Why does increasing the height of a water tower increase water pressure?

[Sphere]

Hello, I was wondering, for a fixed amount of water, why when the height of a water tower increases, the water pressure at the outlet of the pipe at the base of the tower increases ?

I have often read on the internet that it would be caused by the weight of the water above the water at the base of the tower but I doubt this explanation is good.

Example: If we have two identical water towers, with the same amount of water inside, but tower A is 5 meters high, and tower B is 10 meters high, the one that will have the most great water pressure at its base will be that at 10 meters high (tower B) yet the water at their base has the same amount of water above it, so the same weight, so the pressure at the base should be the same for both towers if I followed the explanation I saw on the internet.

Thank you!

 

[Lnewqban]

As pressure depends on area, the important thing is the number of molecules of fluid directly above the unit area at the point of measurement, rather than the volume.

W = mg

W = ρVg

V = Ah

W =ρAhg

As p=FA, then

p=ρAhgA

p = ρhg

 

[jack action]

You have to look at the height of the column of water over a given area to find the pressure:

​

It is also the same thing for air:

Once at the bottom of that column, you may imagine having a small cube of water. The pressure on every side of that cube must be the same. Thus, the cube of water next to it must also be the same, even if there is not as much water above it.

So if you have an elbow in your pipe, the pressure is preserved in the horizontal portion of the pipe.

If you have another elbow with another pipe going down, at the bottom of that pipe you will have the weight of the water in that new column of water PLUS the added pressure on top of it. The total pressure will be the one provided by an equivalent column of water of the total height of the columns.

 

[Baluncore]

https://en.wikipedia.org/wiki/Vertical_pressure_variation#Hydrostatic_paradox
https://en.wikipedia.org/wiki/Hydrostatics#Hydrostatic_pressure

 

[sophiecentaur]

As pressure depends on area,

Pressure is independent of area. Pressure is defined as Force per Unit Area. (You've got to be fussy about the terminology and formulae)

You have to look at the height of the column of water over a given area to find the pressure:

Using a vertical column to demonstrate hydrostatic pressure, could be misleading because you don't need a vertical column. The hydrostatic pressure depends on the difference in height and not the length of the column - i.e. a longer column at an angle can have the reduced height difference if it is tilted.
Here's a helpful video.

 

[Sphere]

Thank you everyone!

If I understood correctly, what determines the water outlet pressure of a water tower is only the water that has above the base of the pipe (which descends to the bottom of the tower) , so the water in the tank at the very top that is not directly above the base of the pipe (the water that is on the side of the tank) is not contributing to the increased pressure?

 

[Baluncore]

The pressure is proportional to the vertical distance, (measured parallel to gravity), between the surface and the point of measurement.

The path taken by the pipe is NOT important.
The cross-section of the pipe is NOT important.

 

[jack action]

so the water in the tank at the very top that is not directly above the base of the pipe (the water that is on the side of the tank)

I'm not sure what you mean by that but it sounds wrong. See the following video to see if it's what you understand (especially the part about the aquarium):

​

 

[Sphere]

I quickly made a drawing to illustrate my previous message, it will surely be clearer:

If I understand correctly, in a water tower, the water pressure in zone A will only be affected by the water in zone D. The water in zones B and C will not affect the water pressure in zone A.

 

[Lnewqban]

...
If I understand correctly, in a water tower, the water pressure in zone A will only be affected by the water in zone D. The water in zones B and C will not affect the water pressure in zone A.

Please, see:
https://en.wikipedia.org/wiki/Communicating_vessels

https://en.wikipedia.org/wiki/Vertical_pressure_variation#Hydrostatic_pressure

 

[sophiecentaur]

Thank you everyone!

If I understood correctly, what determines the water outlet pressure of a water tower is only the water that has above the base of the pipe (which descends to the bottom of the tower) , so the water in the tank at the very top that is not directly above the base of the pipe (the water that is on the side of the tank) is not contributing to the increased pressure?

Sorry but you have got totally the wrong message from a large number of posts above. I wonder if you actually read that link I posted above. It has good descriptions and good diagrams. Hydrostatic pressure is transmitted in all directions. How would household plumbing work if things went the way you describe? Nothing would flow from the tank in the roof to a tap that's not vertically below it

 

[Sphere]

Sorry but you have got totally the wrong message from a large number of posts above. I wonder if you actually read that link I posted above. It has good descriptions and good diagrams. Hydrostatic pressure is transmitted in all directions. How would household plumbing work if things went the way you describe? Nothing would flow from the tank in the roof to a tap that's not vertically below it

I read the link you sent me and I think I understood.

The drawing and explanation I did in my previous post shows the same thing that is explained in your link but less well.

There is even an image that shows the same thing as my drawing but much better:

 

[sophiecentaur]

I read the link you sent me and I think I understood.

The drawing and explanation I did in my previous post shows the same thing that is explained in your link but less well.

There is even an image that shows the same thing as my drawing but much better:View attachment 314681

. . . . .except that the green column doesn't have to be there, to produce the same pressure. A single (thin) diagonal pipe would have the same pressure beneath.

If I understand correctly, in a water tower, the water pressure in zone A will only be affected by the water in zone D.

The two zones B and C have the same pressures at any height in the tank. You could remove B and the upper part of D and the zone C would still contribute the same amount of pressure to the pressure right at the bottom. That vertical column section is no more relevant than any other; It's just a virtual aid to deriving the equation in anybody of water.

Hydrostatic pressure in any small region of the water acts in all directions - against the side or against the neighbouring volume of water. If that were not true then water would flow and establish equilibrium. Note the word "Equivalent" in green column in the diagram.

 

[DaveC426913]

Along with all these excellent answers, consider this:

Take the water tower scenario and reverse it in time. Now you're pushing water up a tall pipe. Imagine doing this by hand. Would you rather push water up a 10 foot pipe? Or a 100 foot pipe? Which one would tire you out more?

 

[Sphere]

So if I summarize, as shown by the formula, pressure only depends on height (difference in height),the volumic mass of the liquid and gravitational acceleration.

The angle of a pipe and the total mass of liquid in a system (water tower, aquarium, etc.) do not change the pressure at the base of the system.

 

[DaveC426913]

So if I summarize, as shown by the formula, pressure only depends on height (difference in height),the volumic mass of the liquid and gravitational acceleration. The angle of a pipe and the total mass of liquid in a system (water tower, aquarium, etc.) do not change the pressure at the base of the system.

Right. Which is why, for example, giant reef aquariums can be unlimited in length and width - the thickness of the plexiglass walls depends only on the depth at the wall.

In fact, an entire ocean can be held back by a similar plexiglass wall, if it's only score feet deep at that point.

 

[sophiecentaur]

,the volumic mass of the liquid

The accepted term is 'density'.