# Pressure in Liquid: Why Height Doesn't Matter

In summary: I think you are misunderstanding the concept of pressure in liquids. The statement that "pressure is transmitted in liquid equally" means that the pressure at a given depth is the same in all directions. This is known as Pascal's principle and is often demonstrated with a hydraulic press. The pressure in a liquid does increase with height, but this is only in the vertical direction. In the case of your ball filled with water, the pressure at the bottom of the ball will be greater than the pressure at the top due to the hydrostatic pressure from the weight of the water above it. However, the pressure at the bottom will still be the same in all directions. Think of it like this: if you could cut a tiny hole in the side of the
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 ?

What makes you think that these statements are in conflict?

Chestermiller said:
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?

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.

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.

nasu said:
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

## What is pressure in liquid?

Pressure in liquid is the force per unit area that is exerted by a liquid on its container or on an object immersed in it.

## Why does pressure increase with depth in a liquid?

Pressure increases with depth in a liquid because the weight of the liquid above the point of measurement increases as depth increases. This results in a greater force being exerted on a unit area, leading to an increase in pressure.

## Why does height not affect pressure in a liquid?

Height does not affect pressure in a liquid because pressure is dependent on the depth and density of the liquid, not the height. This means that the pressure will remain the same regardless of the height of the liquid.

## What is the relationship between pressure and density in a liquid?

The relationship between pressure and density in a liquid is inverse. This means that as density increases, pressure decreases and vice versa. This is because denser liquids have more particles in a given volume, resulting in a greater force being exerted on a unit area, leading to a higher pressure.

## How is pressure in a liquid affected by temperature?

Temperature has a minimal effect on pressure in a liquid. This is because liquids are relatively incompressible and their density does not change significantly with temperature. Therefore, the pressure in a liquid remains relatively constant regardless of temperature changes.

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