Liquid Lateral Force

[handex]

Hey guys,
Purely academic question of interest here. If we have a pure liquid retained in a vertical form (neglecting arching and wall friction etc), does the thickness of retained liquid place any limit on the maximum pressure? For example say I have 1m x 1m form that is retaining a 10mm slither of water. This has a vertical force of 0.1kN so can it still generate the lateral pressure of 5kN? Extrapolating this further, can a 1mm (0.01kN vertical) slither of water generate this 5kN force?

 

[demayeng]

what 5kN?

 

[handex]

(10kN/m3 x (1m)^2 / 2 ) x 1m wide = 5kN

 

[hokie66]

You are all mixed up. kN is not pressure, it is a unit of force. One meter depth of water exerts 10 kPa in all directions, so 10 mm exerts 0.1 kPa in all directions.

 

[handex]

hokie,

Im not mixed up I think I worded it wrong. I was talking about a vertical form of dimensions 1m x 1m with a varied width of liquid being retained (so the height of retained liquid is always 1m). When I said a lateral pressure of 5kN I meant a lateral force coming from gamma x depth ^2 / 2.

My question is can a vertical force of .01kN really produce a 5kN lateral force or is there some kind of theoretical threshold?

 

[hokie66]

I don't know how you got 5kN, but the basic principle is that the pressure in a liquid is the same in all directions. Then the force exerted is the product of that pressure and the area to which it is applied. Of course, your force on the vertical wall will be due to a varying pressure.

 

[handex]

????

height of wall = 1m
width of wall = 1m
density of water = 10kN/m3

therefore pressure at bottom of wall = 10kPa

since wall is 1m wide (probably should have said long in original post), force at top = 0kN/m and force at base = 10kN/m

therefore horizontal load = 10 x 1m /2 = 5kN based on a triangular distribution

 

[IDS]

The answer to the question is, if you are ignoring surface tension effects, yes, in practice no, because the surface tension will have a significant effect.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[nutte]

Hokie, isn't kilobewton a unit of kiloforce?... Oh nevermind...

 

[nutte]

Hmm, kilobewton... That ought to clear things up.

 

[DRC1]

This is how the effect of water in clay tension cracks is modeled. In reality, as IDS said there is surface tension which allows the soil to distribute some of this load.

 

[csd72]

There is no relation between the vertical and horizontal forces, the correlation is between the vertical and horizontal stresses.

The 5kN has no relation to the vertical force as it acts horizontally in both directions cancelling each other out. This is why you were taught vectors at university.

Believe me, a water pipe for a 100m tall bulding does have 100m of water pressure in its base.

Agree that surface tension would probably reduce this amount.

 

[hokie66]

handex,
I obviously misunderstood your question, with good reason, I think. I thought your form was 1 metre square in plan, and you had a bit of water in the bottom. I see now that you are talking about a small horizontal dimension of water. I agree that surface tension will have an effect, but don't know how much.

 

[MiketheEngineer]

Imagine a simple pipe whatever depth(height).

IT DOES NOT MATTER THE DIAMETER. All forces dependent on depth - as expected - neglecting surface tension.