Calculating the upward force (Buoyancy) in a liquid filled column

[Invinci]

Hi all,

Problem:

A packed column completely filled with liquid, a gas sparger is below the packed bed of the column. The gas flow rate through the sparger is 1000 (kg/hr) and the density is 1.56 kg/m3 (641 m3/hr). The liquid flow rate through bed and column is 120410 kg/hr and density is 1100 kg/m3. Calculate the buoyancy (upward) force exerted on the bottom of the packed bed (support grid bottom) by the sparged gas?

Answer:

Fa = V x density x g.

Buoyancy force = Volume of gas x density of liquid x acceleration due to gravity

Basis: 1 hour operation (steady state condition)
Fa = 641 x 1100 x 9.81 = 6917 kN.

I am not sure of the answer, and would like suggestions or possible answers how to solve this problem.

Questions:
1. I want to calculate the upward force exerted by the gas on the bottom of the packing?

Any help is appreciated.

 

[JimCasey]

Figure the volume of the gas entrained in the column liquid at any time. The buoyant force is X times the density of the liquid + (1-x) times the density of the entrained gas.
X is the fraction of the column ovvupied by liquid and 1-x is the remainder, occupied by gas.

If the bubbles are large due to the characteristics of the sparger and the surface tension of the fluid, then you <Might> be able to float some of the individual packing elements.

You will generally find that with the entrained gas, less mass is displaced so there is LESS buoyancy than if the tower were filled with fluid alone.

Example: Municipal waste treatment relies on large, actively aerated tanks with sparger grids on the bottom. Workers know that if they fall in there is not enough floatation in the frothy mixture for them to float or even to swim.

 

[Compositepro]

Bouyancy is a derived or "fictional" force. The only force a gas can apply is due to its pressure. Bouyancy is the net difference of the gravitional forces.

The force the gas applies to the packing is seen as the pressure drop as it flows through. Forget about bouyancy as a way to aswer your question.

 

[BigInch]

NO. Well this part, "The only force a gas can apply is due to its pressure. " is correct (neglecting friction), but then you get the rest all wrong about buoyancy being the, "net difference of the gravitational forces". Let me explain,

The net difference of two gravitational forces of any magnitude would still have to be down, but the direction of a buoyant force would be presumed upwards, therefore buoyancy can't be the result of a "net difference of the gravitational forces". And what gravitational forces are you talking about and acting on what? The fluid and some object immersed in it? Can't be the fluid, because we don't know how much fluid there is and therefore we don't know how much mass. The object could be immersed at the bottom of the ocean or in the bathtub. Independent of mass of the fluid involved. Gravitational force is mass x acceleration due to gravity. So the mass of the object immersed must be one, but what is the other mass? It can't be the mass of the displaced fluid either, as that mass doesn't exist. So, bouoyancy doesn't have a thing to do with gravity acting on the fluid other than in the typical case where pressure in a fluid is caused by gravity, or more correctly, acceleration due to gravity, as is any force or pressure is the result of an acceleration of some kind.

In the atypical case, a fluid pressure could be caused by centripital acceleration, as would be found in a fluid on the edge of a rotating wheel, which if rotating in a horizontal plane, would produce a pressure in the fluid as the result of that centripital acceleration in the horizontal plane. An object immersed in that fluid would have a horizontal buoyant force (in addition to the usual vertical buoyant force) in the horizontal direction as well.

Therefore it is as you said, "the only force that a gas (or liquid) can apply is due to pressure", (ignoring friction) except it, pressure, also causes the buoyancy effect, the result of the net difference in pressure forces acting on an immersed object. That's buoyancy. See, nothing to do with gravity.... really... its pressure difference alone. Net difference in gravity or any acceleration won't give the correct direction of the resulting buoyant force, so we know that's not right.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[Compositepro]

What causes the pressure in a column of water? Gravity!

 

[BigInch]

That's a different question. Of course gravitational acceleration causes the weight of a fluid, which is RESISTED by the pressure of the fluid against a container. Viewing it from that perspective, you get the proper direction of a force resisting graviational acceleration and then the buoyant force also has its proper direction too. If there was no resistant force, the fluid and anything immersed in it would not generate resisting pressures and simply accelerate into the ground, as would a large raindrop, or if in an acceleration free environment, generate no buoyant forces at all.

Show me how you calculate the specific forces you refer to by the, "Net difference of the gravitational forces", using F=M*A and how you get buoyant forces as a result. You have to include the resistance to gravitational force. That resistance causes pressure, gravity does not cause pressure by itself, it only causes an acceleration.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[BigInch]

If it is as you say, how do you know its not the mass of fluid that causes pressure rather than the acceleration? Looks to me that using your reasoning, it could be either gravity or mass that causes pressure. Its not either. Its the resistance by a fluid to the product of the two.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[Invinci]

Hello again!

JimCasey, Compositepro, Biginch: Thanks for you replies and clarifications.

Now agreed that the buoyancy may not be the best way to solve this problem. How do i calculate the pressure drop of the gas leaving the sparger embedded in a liquid column...?

Could anyone assist me with the formula or approach to solve the force exerted on the bottom of packing support with 1000 kg/hr of gas (density: 1.56 kg/m3)?

Thanks in advance

 

[BigInch]

That's not a very big number of kg/second, so I wouldn't think it translates into a whole lot of newtons, but that would also depend on the velocity of the gas, as well as I presume a number of other things. It would help, if I knew what this thing looks like, but packing supports are not my field, so I'm at a loss to say if I can help with that.

"I think it would be a good idea."
- Mahatma Gandhi (1869-1948),
when asked about Western civilization

 

[JimCasey]

The pressure drop of the gas leaving the sparger:
The pressure at the sparger outlet is the height of the liquid above the sparger outlet, multiplied by the specific gravity of the fluid. conveet the values to compatible units and Add the pressure resident in the column, if other than atmospheric.

The pressure at the surface of the liquid, if not atmospheric, is controlled by other phenomena or devices outside the definintion of the question. Backpressure control valve, pressure resident in downstream system, etc.

THe hard part is that the specific gravity of the fluid is not well known because it consists of both liquid and gaseous phases, mixed, in a nondefined fraction. You said 1000 kg/hr of gas, but not how long it takes to transit through the column