# Given a wall on planet earth with a constant height is there a point at which a physicist needs to worry about the volume of water behind the wall?

I have a quick question, on the media outlet "Sploid" a post recently came out about this interesting flood wall in Austria that keeps water from destroying a community. The wall seems to contain a massive amount of water but the wall itself looks pretty flimsy.

I was wondering if there is a point at which a physicist or engineer, when designing a dam or flood barrier, has to take into account the volume of the water behind the wall.

One of the commenters to the sploid post said:

Because the force on the wall does not depend on the quantity of water behind it but only on the height of the water. The pressure on the wall has a linear distribution.If we consider a piece of wall of unitary length ( 3m of height by 1m of lenght) the pressure goes from 0 kPa (on the top) to 29.4 kPa on the bottom . The critical point would be the base with a bending moment of 44.1 kNm. If the beams are made of steel, which has a breaking tension of 450 N/mm^2, an I-shaped beam with dimension of 16x7.4 cm would be more than enough to hold that water in place. If my calculations are correct they would need to have a wall made of 16x7.4cm beams placed 1 meter apart. This is valid for static water. Dymanics introduce inertia forces but the concept is the same.

His answer is what got me started wondering about this in the first place. If you understand his calculations and agree with them can you explain why they are correct?

Thanks!

• Damn walls are counter-intuitive. It doesn't matter how much water is behind them, only how tall they are. All that matters is the pressure of the water and the pressure depends on depth only and not on volume. You could hold an ocean back with the same wall used to hold a lake, as long as they're the same depth at the point where you stick the wall. – Brandon Enright Jan 5 '15 at 22:31
• I think what you're stumbling over is that it seems like it must take a larger force to constrain a larger body of water. And it does! But most of that force is supplied by the floor and other sides of the body of water. Increasing the lateral size of the body of water increases the total force that must be supplied by the ground, but the area of the ground increases at just the same rate, so the pressure (force/area) stays constant. The only way to increase pressure is to increase the depth of the water. – user27118 Jan 5 '15 at 22:51
• So lets say for example you measured the pressure in the corner space right where the wall meets the ground. You would find the pressure on the side of the wall to be equal to the pressure at the floor? – user66104 Jan 5 '15 at 23:20
• I can't seem to find it now, but I recall a company makes temporary (ie. deployable) walls to build dams for flood events. The wall is L shaped with the water against the long edge and the short edge is actually under water. No bracing is needed to keep the wall from sliding outwards because the weight of the water on the submerged part is enough to offset the outward pressure. – tpg2114 Jan 5 '15 at 23:53