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Concept Question (Delta P or Differential Pressure)
2

Concept Question (Delta P or Differential Pressure)

Concept Question (Delta P or Differential Pressure)

(OP)
The question I have relates to basic fundamentals of fluid dynamics. Here is my way of thinking: The driving force for fluid movement is Delta P.

If you have two tanks with an equal volume of 20 cubic meters absolutely full of water and tank 1 is at 500 kPag and tank 2 is 100 kPag. Furthermore, there is a line connecting both tanks with a valve at the direct midpoint of this pipe from T1 to T2.  If I open the valve, what is the direction of flow if both tanks have NO vent lines to atmosphere.  Fundamentally, one would think flow would be from high pressure to low, but what replaces the liquid. Could some explain this concept at a conceptual/fundamental level?


RE: Concept Question (Delta P or Differential Pressure)

I think that you actually have no flow. As you have two completely full tanks of water (assumed non-compressible in this case), you system is completly filled and you're not able to get any movement of mass.
Is this a question raised in some IQ test or am I completely off the track??

RE: Concept Question (Delta P or Differential Pressure)

First off, while dP defines a direction of flow, it's magnitude is a result of a combination of the flow and the total resistance to flow. I know this seems pedantic, but right now I'm involved in a heated argument with someone who feels that for a given flow rate, a higher dP is somehow "better" than a lower dP.

With two liquid-full pressure vessels at the same pressure, if you cross-connect them, Archimedes Principle would say that the pressure will equalize without any mass flow.  The liquid doesn't have to "go" anywhere for the pressure to change in both vessels.  

Think about a liquid-full vessel at a stable temperature.  If you add heat to that vessel (through the wall) to raise the temperature 1F, then the pressure will increase about 100 psi.  This is an example of a pressure change with no mass transfer.  Your cross-connected vessels are another.

David

RE: Concept Question (Delta P or Differential Pressure)

Okay, but back to the flow; as there is no mass transfer, there is no flow. So the answer must be that there is no flow (ie no movement of mass) between the tanks. Or?

RE: Concept Question (Delta P or Differential Pressure)

If there is a pressure difference then there will be flow until the pressure equalizes. It may only be a fraction of a liter but there will be flow. The water will expand and the tank will shrink slightly.

RE: Concept Question (Delta P or Differential Pressure)


Assuming the containers are rigid, T1, at 6 bara, would decompress to about 4 bara, while T2, originally at 2 bara, would increase its pressure to the same level.

Considering a small change in specific volume, the transfer T1→T2, at 20oC, would be about 1.8 kg.

RE: Concept Question (Delta P or Differential Pressure)

Zdas04, So higher energy cost for higher dP is better?  Sounds like you are argueing with an account that likes simple rule.

Think about how two tanks of equal size temperature got different pressures.  They added more molecules with a pump to the one with higher pressure.  When you open the valve, the same number of molecules will need to be in each tank.

RE: Concept Question (Delta P or Differential Pressure)

(OP)
Thanks for your help!

zdas04 (Mechanical)..."With two liquid-full pressure vessels at the same pressure, if you cross-connect them, Archimedes Principle would say that the pressure will equalize without any mass flow... Do you mean different pressures?... How does Archimedes Principle state this...Mathematically?

25362 (Chemical). How did you calculates the above?

RE: Concept Question (Delta P or Differential Pressure)

Dcasto,
Actually, the guy is a Chem E with a Masters who has spent his whole life in Artificial Lift with what is now a Major Oil Company.  He keeps saying that if q=c(Pr^2-Pbh^2)^n then a bigger dP is more flow, so it follows that more dP is better for any flow.  In a meeting last week I was reduced to yelling epithets at him because I couldn't get him to see that there is a certain resistance to flow built into the "c" term, and if resistance increases (through scale, or multi-phase flow) then for a constant "q", dP must be higher.  I may start screaming again.

Poppapetro,
I haven't seen the mathmatical representation that the a force applied to a liquid will be transmitted throughtout the liquid in a very long time (first semester physics in the '70s?).  I don't even know where to start looking for it.  Some of the other posts have been correct that a measurable mass will transfer from one vessel to the other, since no liquid is truly incompressible.

David

RE: Concept Question (Delta P or Differential Pressure)

So, then he could approach the speed of light given enough dP with that logic.

RE: Concept Question (Delta P or Differential Pressure)

More like the volume of the universe traveling at the speed of light, not sure what that volume flow rate works out to (at standard conditions).

RE: Concept Question (Delta P or Differential Pressure)

The assumption of non compressibility is wrong here and infact you should use that concept to solve the problem. The bulk modulus of water is 2.2x109Pa. The equilibrium pressure will be 500+100 = 300 kPag.

There is 200 kPa increase in pressure, so the volumetric increment will be (200 kPa/2.2x106kPa)x20000kgs = 1.8kgs (I would prefer it to be in liters but there may be some reason why 25362 mentioned it in kgs)

RE: Concept Question (Delta P or Differential Pressure)


To quark, I did simply because I used a table of densities in kg/m3 from NIST.

RE: Concept Question (Delta P or Differential Pressure)

Ah, simple yet perfect. Now I know why you were considering pressure in absolute terms. Get the star.

RE: Concept Question (Delta P or Differential Pressure)


quark,

your approach is, at least, more apodictic and valid than mine, thus you certainly deserve a star.

RE: Concept Question (Delta P or Differential Pressure)

If you have two tanks "absolutely full of water" (also assumed at the same elevations), but at different pressures, the water in the high pressure tank is more compressed (yes water is compressible) than the water in the low pressure tank.  When you open a connecting valve, the water will flow from the high pressure tank to the low pressure tank.  Only enough water will flow (expand is a better concept) from the high pressure tank to the low pressure tank until the density of the water in both tanks is exactly equal, which also equalizes all pressures.

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

BTW, the fluid usually oscillates with back and forth flow in the connecting pipe around three or four times, until it settles down.  (If you open the valve quickly.)

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

With regard to final equilibrium pressure--
The mass inventory in each tank should be readily calculated from the initial conditions.

After the valve is opened and the pressures equalize, the final pressure may be calculated assuming internal volume of tanks remain constant. Since system liquid mass is constant, system specific volume is constant and known.
For ISOTHERMAL conditions and complete mixing, the known specific volume and temp will yield final equilib pressure.

Similar to the above, if the process is ADIABATIC, use the known initial total suste, internal energy to balance the final total system internal energy. When this occurs,the equilibrium press is obtained.
Regards

RE: Concept Question (Delta P or Differential Pressure)

BigInch (Petroleum)Without a knowledge of lengths between the interconnecting piping to the quick opening valve nor the diameter, how can you justify the 3-4 oscillations?
Regards

RE: Concept Question (Delta P or Differential Pressure)

zdas04,
Apparently you and your colleague are talking past each other.  Your colleague is correct.  The equation that you wrote, q=c(Pr^2-Pbh^2)^n, appears to be a variant of the pipeline equation for high pressure gas.  Pipeliners usually write (P1a2 - P2a2) =kQ2 where P1 is the source pressure P2 is the terminal pressure, the a subscript signifies the absolute pressure, k stands for all of the other parameters in the equation that are being held constant and Q is the flow rate.  The term (P1a2 - P2a2) is commonly referred to in conversation as K Q Squared.  The relationship is nonlinear and operating the pipeline at a higher source pressure will give you a greater flow rate under the same pressure drop.  Look at the example below.  Operating the pipeline with a source pressure of 300 psig will give you 27% more flow than if you operated it with a source of 200 psig while in both cases the pressure drop is 100 psid.

P1     P2   P1-P2   P1a     P2a   (P1a2-P2a2)   (P1a2-P2a2)0.5    
200   100   100   214.7   114.7   32940         181.49
300   200   100   314.7   214.7   52940         230.08    
                             
                                                230.08/181.49 = 1.27
 

RE: Concept Question (Delta P or Differential Pressure)

Vzeos,
You should probably read my post more closely.  His point was for the same mass flow rate a higher dP is "better" than a lower dP.  He doesn't really define what he means by "better".  

I don't think that anyone reading this thread would disagree that for the same pipe and fluid conditions increasing dP will increase flow rate.  But we were talking about pressure drop caused by the gas doing work on the liquid in multi-phase flow (i.e., for a given flow rate, the dP is much higher than single-phase equations like the AGA equation or your simplistic equation would predict).  

The equation I referenced is called many things, but originally it was the Bureau of Mines Method of calculating flow through a permeable media.  Now it is mostly called the Absolute Open Flow (AOF) equation.

Your example was pretty, but pretty much not on point.

David

RE: Concept Question (Delta P or Differential Pressure)

Sailoday,

Experience.  Just do a transient flow simulation using water.  Pick any two completely full tanks with/at the same levels and a reasonable pipe configuration, similar to what the OP describes.  Waters very small compressibility almost always guarantees that only a few oscillations will occur before things arrive at a pretty much static condition.

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

BingInch
I find it hard to comprehend how any diameter or or pipe lengths will lead to your conclusion. Friction/no friction-geometry of source and receiving tanks, etc.
Regards



RE: Concept Question (Delta P or Differential Pressure)

Hydraulic simularity.  Relatively the same principle as the pump affinity laws and other means of nondimenional analysis commonly used in testing smaller models of ships, airplanes and submarines in wave tanks.  Similar small <=> similar big.

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

I don't know the wave decay rate, but amplitude must be something proportional to 1/n! of the wave number, so there isn't much left after the 3rd wave and, after the 5th, its relatively academic.

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

How do you get the wave number?

RE: Concept Question (Delta P or Differential Pressure)

Quote (BigInch):

Count them as they pass by.

Do we require a transparent connecting pipe and a kind of 2-way deflector, then?4 eyes

RE: Concept Question (Delta P or Differential Pressure)

Just a very good pipeline transient simulation program or, a pressure transmitter and data logging equipment.

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

BigInch (Petroleum) 30 Sep 07 20:53  
Count them as they pass by.
How does this help engineers that wish to learn?

RE: Concept Question (Delta P or Differential Pressure)

Sailoday,
I think BigInch's answer helps a lot.  There are times when experimentation is a far more useful approach than developing esoteric arithmetic that always runs that risk that you have assumed an important parameter out of existence.  

Every engineer who has ever worked in the field has a list of seat-of-the-pants solutions to real-world issues that result in "good enough" answers (i.e., answers that are conservative enough to ensure that their application won't put anyone at risk, but no so conservative that they destroy economics for no good purpose).  For example, I "know" that hydrotest water volume requirement will be about ID^2 bbls per 1000 ft (e.g., 10 inch pipe is 100 bbl/1000 ft).  The arithmetic really works out that this is about 8-12% too much water, which is perfect for the real-world conditions that not every water truck will be pumped all the way dry.

I don't see any problem with an answer that an experienced engineer has observed that in a sloshing situation in liquid-full vessels that you can expect around 3 major transients, followed by some small number of minor transients (which is another way of saying "count them as they pass by").

David

RE: Concept Question (Delta P or Differential Pressure)

On a good size pipeline they pretty obvious when they pass by.  No data logger required!

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

I don't see any problem with an answer that an experienced engineer has observed that in a sloshing situation in liquid-full vessels that you can expect around 3 major transients, followed by some small number of minor transients (which is another way of saying "count them as they pass by").

To me sloshing means that there is a space above the liquid.  Is that true in the present case? If so a basis for that assumption/statement should be made--other than "experience"
Regards

RE: Concept Question (Delta P or Differential Pressure)

put a micromotion mass meter in the line.  Not only does it measure mass, it knows which direction the flow is too.

RE: Concept Question (Delta P or Differential Pressure)

I thought the tank was full, but that makes no difference, just less pressure to drive any flows since the vapor above would be guaranteed to be at vapor pressure (generally pretty low for water unless it was very hot).

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

zdas04 (Mechanical)
My original response was
BigInch (Petroleum)Without a knowledge of lengths between the interconnecting piping to the quick opening valve nor the diameter, how can you justify the 3-4 oscillations?

You state experienced engineer has observed sloshing, etc.
How is the "quick opening" valve defined without a knowledge of interconnecting lenths or diameter.
BigInch (Petroleum) 1 Oct 07 16:59  
I thought the tank was full, but that makes no difference,

Are the above "observations" seat of the pants engineering?

 

RE: Concept Question (Delta P or Differential Pressure)

Pause the simulator, open valve to full open positon... resume.  I can't do it faster than that.  

http://virtualpipeline.spaces.msn.com

RE: Concept Question (Delta P or Differential Pressure)

BigInch (Petroleum) 1 Oct 07 21:03  
Pause the simulator, open valve to full open positon... resume.  I can't do it faster than that.  

Sorry, but that is not the definition of a fast or quick opening valve.  Think about the water hammer equations.
Regards

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