Hydrostatics - force on pistons in fluid

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SUMMARY

The discussion centers on calculating the increment in pressure at the center of a cubical container filled with liquid when an additional force F is applied to pistons covering holes on its lateral faces. The solution confirms that the increment in pressure is directly proportional to the applied force, expressed as F/A, where A is the cross-sectional area of the pistons. This relationship is derived from the principles of hydrostatics, specifically the equilibrium of forces acting on the fluid within the container.

PREREQUISITES
  • Understanding of hydrostatic pressure principles
  • Knowledge of force and pressure relationship (P = F/A)
  • Familiarity with fluid mechanics concepts
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the principles of Pascal's Law in fluid mechanics
  • Learn about hydrostatic pressure calculations in different geometries
  • Explore applications of fluid dynamics in engineering
  • Investigate the effects of varying cross-sectional areas on pressure distribution
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Students studying fluid mechanics, engineers working with hydraulic systems, and anyone interested in the practical applications of hydrostatics in real-world scenarios.

Mandeep Deka
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Homework Statement


Assume a cubical container with liquid filled in it and with one hole in each side in its four lateral faces with same cross-sectional area A. Now there are pistons covering these holes which keep the fluid inside it in equilibrium. If there is an increment of force F on each piston, what is the increment in the pressure at the center of the container?


Homework Equations





The Attempt at a Solution



I am not getting any way to get out with this problem, the answer is F/A but i am not able to figure out anything that i can really use to find the answer.
Please provide some clue, as to how do i get out of it!
 
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Hi Mandeep! :smile:

Look at it the other way round …

how much would you have to increase the pressure inside the cylinder to make each piston exert an extra force F on something outside? :wink:
 


Thanks a lot...
I got it. If there is an increase of pressure of magnitude F/A in the center of the liquid, an equal pressure F/A will be exerted in all the directions which will balance the increase in the pressure in the pistons!
 

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