Mixing Tank - Pressure Calculations 1

[zelgar]

Are there any formulae for determining what the pressure increase (if any) for mixing in a tank? I know how to calculate the hydrostatic condition, but am uncertain if mixing would result in an increase in pressure along the shell of the tank.

Zelgar

 

[Ashereng]

Zelgar,

I would think that your question would be dependent on how you are "mixing" the tank, and also, what exactly do you mean by mixing?

If you mix by "turning over" the tank - pump it out the bottom and in the top, I would think there is no additional pressure along the shell of the tank.

If you are mixing by a side mounted impeller style mixer, then there probably is more pressure espcially where the mount is.

If you are mixing by an impeller top mount a 90°, I have no idea. But it may be different than if you are mounting at 15° offset.

What I am trying to say is, you may need to provide more information to get an anser.

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
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[zelgar]

I am interested in finding out about mixing for top or bottom mounted mixers. I would think that the calculations would be effected by the type of mixing (laminar or turbulent flow), the viscosity of the material and if there are baffles on the side of the tank.

In general, though, would there be a significant amount of pressure on the tank due to mixing, or is the hydrostatic pressure and any induced pressure be the pressure used for determining minimum shell thickness for the tank design.

 

[25362]

If I understood your query correctly here is my approach: a liquid rotating coaxially in a cylindrical container of radius r with angular speed [ω] will exert a pressure on the bottom plate equal to:

P = P_a + [ρ]gh_o + [½][ρ][ω]²r²​

where

P_a is the pressure above the liquid
[ρ] is the fluid density
h_o is the (reduced) height of the liquid at the axis of rotation
g is the acceleration of gravity

The maximum liquid height at the containers periphery would be

h_max = h_o + ([ω]²r²[÷]2g)​

An example: r= 2 m, [ρ] = 1000 kg/m³, [ω] = 4 rps.
The pressure exerted just by the rotating fluid, [½][ρ][ω]²r², would be:

([½])(1000)(16)(4) = 32,000 Pa = 4.64 psi​

 

[Ashereng]

Mixing does not always result in rotating fluid around the longitudindal axis.

Mixing impellers designs are an engineered prodect (I worked for Pro Chem, way back, which became Chemineer). The impeller can be designed to rotate fluid longitudinally (think straw stirring a drink), or it can rotate is latitudinally (think something like a coffee percolater's pattern of flow - up the center and down the sides or the other way).

When I worked for Pro Chem, we often did the calculations for our client, to ensure a complete mixing solution. I suggest you contact your mixing vendor. There are very specialised engineering that goes into mixing.

Unless your mixing needs are very simple (disolve sugar in water), you should contact a specialist.

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[zelgar]

Would the pressure increase only occur on the bottom plate, or would the sides of the tank have the same pressure exerted?

Also, based upoon a hydrostaic condition the pressure is the following equation:
P = P_a + [ρ]gh

Since the height to determine the potential engergy of the liquid will drop with the mixing (i.e., h_o, will the pressure within the tank change when mixing occurs?

I know that based upon the Bernoulli equation (assuming that there is no friction), that in a pipe the sum of the heads from pressure, Potential energy and Kinetic energy is constant. Is this true in a tank as well?

 

[Ashereng]

Bernoulli's equation for pressure drop in a pipe applying to a tank? I would think that the answer is no. In a tank, you have stuff, such as baffles (maybe), bracing (maybe), the impeller shaft, piping, etc.

The pressure in the tank depends on how you are mixing.

"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[zelgar]

Unfortunately, I'm not the one designing the equipment. I'm the State engineer reviewing the integrity assessment of the tank. The facility is not using a tank design standard, but only using structural calculations to determinine the minimum shell thickness based upon hydrostatic conditions in the proposed tank (+ induced pressure if applicable).

Also, it appears that a lot of the tank design standards (or at least the versions that I have copies) do not even consider mixing as a concern when determining the minimmum thickness required for a tank. Based upon my experience, the tank standards minimum thicknesses are greater than the thicknesses you'd calculate based upon structural conditions alone, but the min thickness have a factor of safety incorporated into them which may accout for mixing.

How would you verify that a tank was adequately designed for mixing if they are not using a tank design standard and are mixing wastes within the tank? Would you require a Factor of Safety of at least 2.0 or greater?

 

[Ashereng]

That I don't know.

I have seen tanks that originally did not have a mixer have one added, so I would think that additional forces for the mixing is relatively small and within the safety factors of the original constructions.

But, I am guessing.

I do not have the expertise to calculate the stress imposed by a mixer on a tank. Perhaps a mechanical colleague can help.



"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[25362]

You are dealing with mixers not centrifuges.
The formula I submitted would be an extremely conservative case. But you can use it to see whether the imposed stress is at all appreciable. In household blenders it isn't, so I pressume it would be the same in the case in hand.

 

[StoneCold]

I have had several reactors designed to ASME code and there was no allowance given for mixing. There is a calculation done for the nozzel loading on the top of the tank due to the mixer but nothing that affected the shell thickness. They never asked me how many horsepower is the drive, RPM? Impeller Diameter? Etc.
Just thinking out loud, I don't see how the force on the vessel wall could be much more than the difference in liquid height between the vortex at the center and the wall. Otherwise the fluid would move up the wall in responce to the increased pressure. Just my thought. I don't have math to back it up.

Regards
StoneCold

 

[JStephen]

Generally, no tank would be designed for increased pressures due to mixing unless the customer actually knew what those pressures were and requested that additional design.

A lot of the engineering methods are based on past experience. If tanks never fail due to mixing loads, then they won't be designed for it. How do you know turning the fan on in your house won't blow the walls out? Nobody checks the loads involved, you just know from experience that it is not an issue.

API-650 does have certain requirements concerning mixers- for example, thicker flange manways when mixers are mounted to them, and some wording about the effect of mixers on floating roofs. But not the pressures from it. If the pressures were an issue, I think you'd probably be more concerned about vibration in the tank walls than actual static pressures.