Validity of hydrostatic pressure equation

[pgirl1729]

The hydrostatic pressure equation, P=hρg is derived from P=F/A where F=mg and A=cross sectional area of the water column. As weight only acts downwards and it's force is only exerted in downward direction. Then why does pressure acts in all directions? How is the P=hρg still valid?

 

[jbriggs444]

The hydrostatic pressure equation, P=hρg is derived from P=F/A where F=mg and A=cross sectional area of the water column. As weight only acts downwards and it's force is only exerted in downward direction. Then why does pressure acts in all directions? How is the P=hρg still valid?

A short and not very revealing answer is that fluids are fluid. At equilibrium, they cannot sustain a shear stress. [Stress is a generalization of pressure that one may eventually learn about]

Perhaps more appealing is to think about a water balloon. If you press down on its top, it expands out the sides. Your top pressure has become a side pressure.

Or consider a vertical pipe connected by an elbow to a horizontal pipe. Seal the horizontal pipe at its free end. Fill the pipes with water and apply pressure at the top. Would you agree that the longitudinal pressure in both pipe segments should be the same? Remove the pipes and replace them with a bath of water. Maintain the pressure on the top of the bath. Would you expect the pressure anywhere to change?

 

[A.T.]

As weight only acts downwards and it's force is only exerted in downward direction. Then why does pressure acts in all directions?

The weight of the balls in the below image is also only exerted in downward direction, and yet they will push sideways against the walls. You don't need complex fluid dynamics to understand the basic principle qualitatively.

 

[Pisica]

Then why does pressure acts in all directions? How is the P=hρg still valid?

The pressure on which the water column fron the left is "pressed" is equal to the pressure with which it is fron the right and they cancel each other out.

 

[jbriggs444]

The pressure on which the water column fron the left is "pressed" is equal to the pressure with which it is fron the right and they cancel each other out.

Yes. This is a correct observation. If we imagine a small parcel of water (perhaps a cube), the force from the left will match the force from the right. So there is no net force in that direction. The parcel remains at rest, not accelerating.

This must be the case if the fluid is in an equilibrium state.

This is the sense in which the left and right pressures "cancel out". It is not that there is no pressure. It is that there is no acceleration of the fluid parcel.

 

[Lnewqban]

... As weight only acts downwards and it's force is only exerted in downward direction.

Not within liquids.

Please, see:
https://en.wikipedia.org/wiki/Pascal's_law

https://byjus.com/physics/pascals-law-and-its-application/

https://en.wikipedia.org/wiki/Torricelli's_law

https://byjus.com/physics/torricellis-law/