Analyzing Tank Breakage at 10m: Calculating Pressure and Tension | Forum Post

[Forensic-guy]

Hello people,
This is my first forum post, so i hope I'm posting my problem in the right area.
I have been looking trough books, internet and forum posts but i could not find anything helpful.

Homework Statement

A circular tank holds a liquid with a density of 13000 kg/m3.
The tank has the following dimension:
radius: 14m
height: 12.15m

The problem is that the tank broke and i have figure out why the tank broke.
The tank probably broke at a hight of 10m.
I do have a tensile test result at 10m which is 200 to 300 N/mm2.

The Attempt at a Solution

Volume =¼* π *diameter2*h
Volume = ¼* π *14^2*2,15
Volume = 331,0 m3
331,0 m3=331000 liter

p=m/v
1,3 ton/m3=m/331,0 m3
m=430300 kg

I hope one of you guys can point me in the right direction

 

[nil1996]

check

can you please check the density of your the liquid.For density 13000kg/m³ the material cannot be liquid.the density of iron is 7870 kg/m³.

 

[SteamKing]

Ever heard of mercury? It's known to be a dense liquid.

 

[haruspex]

The tank probably broke at a hight of 10m.

Probably? Is this part of the given information or a guess on your part?
Do you mean it broke at a point 10m above the base of the tank, or that it broke when the liquid filled it to that height?

I do have a tensile test result at 10m which is 200 to 300 N/mm2.

What does that mean? Are you saying that the vessel is known to withstand that pressure? If so, where does the 10m come into it?
I would have thought a relevant quantity would be the pressure near the base of the tank.

 

[SteamKing]

It's going to be hard to figure out the stress in the tank since no thickness information is given.

 

[Forensic-guy]

Thank you for all your replies.

The liquid in the tank is biological compound which makes the density that high.
A short time before the tank broke the tank filled to its maximum capacity.

After the tank broke, four pieces were sent in for further investigation. A tensile test was performed on only one of the plates.
Different pieces where cut out of the plate for a tensile test a few over a weld and some are not. All pieces have a yield from 200 to 300 N/mm²
The pieces that wend over a weld had a tensile strength of 250 to 300 N/mm² and one has a tensile strength of 150 N/mm².
The pieces that did not go over the weld have a tensile strength of 300-400 N/mm²
There is a lot of corrosion on the plate which can explain the weak weld.

This plate was located at approximately at a height of 10m, this makes me think the tank broke at that height.

I do have results from a thickness measurement with ultrasonic all four plates:
The thickness on the plate where the tensile test was performed on varies from 3,0mm to 5,6mm on a surface 4665 cm²

I do have some more information but i don't know if it is relevant.
Again thank you guys for your time and effort.

 

[SteamKing]

As a first cut, I would calculate the hoop stress in the side of the tank.

Hoop stress = P*r / t, where P is the pressure at the location, r is the radius of the tank, and t is the wall thickness of the side. P is equal to rho*g*h, where rho is the density of the fluid in kg/m^3, g is 9.81 m/s^2, and h is the depth of fluid in meters at the location.

If the hoop stress > tensile test, then you have your answer

 

[Forensic-guy]

Ok so if I understand you correctly.
The result of the tensile test are from a height of 10 meter so that leaves 2,15 meter
p=rho*g*h
p=1,3 kg/m³*9.81m/s²*2.15m= 27.41 (unit=kg/m/s?)

My earlier post of the radius is wrong the diameter=14m and the radius=7m
lets take a thickness of 5mm for the stress calculation

stress = P*r / t
stress = 27.41*7/5
stress = 38.39 (unit=N/mm²?)

but when one takes a smaller number for the thickness for example 3mm,
stress = P*r / t
stress = 27.41*7/3
stress = 63.97 (unit=N/mm²?)

This means that a thinner wall has more stress and is there for more likely to break.
Can you check if I used the right units?

 

[SteamKing]

The pressure P will have units of N/m^2, or Pascals.

Remember, rho is in units of kg/m^3. Your OP indicates rho = 13000 kg/m^3, but you have used 1,3 in your calculations. Confirm which density is correct.

 

[SteamKing]

In your hoop stress calculations, the thickness must be measured in m rather than mm. The stress will have units of Pascals. For your tensile test data, 1 N/mm^2 = 1 MPa = 10^6 Pa.

 

[Forensic-guy]

You are right,
I made a big mistake, i typed one 0 too much. The correct density is 1300kg/m^3

P=rho*g*h
P=1300*9.81*2.15 = 27419 N/m^2

(for the stress test again 5mm wall thickness)
stress= P*r / t
stress= 27419 N/m^2 * 7 meter/ (5*10^-3) meter = 38 386 600 Pa

Tensile test = 250 N/mm^2 = 250 000 000 Pa

Thank you very much.
I'm happy i found this forum. People are really helpful towards each other and there are some interesting forum posts and discussions.