Weight Or Pressure On A Cylinder Wall

I'm no civil engineer, so I can't comment on the spec. of the original wall.

It is true, however, that the pressure on the walls depends only on the water depth - the tank diameter doesn't affect it (provided the water is more-or-less still, i.e. no waves etc.).

Here's a little tidbit from Wiki:

Cylinder stresses - Wikipedia, the free encyclopedia

Increasing diameter means increasing tensile force on the wall.Strength has tobe improved by adding few steel wire

The hoop stress in the tank walls is proportional to both the depth below water level and the tank's inside diameter. Thus the larger diameter tank will need thicker walls or stronger material.

There is no difference.

You're fine.

There is, you're not.

Wow - thanks for the replies however I'm still unsure.

JohnDG and Shawdog2 say I can use the same spec wall for the larger diam.

Nairck and Tornado - say I have to strengthen the wall

Lyn, thanks for the link, however I read it before I posted the question and it's a bit difficult to understand for a simple farmer

I think the summarised question is.... Does the increase in diam of a cylinder, with an increase of volume of it's liquid content, place more stress on the wall, or not. I can understand that in a cylinder, the weight of the liquid is directly proportional to the height, but what about the wall?

Is it easier to contain 10 tonnes of water or 100 tonnes of water?

Strengthen the wall.

I said the pressure is the same - I did not say that the same spec. could be used for a larger tank.

The pressure is the force per unit area. As the pressure acts over a larger area, a stronger wall will be needed.

Imagine building a dam across a canyon. I think it's pretty intuitive that a wall which will hold a given level at a narrow point of the canyon would need to be stronger if built at a wide point. Not a very good analogy, but it gives an idea.

No coffee yet, so it's way to early to start doing the sums.

I also pointed out that I'm not a civil engineer.

The pressure against (normal to) the walls does indeed vary only per the water depth...
but the stress resisted by the walls is in the circumferential direction, and it varies by both depth and diameter.

Lyn - my kneejerk reaction to your last post is YES, let me strengthen the wall as there is a huge increase in cylinder volume there has got to be an increase in pressure on the circumferential wall, so part of me wants to agree with your logic - however - many experts have told me that I could go to a 100m diam reservoir with the same wall spec - PROVIDED the wall height stays the same. I'm looking for the scientific equation that proves that an increase in diam adds no additional pressure or stress to the wall

Tornado - you are introducing a new angle to this question. IF there was no increase in water pressure against the inside of the wall in the larger diameter vessel, where would the additional stress on the wall come from. Surely wall stress is directly proportional to the pressure being applied to it by the water

Could it be that your original tank was built exceeding the required strength, thus the proposed model would be able to be built to the same specifications?

Imagine if you will a 100mm cylinder of plastic "cloth", as in a childs wading pool, 1m deep. I think you can see it would be well strong enough to hold the 1m head of water.

Now make a pool 15m diameter from the same stuff, still only a meter deep, take deep breath and poke the side with your finger!!!!!!

Get it?

I have given your answer a GA because you partially answer and refer OP to seek professional help. There remain unanswered questions as to how much fluctuation there will be of water levels in the reservoir. The water when the tank is filled will exert a different pressure when the tank is empty. I doubt this will help OP but here is a series of formulae that should be considered regarding the pressures on the wall. It is best for a professional to assist Dali with his problem and I agree.

Hi Garyvan - I have also awarded you with a GA as you have pointed out a very important fact: "if you keep the pressure and the wall thickness constant, then the stress remains the same." My reservoir will keep the wall thickness constant and the pressure will remain the same, due to the unvarying height/depth of the water level. This will be controlled with a ball valve on the inlet pipe, so that as water is drawn out the bottom pipe, the ball valve will allow new water to flow back in to the top.

What I still don't understand is how the stress increases against the inside of the wall if the diameter is increased but not the wall thickness or depth. What is the difference between stress and pressure. If the pressure against the inner wall does not increase due to the larger volume of water (due to a larger diameter reservoir), and there is no difference in depth, then how can there be more stress in the wall?

Rephrasing post 8, the pressure is sideways to the wall; the stress is along the wall; and it varies with the depth of the water and the tank diameter.

Ok Tornado - GA for that! Now I understand that the wall pressure is the force acting against the inside of the wall (trying to break the wall outwards) this does not change...as long as the depth/height remains the same, even if the reservoir diam increased to 100m.

Stress is a force that acts along or with the wall and increasing the reservoir diam will increase the volume of water and therefore wall 'stress'.

Am I correct in assuming that it's the increase in water volume that increases the wall stress. If so why... if there's no increase in pressure on the inside wall?

Is the additional wall stress not offset by the longer wall due to the bigger circumference and thereby more wall area?

The cross-sectional area of the wall (not its length x width area) is what counts.

[The whole story is more complicated. A "buttress-type" wall (like Grand Coulee Dam) can be built in a straight line, but it is very thick at the bottom. A "thin-shell" dam (like Hoover Dam) is curved, and not so thick even at the bottom.]

But the Hoover Dam, like any other curved dam I know of, has the curve in towards the body of water (exactly opposite to a watertank), so that the pressure/force _{call it whatever} puts the wall in compression (which concrete is pretty good with).

Jus' sayin'.

True, which is one reason that I bracketed the comment--in the hope of providing an analogy without delving too much into further issues. For instance, it is possible that the older tank was already overdesigned enough to equal a buttress wall. In that case, there need be no change for larger tanks of the same depth. But if the original design relied on hoop stress, increasing the diameter would result in more hoop stress, hence a thicker wall.

The force on the walls that acts to pull them apart (called hoop stress) is a function of the pressure on the wall and the area of the wall. As the tank gets larger, at the same height, it stores more water and has more wall area, even though the wall pressure profile does not change you need a stronger wall.

concrete makes poor rope, so your hoop strength comes from the rebar.

It is possible your original design was very conservative, and is OK when scaled up.

Use on of these links to calculate it. A water tank is a specials case of pressure vessel with the pressure going from zero at the top to about 3 PSI at the bottom. Since the hoop stress is the integral from 0 to 3 PSI times the total wall area divided by two it is easy to calculate. The links will show it. You need more hoop strength at the bottom than the top, which will allow you to use more of the rebar in the lower courses instead of a uniform use, which can leave the bottom weaker.

Hoop stress and water tanks

This forum has been really fun.

Being a PE, it seems only Aurizon gets it.

Concrete is never designed to have any tensile strength. It contracts while curing, causing hairline cracks.

The only tensile strength the wall has is the rebar, which is deformed in a manner to adhere to the concrete.

The pressure doesn't vary, even if it's the Pacific Ocean. (OK salt water is lighter, sorry)

Please read all prior comments.

Saltwater is denser than fresh water.

PE or not, I wouldn't let you design any pressure vessels or tanks that I might be involved with.

Ok, so after 29 replies to my original question, I have learned the following.

The pressure acting on the inside of the reservoir wall does not increase with the increase in diameter, provided the wall spec stays the same both in thickness and in height, the water level remains the same and the water is more or less still

HOWEVER

Many contributors maintain that there is a force called 'wall stress', which is applied in the same direction as the wall.

What causes this stress if there is no added pressure caused by the additional volume of water against the wall?

If the wall stress is directly proportional to the pressure being applied by the water then there can be no increase in wall stress.

WRONG!

However, in your particular situation, it is not entirely clear whether you are relying on circumferential (tension) vs. radial (compression) forces to contain the water. For a tank built of metal sheet or plate, it would typically be circumferential tension. For a buttress-type wall, it would typically be radial compression. Your wall might be considered as somewhere in between. This thread has shown some calculations for the former, but none for the latter.

Thanks JohnDG. Just two questions.

P = ρ x g x h,

where

• ρ is the density of water (about 1000kg/m³)
• g is the acceleration due to gravity (9.8m/sec²)
• h is the height (or depth)

1) Does this formula not applies to vertical down pressure -applied on the floor - not sideways to the inner wall? "pressure is linear with depth"

2) If that's the case, then the pressure is directly proportional to the height. The pressure pushing the wall out remains the same as long as the reservoir height remains the same. Is this not so?

Thank you for your input - the formula def worth a GA

1) Pressure acts in all directions. If you immersed an inflated balloon, weighting it so that it sank, it would get smaller in all dimensions, rather than just flattening. Agreed?

2) Yes, if the depth is the same the pressure (which is the force per unit area) remains the same. But with a bigger diameter tank, there is more wall area on which it can act.

Just been re-reading your questions - maybe you weren't clear about the "variation of pressure is linear with depth" statement.

Looking at the formula P = ρ x g x h, the pressure at 200mm would be twice the pressure at 100mm (since the "h" would have doubled, but ρ and g remained the same). At 500mm it would be 5 times the pressure at 100mm, and so on. In 'mathspeak', the pressure varies linearly as the depth increases.

This is what justifies the calculation of the average pressure acting on the wall as half the pressure at full depth.

Best answer. GA.

Hi Bruce - Thank you. GA for the math - easier to understand now. One question - at 6m diam the wall length is 18.85m and the 20m diam wall length is 62.84m

There are approx 7 courses of brick in the bottom 500mm of wall height, with 3 x 6mm rebar in each course.

6m reservoir = 18.85circum x 3 x 7 = 395.85m of 6mm rebar - 50 900l vol

20m reservoir = 62.84circum x 3 x 7 = 1319.64m of 6mm rebar - 565 560l vol

You calculate the ring tension of the 6m diam to be 54kN/m and the 20diam 180kN/m.

There is 3.33 times more steel in the 20m reservoir in the bottom 500mm.

The wall is 3.33 longer in the 20m diam

The ring tension increases by 3.33 times in the 20m diam

The volume of water however increases by 11.11 times in the 20m diam

I do not doubt your answers and I only ask because I am ignorant humble farmer but can I get 11 times more water storage for just a 3.33 increase in wall length, cost, ring tension etc?

Lastly, what safety factor would you use for a 20m diam reservoir?

"Your steel reo may hold but your bricks may not." Sounds like a song by Bob Dylan.