Why does water pressure only depend on the height of the water column?

532 views

[ad_1]

And not on the amount/weight of the water in let’s say a conical container?

In: Physics
[ad_2]

Pressure is Force × Area.

Assuming I keep the **area** over which I measure the Pressure as a **constant**, Pressure will only depend on the Force.

Now, the question arises, what Force? The force we are talking about is the Force of Gravity. We know that Gravity only occurs in one direction, downwards.

Therefore, only water molecules **directly above** the area we want to measure needs to be counted.

To count the **mass** of the water above the area, all we need to do is multiply the density of water with the volume of water.

Volume is Height × Bottom Area

As the area of the measured surface is constant, volume only depends on the height.

TL;DR ::: Assuming area being measured is constant, only the mass above that area exerts its weight and is counted for pressure.

By definition, pressure is force per unit area. The weight/ mass are the major contributors to pressure on an area but you have to see what area it is contributing on. Let’s take your conical tank as an example. Which is shaped like a funnel with the smaller cross section on the bottom. At the exit area, the pressure the water will be carrying will be weight of the water above that area divided by the area of the cross section. Since the weight of water is directly dependant on the area and you’re dividing it with the area you’re left with just height of the column in the equation with other constants.

The weight of water in the conical section of the water vertically downwards is supported by the conical tank upwards since it exerts pressure on tank walls as well. Hence the only weight you’re left with is the weight of the water directly above the area you’re considering. And that’ll be a cylinder.

Get a 2×4 and lay it flat in the ground. Now stick your hand under one end. Then have someone lift the other end so it’s standing up on your hand. You’ll feel the pressure change even though it’s the same amount of wood. That’s because gravity is now pulling all the wood onto your hand, when it wasn’t before. Same with water, it’s like a bunch of 2x4s stacked up.