Pressure in Liquid: Why Height Doesn't Matter

[PrakashPrasad]

I am reading pressure in liquids and at one point it states that

Pressure of liquid at any point = Depth x Density of Liquid x g (gravity)

But then it continues to state that

Pressure is transmitted in liquid equally

when I studied earlier that pressure in liquid increases with height then how come the other statement is correct - I mean why here height does not matter ?

 

[Chestermiller]

What makes you think that these statements are in conflict?

 

[PrakashPrasad]

What makes you think that these statements are in conflict?

As per the experiment if I have a ball filled with water and make holes in it in many places - now pressure exerted by water on the walls of the ball is same across the surface of the ball - now this is what confusing me - let us say that the height / depth of ball is h. So the pressure exerted at the hole in the bottom of the ball should be more than the hole at its top.

But what would happen if we squeeze the ball filled with water and having holes across?

I may be missing something please correct my understanding?

 

[Chestermiller]

As per the experiment if I have a ball filled with water and make holes in it in many places - now pressure exerted by water on the walls of the ball is same across the surface of the ball - now this is what confusing me - let us say that the height / depth of ball is h. So the pressure exerted at the hole in the bottom of the ball should be more than the hole at its top.

You're right that the pressure exerted at the hole in the bottom of the ball is more than the hole at its top. I think your issue is with the phrase "pressure is transmitted in liquid equally (in all directions)." What this means is that, at a given depth (i.e., locally), the pressure is acting equally in all directions. This means that if you could situate a tiny element of surface area within the liquid, the force per unit area acting on that tiny element of surface area would be independent of the direction you oriented the element. So, for example, in the case of your ball, the pressure would be the same at all the holes that are located at a given depth.

 

[nasu]

The pressure that is "transmitted" usually refers to a pressure exerted from the outside, like with a piston. This is called Pascal's principle and is illustrated many times with a hydraulic press with two cylinders of different diameters.
At any point in the liquid you will have that pressure plus the hydro-static pressure, that one that depends on height.

 

[Chestermiller]

The pressure that is "transmitted" usually refers to a pressure exerted from the outside, like with a piston. This is called Pascal's principle and is illustrated many times with a hydraulic press with two cylinders of different diameters.
At any point in the liquid you will have that pressure plus the hydro-static pressure, that one that depends on height.

In my judgement (based on over 50 years of fluid mechanics experience), this is not a good way to look at it.

Chet