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

AI Thread Summary
The discussion centers on the principles of fluid pressure calculations, emphasizing that the shape of a container does not influence the pressure at a given depth, which is determined by the equation p = patm + density * g * depth. Participants clarify that the force exerted by the container's curved surface acts along its entire area, not just at a single point, and that this force can be analyzed using differential force balance. The conversation highlights that pressure acts perpendicularly to surfaces, in accordance with Pascal's Law, and that this allows for macroscopic force balances that account for various surface orientations. The conversation underscores the importance of understanding fluid mechanics as a continuum rather than focusing solely on individual points. Overall, the principles of fluid pressure remain consistent regardless of container shape, as derived from fundamental laws of physics.
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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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