett351
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My understanding is that the pressure below the surface of water is pgh.

p - density of water, g - accel of gravity, h - dist below surface

And that this relationship holds regardless of the shape of the container of water. (also, I'm neglecting the atmospheric pressure at the surface)

If I have a cylindrical beaker of water of height H and area A and put it on a scale, I can calc the reading of the scale two ways...

1) pressure at bottom times area is pgHA.

2) density times volume times g is also pgHA.

Both ways give the same reading. Now if the shape of the beaker is an hourglass which has an area at top and bottom of A (same as top and bottom of cylindrical beaker), the two ways don't yield the same result.

Method 1) yields the same result for both shapes but method 2) yields a smaller result for the hourglass. What wrong with my logic? Thanks, Brett.
 
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I don't understand how you are measuring things. The two pressures are equal, but your method for measuring them is wrong.
 
brett351 said:
My understanding is that the pressure below the surface of water is pgh.

p - density of water, g - accel of gravity, h - dist below surface

And that this relationship holds regardless of the shape of the container of water. (also, I'm neglecting the atmospheric pressure at the surface)
OK.

If I have a cylindrical beaker of water of height H and area A and put it on a scale, I can calc the reading of the scale two ways...

1) pressure at bottom times area is pgHA.

2) density times volume times g is also pgHA.
The scale just measures the weight of the beaker of water. Method 1 gives the water pressure*area on the inside bottom of the beaker--this only equals the weight in the special case where the walls are vertical.

Both ways give the same reading. Now if the shape of the beaker is an hourglass which has an area at top and bottom of A (same as top and bottom of cylindrical beaker), the two ways don't yield the same result.
Because the pressure*area on the bottom of the hourglass beaker does not equal the net force on the beaker due to the water. The water also pushes up on other areas of the beaker surface. If you added up the net force that the water exerts on the entire beaker, that would equal the weight of the water.
 
Thanks Doc Al. Now I see that I forgot to take into account the vertical components of the pressures on the side of the hourglass, Brett.
 

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