# Calculating a Submerged Tank: Questions & Answers

• Gunter1977
In summary, Gunter attempted to calculate the stress and strain on a tank submerged in water using an approach based on beam theory, but found that the results were not accurate. He recommends using a more accurate method, such as applying the stress and strain to a plate that is supported on three edges.
Gunter1977
Dear People

I am busy with a tank that is submerged in water. The tank is mounted against concrete wall isolating the water. The tank is pressed against the wall due to the water pressure. When the tank is installed the water can be pumped away.

The material used for the tank is stainless steel. The pressure acting on the tank wall I used the statics pressure part of Bernoulli equation. Knowing the pressure is also known the distributed force over the tank wall. I assumed that the plate can be approached as a small beam.

• Loadcase1: is based over the length of the tank in the lower section of the wall (where the load is at its highest point, disturbed load rectangular)
• Loadcase2: Is based on the height of the tank. ( due to Bernoulli a Triangular load.).

I calculated the reaction force in both cases and also the maximum bending moment in the plate. I used the maximum bending moment to determine my dimension of my profile to support the tank.

My question is am I allowed to calculate the tank like this and if I am not allowed to use this method what method should I use to calculate a case like this? I am allowed to approached sheet metal as a small beam?

I added my calculation and drawing in the attachment.

Gunter.

#### Attachments

• Bak55xx.pdf
231 KB · Views: 346
• calculation2.pdf
558.9 KB · Views: 356
This is all pretty fuzzy because you have not provided the proper free body diagrams (FBDs). Even so, I see a few comments that can be made, in somewhat random order:
1. It is not at all clear where your P1 = 0.196 bar comes from.
2. You do not make clear what the direction of increasing y is in your figure. It appears that you intend to take this downward, but that is not entirely obvious.
3. You say Fwall = 49.033 k, but what is k? What units do you attach to this value?
4. I completely fail to see the relevance of the second calc, the simply supported beam with a triangular load. In your original problem statement, where do you see anything that looks like simple supports?
5. You also ask in the discussion if you are allowed to approach sheet metal as a small beam. Why would you expect that to be true? You have wide sheet metal expanses, much wider than the beam depth, so at the very least, this would require a plate bending analysis.
6. You don't say what this is for, or really what you need to determine. Please try again, at least with a statement of what you want to find.

Good day,

My calculation for Fwall:

Fwall = 0.5x(1000x9.81x2)x(2x2.5) basically the area of a pressurexheight graph multiplied by = 49.05 kN (corresponds with your calc) the width of the tank

Now you make an assumption that the plate structure is a beam. You are looking at a 1 meter strips of the plate and then treating them as if they are beams with simple supports. I'm no expert, but I don't think this will give you good results . I think you will be better off applying the 49 kN force to a plate that is supported on three edges. In other words, I think you are beyond beam theory and you are in plate theory terrain. I'm assuming that the tank will be bolted rigidly to the concrete along it's length and width to avoid leakage.

I agree with the fact that you want to put beams across the back to reinforce the structure. It makes perfect sense. Whether it is better to put one massive beam or a few smaller ones is something you will have to consider. A few smaller ones might be better.

Also, a 6mm stainless steel plate will weigh quite a bit, you might want to factor in self weight and you might want to look up codes of practice. They might steer you in the right direction.

I have only skimmed your calculations but the idea of flat plates being treated as beams is definitely not viable. You need to reference "Roark's Formulas for Stress and Strain", Flat Rectangular Plates section and an appropriate case no. for your situation for your distributed pressure plate loading stresses.
I also have not reviewed the dimensions of your tank or depth of water; but, if the tank is of any substantial size then the following procedures, at a minimum, will probably be required for designing your tank structure.
For back plate your are probably going to require a series of beam supports across the the face of the plate and the number of those will be determined by the maximum unsupported area of your plates.
With that you will then need to calculate the size of the required beams to resist the bending force of their respective plate areas and then the perimeter frame supporting those beams. Additionally the back plate horizontal perimeter horizontal frame members will be subjected to a compression loading from the tank's side plate pressure loads.
The same will be true of the side and bottom plates except their top and bottom perimeter frames must not only resist their plates pressure loading; but also their compression loading from the back plate pressure load as well. Additionally the side plate perimeter frames will be subjected to a shearing load from the bottom pressure trying to lift the complete structure; and; as a result, those side structures will most likely require diagonal beams to stiffen the sides from parallelogram type distortion and stress from that same lifting force.
Of course, finally you will need to determine how you are going to attach the tank to the dam with sufficient shear resistant connections to resist the lifting force on the tank.

## 1. How do you calculate the volume of a submerged tank?

To calculate the volume of a submerged tank, you will need to know the dimensions of the tank (length, width, and height) and the depth of the water. The formula for calculating the volume is length x width x height x (1- depth/height).

## 2. Why do you need to subtract the depth from the height in the volume calculation?

In order to accurately calculate the volume of a submerged tank, you need to take into account the space that is already occupied by the water. By subtracting the depth from the height, you are accounting for this space and getting an accurate measurement of the remaining volume.

## 3. How can you calculate the weight of the water in a submerged tank?

To calculate the weight of the water in a submerged tank, you will need to know the density of water (which is approximately 1000 kg/m³) and the volume of the water. The formula for calculating weight is density x volume.

## 4. Is it necessary to know the density of the liquid in the tank for calculating the weight?

Yes, the density of the liquid is an important factor in calculating the weight of the water in a submerged tank. Different liquids have different densities, so it is important to have this information for an accurate calculation.

## 5. Can this calculation be used for any shape of tank?

Yes, the formula for calculating the volume of a submerged tank can be used for any shape of tank as long as you have the necessary dimensions and depth information. However, it is important to note that the formula assumes the tank is a perfect rectangular prism, so the calculation may not be 100% accurate for irregularly shaped tanks.

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