Why Does the Shape of a Container Not Affect Fluid Pressure Calculations?

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Discussion Overview

The discussion centers around the principles of fluid pressure calculations in static fluids, particularly questioning why the shape of a container does not influence these calculations. Participants explore the implications of curved surfaces in fluid mechanics, the nature of forces acting on fluids, and the application of fundamental laws such as Pascal's Law and Newton's laws.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the omission of forces exerted by the curved surface area of a container in fluid pressure calculations, suggesting that these forces do not cancel out and should be considered.
  • Another participant emphasizes that fluid mechanics does not focus on single points, indicating that the force exerted by the fluid acts along the entire curved surface area of the container.
  • A different viewpoint suggests that flat and curved surfaces can be analyzed using the same differential force balance approach, treating the container as a rigid body.
  • One participant clarifies that the pressure in a fluid acts perpendicular to any solid surface, and that this principle allows for macroscopic force balances that account for various surface orientations.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of curved surfaces in pressure calculations, indicating that the discussion remains unresolved with multiple competing perspectives on the topic.

Contextual Notes

Some assumptions regarding the nature of forces in fluid mechanics and the applicability of certain laws may not be fully articulated, leading to potential gaps in understanding the implications of different surface shapes.

ajaysabarish
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for static fluids we have studied that p=patm +density*g*depth.
and this equation is derived from Newton's laws,but in fbd why didn't we consider the force exerted by curved surface area of container,it doesn't cancel out when containers are in frustrum shape.and the vertical components add up.
please help
 
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How can we describe the force by liquid to one specific point?
This is not single point mechanics.
 
I'm not sure I follow the question. Could you provide a diagram, perhaps?

Also, @theodoros.mihos, the bulk of fluid mechanics is predicated on the idea of a continuum do picking out a single point does work in that sense.
 
theodoros.mihos said:
How can we describe the force by liquid to one specific point?
This is not single point mechanics.
thank you for replying sir,
the force exerted by a container on the fluid does not act at one point but it acts all along the curved surface area.
just like the force exerted by the bottom of the fluid,curved surface area also exerts a force,how can this be neglected?
 
Flat and curved surfaces can calculated by the same way as ## \delta{F} = p\,\delta{A} ## with ##\delta{A}\to0##.
This is distributed load force and container is rigid body.
 
Your equation originates from differential force balance on any arbitrary fluid parcel (using a fbd on the parcel), not necessarily at any solid surface:

$$\frac{\partial p}{\partial z}=-ρg$$
$$\frac{\partial p}{\partial x}=\frac{\partial p}{\partial y}=0$$

At any solid surface, the pressure of the fluid always acts in the direction perpendicular to the surface (Pascal's Law), irrespective of the orientation of the surface. From Newton's 3rd law, the surface pushes back on the fluid with an equal but opposite force. This allows you to do macroscopic force balances on the fluid that include the effects of solid surfaces that are not horizontal.

Chet
 

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