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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?

Physics Asked by user66104 on October 5, 2021

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 16×7.4 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 16×7.4cm 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!

3 Answers

A similar issue is present for tap pressure when fitting bathrooms http://www.mbd-bathrooms.co.uk/Information/Understanding_Water_Pressures_and_Bar_Ratings.php note the diameter of the pipe (volume of water) is not a relevant factor for calculating pressure

Answered by Daz Hawley on October 5, 2021

The force against the wall is not a function of the dimension of pool perpendicular to dam. The reason has nothing to do with hydrostatic pressure because force exerted by water is not a function hydrostatic pressure (I know the texts state it is) but the force is a function of the mass of water. this is very easy to prove. Based in this principle, the dimension perpendicular to the wall is irrelevant.

Answered by john on October 5, 2021

No, the physicist or engineer never needs to take into account the volume of water. Only the height of the water. For the flood wall you have cited in Austria, the point being made is that the strongest area of the wall has been constructed at the base where the pressure is the greatest. We typically think of a damn or containment wall as being uniform thickness and strength throughout. But this does not need to be the case. The top of the barrier can actually be flimsy (as you have described) as long as the strength of the wall increases as you move toward the base.

Answered by JRL on October 5, 2021

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