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

[ajaysabarish]

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

 

[theodoros.mihos]

How can we describe the force by liquid to one specific point?
This is not single point mechanics.

 

[boneh3ad]

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.

 

[ajaysabarish]

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?

 

[theodoros.mihos]

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.

 

[Chestermiller]

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