Flow from low pressure to high pressure? 1

[mochi11]

Hi everyone

I have been working on an Excel spreadsheet on the piping design for compressed air. I am required to calculate the pressure at every point in the different segments of the system, such as the pipes, fittings etc. On the portion of the piping along the riser, I calculated that there is a rise in pressure as the air flows down the riser, due to the decrease in elevation (which makes sense as the higher the elevation, the lower the pressure). However I also realised that the air would be flowing from a lower pressure point (at the higher point in the pipe) to a higher pressure point (at the lower point in the pipe), and this had me becoming very frustrated for some time already as I cannot figure out how a flow can occur from low pressure to high pressure, even as I read articles and forums online.

To add on: the density for the compressed air is about 10kg/m3 (at 8barg and 30degC), and the drop in height along the riser piping is about 6m. Calculating the pressure gain from the drop in elevation using density*height*gravitational acceleration = 10*6*9.81 = 589Pa. Which I agree is small relative to the compressed air pressure.

Then I calculated the pressure drop due to friction from the flow, for a flow speed of about 9.7m/s , the fanning friction factor is about the magnitude of 0.004 (which is quite typical), for pipe diameter 108mm, using deltaP=2*f*density*pipe length*speed^2/diameter = 2*0.004*10*6*(9.7^2)/0.108 = 418Pa. This gives me the pressure drop from frictional force.

Hence the net pressure drop = (-589P)Pa + 418Pa = -171Pa. The negative pressure drop means that pressure increases as the air flow from the top of the riser pipe to the bottom of the riser pipe. However like what I stated earlier, what puzzled me was that the flow of the air was from lower pressure to higher pressure, which is very counter-intuitive.

I would like to know if it is absolutely possible for the flow to occur from low pressure to high pressure? The pressure of the gas that I am calcuating here refers to the total pressure of the gas contributed by the static pressure, kinetic pressure and the gas head pressure right?? Please help as I am really puzzled, and I would definitely appreciate it if the experts can help explain.

 

[zdas04]

None of your numbers make much sense. I did the calculations before I saw this was your first post and then reread your problem. It sounds too much like a homework problems for me to believe that it will stay without being red flagged. Please convince us that you are not a student and you might get some help.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[BigInch]

I'm not convinced it's homework just yet.

Sure it is possible to flow from lower pressure to higher pressure, because pressure alone does not describe the total energy of a point. A difference in total energy is what drives flow. Pressure alone does not describe the total difference of energy between two points. (See the Bernoulli equation)

If you have an open vertical tube filled with water, will not the water flow down and out, even though the pressure at the top of the water in the tube is 0 kPag

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[mochi11]

Thanks for the reply.

Hey David, I am indeed NOT a student and currently working for a design company, and no disrespect, I don't see why the numbers don't make sense (can you clarify which are the ones that don't make sense?). I am not a student who comes here to ask for a solution or how to do my calculations, I am here to ask for an explanation for that calculation because it is puzzling to me. I would like to ask, from your experience, when you do such calculations does the fluid ALWAYS flow from high to low pressure? Even in the case of flowing down the riser pipe. It's my first post because I felt the need to get an explanation which I cannot find online or anywhere else, hence I am resorting to the forum.

Hi BigInch, I don't understand the sentence "a difference in total energy is what drives the flow". Per Bernoulli's equation, the pressure head term + velocity term + potential term is constant (including energy losses from work done and against friction). i.e. Change in Pressure term + change in velocity term + change in potential term + Energy change from work done and friction = 0. So take for example a streamline flow, when 2 different points along the streamline have the same total energy (no difference in total energy) but yet there's still a flow!
Per your explanation is the following what you are trying to say?
delta(P term) + delta(kinetic term) + delta(potential term) + delta(energy loss from friction) + delta(energy loss from work done) = 0
delta(P term) constitutes of delta(P friction) and delta(P elevation)
delta(P elevation) will cancel out delta(potential term) since pressure gain from elevation negates the loss in potential from elevation.
So, delta(P friction) + delta(kinetic term) + delta(energy loss from friction) + delta(energy loss from work done) = 0

With that in mind, then what drives the flow? The "fluid always flow from high to low pressure" theory that stayed with me since school days is flawed?? And only under what conditions will it apply?

 

[BigInch]

What I was trying to get across was that the pressure at the top of the liquid column is 0, at the bottom, den * height/xsectional area and is greater than zero, but the fluid manages to flow downward none the less. Potential energy at the top is greater than that at the bottom.

Flow through a reducer in the direction of smaller to larger diameter creates a pressure increase towards the larger diameter due to the slower velocity.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[BigInch]

Forget the first example. I don't know what I was thinking. When you open the bottom of the tube, the pressure becomes lower than the top.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[zdas04]

I wrote my post as I was running out the door, and have been driving all day. Sorry for not responding sooner.

The numbers that bothered me were
[ul]
[li]Velocity of 9.7 m/s in 108 mm pipe is 65 e3m3/day or 2.3 MMSCF/day. That is a really big number for an air system[/li]
[li]Your pressure drop equation looks like Darcy, but you are using a friction factor consistent with Fanning. I always use equations that require Fanning for gas flows, but the one you are using looks like one that requires Moody. If I use the Isothermal Gas Flow Equation and itterate on Reynolds number the dP due to friction is 480 Pa or 20% lower than you got[/li]
[li]The equation you used for static head ignores the compression of gas in the column. I used the proper equation (which is an exponential) and got 0.1% better number, so what that isn't within the accuracy of the calculation? If you never get in the habit of pretending a gas is a liquid then you won't ever use that math for a 6000 m vertical swing where the difference is 30%[/li]
[/ul]

That was where I stopped this morning. BigInch provided the answer to your basic question--we use short-cut terminology and say "fluids always flow from high pressure to low pressure" when we actually mean "fluids always flow from high energy to lower energy". The equations we use in wellbore gas flow in Oil & Gas handle this explicitly and for low flow rates the hydrostatic component of bottomhole pressure can be orders of magnitude higher than the friction component.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[BigInch]

I've been suffering from attention deficiency relapse.
THIS is what I was trying to do. See attached.


"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[katmar]

mochi11, you really have nailed the answer by describing it in terms of Bernoulli. As you have noted, the original equation developed by Bernoulli did not include the friction term and if you include that it all balances perfectly.

Your numbers look correct to me. On the attached print-out I have tweaked the pipe roughness to give a Fanning friction factor of exactly 0.004 (to match your calculation) and the pressure drop results are very close to yours. I see no problem in using the Fanning friction factor with the Darcy-Weisbach equation, as long as you use the correct constant in D-W. If you were to use the Moody friction factor, you would have to use a constant of 0.5 where you have 2. Or if you follow the practice in the Chemical Engineering series by Coulson and Richardson (who use the Stanton form of the friction factor) the constant would be 4. The friction factors are all exact multiples of each other.

A question to David: why would you iterate over only 6 m? Unless this is also a built-in facility in your software I cannot see any reason for it. What difference does it make to your results if you do it in just one step? The isothermal compressible equation automatically takes into account the change in density due to pressure drop (although it does ignore the compression due to static head) and the viscosity will not change over this short distance.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[25362]

On the subject of flow in the direction of falling pressures. As an example, take the typical every day instance of a horizontal pipe in which flows run from a smaller into a larger diameter. The pressure before the expansion is lower than the one after it. Bernoulli vindicated.

 

[mochi11]

Hi David, with regards to your points you are right that the air consumption is big, because we have quite a number of equipments which uses a lot of compressed air, hence the compressed air requirement is pretty high for an air system. It's not the usual compressed air being used just to drive some pneumatic valves/pumps or some simple processes. And as stated by katmar i am indeed using the Darcy weischback equation for the fanning friction factor. Your third point is a good reminder for me to not neglect the change in density for gases which is why over 6000m the gas density can change quite drastically and the pressure drop calculation can be very different. In my calculation, the section of pipe that I am calculating is relatively short hence the density still almost remains the same. Which is why i would still use the density*height*gravitational acceleration equation. It would be good if you can let me know the proper equation that you were talking about (which is an exponential) and how it was derived.

Hi katmar, thanks for your time in helping me with check my calculation with your software. Although I think there is some error with my Bernoulli equation breakdown previously. It should be:
delta P(static P term) + delta P(kinetic term) + delta P(potential term) + delta P(friction term) + delta P(work done term) = 0
Hence Pressure drop calculation = -delta P(static P term) = delta P(kinetic term) + delta P(potential term) + delta P(friction term) + delta P(work done term). Correct me if i am wrong.

To my most puzzling question: if it is absolutely possible for the flow to occur from low pressure to high pressure?
I think Steve Hall from another forum probably explained it best. Flow is only achieve when there is an overall driving force. Where is this pipe leading to and what is the pressure at its terminus. So for my case the terminus pressure is much lower than the start pressure of my whole piping network, and this constitutes the driving force which can drive against the flow from low pressure to high pressure. Which makes me understand that, in other words flow from low pressure to high pressure in a section is possible if the overall driving force (overall static pressure difference) can drive against that.

Hi BigInch, I think for your example it is exactly that. The net overall driving force is actually the gravitational force acting on the fluid, since the atm pressure at top cancels out the bottom-acting atm pressure. With flow, the drop in potential energy would be converted to the gain in kinetic energy totally (neglecting friction). Total energy would still remain the same for the top point and the bottom point even during flow (since potential converted to kinetic), so total energy is not the factor to drive for flow. With your statement that the decrease in potential energy drives flow, it is also not totally correct as I can also say that the rise in kinetic will be the driving factor for flow based on your example. Which is not absolutely true as I know for sure that in the case of a flow slowing down (kinetic energy drops), the flow is still occurring.

Thank you all for your time and coming forward with your answers. I totally appreciate it and I want to thank Steve Hall too.

 

[BigInch]

Yes of course potential energy must be converted into kinetic energy to drive anything.

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

 

[zdas04]

Katmar,
My sheet makes iterating trivial, so I always do it. It really doesn't matter over 6 m

As to "just" adding friction to the Bernoulli Equation, that makes it a different equation and should not have Bernoulli's name on it. The Bernoulli Equation is one of the very few closed form solutions to a VERY specific subset of the Navier Stokes Equation. He had a long list of simplifying assumptions like "no friction", "no change in density", "swirl is zero","no work is done on or by the fluid". Those assumptions let him discard the hardest bits of Navier Stokes. Adding back a friction term invalidates several of the assumptions and makes the resulting equation "empirical" instead of "closed form". I know it seems like a little thing, but when we start down the road of knowingly violating underlying assumptions while calling something by the same name, where do we stop? Do we honor any boundary conditions or underlying assumptions? It is just terminology, but it points to an underlying lack of rigor in our work, just like using the AGA Fully Turbulent equation to the left of the fully turbulent line (usually I get a 25% variation from field data when that happens), or Weymouth at high pressures. Ignoring boundary conditions is the first step to not knowing that they exist, which is the first step towards just making shit up.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.

 

[BigInch]

Zap!

"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek