How do i figure out the hydtostatic pressure in the tank

In summary, the unpressurized cylindrical storage tank has a thin wall with a thickness of 5mm and is made of steel with a maximum strength of 400Mpa in tension. The tank has a radius of 3.75m and a height of 20m, and is standing on its base like a tower. When filled with water, the pressure at the bottom of the tank will be 9800h, where h is the height of the water. The maximum height the tank can be filled with water is 108.8435m, which is higher than the actual height of the tank. This means that the tank is built to withstand the pressure of a full tank. To find the tension in the tank
  • #1
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an unpressurised cylyndrical storage tank has a thin wall of 5mm thickness and is made of steel with a maximum strength of 400Mpa in tension
the tank radius is 3.75m
the tanks height is 20m
(the tank is standing on its base like a tower)
Determine the maximum height it may be filled with water if the density of water is 1Mg/m^3

i first thought i could use hydrostatic pressure here, saying that the pressure in the tank is uniform ? but now I am not so sure, that's the only kind of problem i have had so far, one where the pressure is uniform. if not how do i find the pressure? i think that logically the pressure at the bottom of the tank must be the highest, but how do i know exactly?
 
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  • #2
this is definitely not hydrostatic pressure like i thought before, the lower down i g the higher the pressure will be,

since the tank is unpressured, the force on the tank at the surface of the water will be 0, and the force will increase linearly

F(y)=9800*(pi)*(R^2)*y
(where R is the inner radius and y=0 is at the surface of the water and y=h at the base of the tank)

now that i have my Force i i need to find the pressure.
as far as i know, the pressure on the base will always be much higher than the pressure on the sides of the tank,

the force on the bottom of the tank = 9800*(pi)*(R^2)*h
the area of the bottom of the tank = pi*R^2

the pressure on the bottom of the tank= F/A=9800*h

i was given the maximum strength, can i compare this to the pressure i found at the bottom of the tank?

but i get a massive number as a result since my maximum strength is Mpa and here i have 9800*h (Pa)

also where do the radius radius and thickness come in, my result was independent of both

i know that for hydrostatic pressure the stress at the base of such atank is equal to

P*r/(2t)
where P is the hydrostatic pressure, can i use this here too, according to the way i proove the expression i would think so
i disconnect the base and use equilibrium equations on it.

if so

9800*h*r/(2t)=400e6

h=400e6*2*t/(9800*r)

but i still get a large answer
h= 108.8435m which is higher than the tank

this is possible, but means that the tank is built to withstand the pressure of a full tank

but am i doing this correctly??
 
  • #3
Assume side can slide over the base without water leakage! Consider lowest "ring" say 10mm high. The tension in that ring comes from pressure d g h where d is density of water, h is height of water. Equilibrium of half a ring in plan will reveal the tension in it. Then to stress etc. When I did it I made a lot of mistakes with units; so be careful.
 
  • #4
i still get an answer larger than the height of the tank, using the same principle .

i got about 50m
 

Related to How do i figure out the hydtostatic pressure in the tank

1. How do I calculate the hydrostatic pressure in a tank?

To calculate the hydrostatic pressure in a tank, you will need to know the height of the liquid in the tank, the density of the liquid, and the acceleration due to gravity. The formula for calculating hydrostatic pressure is P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the liquid.

2. Can I use the same formula for any type of liquid in the tank?

Yes, the formula for calculating hydrostatic pressure can be used for any type of liquid as long as you use the correct density value. The density of a liquid can vary depending on its temperature and composition, so it is important to use the correct value for accurate calculations.

3. How do I convert the height of the liquid in the tank to the correct units for the formula?

The height of the liquid in the tank can be measured in any unit of length, such as meters, centimeters, or feet. Just make sure to convert the height to meters before using it in the formula. For example, if the height is measured in feet, you would need to multiply it by 0.3048 to convert it to meters.

4. Is the hydrostatic pressure the same at every point in the tank?

No, the hydrostatic pressure can vary at different points in the tank depending on the height of the liquid at that point. The pressure will be highest at the bottom of the tank where the liquid depth is greatest, and lowest at the top of the tank where there is little to no liquid.

5. Can I use this formula to calculate the pressure in a tank with a non-uniform shape?

Yes, you can still use the hydrostatic pressure formula for a tank with a non-uniform shape. However, you will need to calculate the average height of the liquid in the tank in order to use in the formula. This can be done by measuring the height at different points and taking the average, or by using a volume measurement tool and the total volume of the tank.

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