36 replies to this topic

[jamese]

Hello,

 

Imagine we have a vertically orientated pressurised liquid filled closed pipe.

 

The pipe is shaped like a spring, such that the distance between the ends can be adjusted vertically whilst the pipe remains liquid filled.

 

If the distance between the ends of the pipe is adjusted vertically;

Will the pressure change at one end of the pipe, or at both ends of the pipe?

 

Thanks

[Bobby Strain]

This sounds like a homework assignment. We don't do those.

 

Bobby

[jamese]

Hi Bobby,

 

No it is not a homework assignment, it is a discussion we have been having at work and we cant agree on the answer.

 

I would also like to clarify that in the hypothetical example the volume of the system is completed unchanged as the distance between the ends of the pipe is changed,

 

Thanks

[samayaraj]

With reference to sea level, the top end pressure will remain same where as the bottom side pressure will rise because of increase in head of liquid.

[jamese]

Hi Samayaraj,

 

Thanks for you response.

 

I am not sure what you mean by "reference to sea level".

 

In the hypothetical case the upper end of the pipe is closed.

 

It seems to me, and in accordance with what you say; that as the distance between the two ends is varied, pressure will only increase at the lower end according to rho x g x h.

 

However, someone told me that if it is a closed system then the pressure at the upper end will also change (with the difference between both ends still being according to rho x g x h), and this confused me,

 

Thanks

[Bobby Strain]

Theoretically the presssure at the upper end will reduce. Because water is slightly compressible.

 

Bobby

[samayaraj]

Hi,

 

I said the datum as "sea level".

 

In other words, Lets assume Pressure in top of pipe P_top = X bar(a) and bottom P_bot = Y bar(a).

 

After expanding the coil to height 'h', P_top = X bar(a) and P_bot = Y bar(a) + (rho x g x h x 10^-5) 

 

where as h in m, rho in kg/m³ & g as 9.81 m/sec²

 

As you said, volume of coiled pipe/tube remains same, hence the top end pressure will not change if the density does not change.

Edited by samayaraj, 07 October 2015 - 10:30 AM.

[Bobby Strain]

But the density does, in fact, change. The water becomes denser because it is compressible.

 

Bobby

[jamese]

Hi,

 

I clarified this further with my colleague (PHD in physics and works with fluid dynamics).

 

Wierdly (to me anyway) apparantly the pressure will change at the top and bottom of the pipe.

 

The difference between top and bottom varies in accordance with rho x g x h, however the average pressure (the pressure at the vertical midpoint) always remains the same in a closed system.

 

He made an OLGA model to demonstrate this.

There is a slight change in pressure due to denisity variation as Bobby mentioned, however it does not contribute much.

[Bobby Strain]

I'm not sure I buy that. " The difference between top and bottom varies in accordance with rho x g x h" seems true enough.

"(the pressure at the vertical midpoint) always remains the same in a closed system." somehow doesn't make sense. Maybe your colleague can draw a picture along with a few equations. Maybe some differential calculus.

 

Bobby

[jamese]

"I think the most persuading argument is that the average pressure in the horizontal oriented closed pipe has to be the same as in the vertical pipe (let's assume 100 bara) – if not the extra pressure has to come from somewhere.

 

On the second argument we all agree, the pressure distribution will be (in first order) linear with rho x g x h. So, if we agree on both statements, we can calculate the pressure at the top and the bottom of the pipe:

 

p_average = (p_top + p_bottom)/2 = 100 bara

and

p_bottom – p_top = rho x g x h =10 bara

 

we get p_top = p_average – (rho x g x h)/2 = 95 bara

and

p_bottom = p_average + (rho x g x h)/2=105 bara"

[samayaraj]

Consider a coil pipe filled with liquid. Lets assume the top end pressure be atm. pressure and bottom pressure as rho x g x h + atm. pressure.

 

As you increase the height of coil by keeping the volume constant, the top end pressure will not change unless there is a change in density. The bottom pressure will be rho x g x h + atm. pressure + rho x g x Increase in height.

[samayaraj]

Average pressure of the system will change due to increase in height of coil.

 

Case 1: P_top = 90 Bar (a) & P_bot = 110 Bar (a).

 

              Avg Pressure: 100 Bar (a)

 

Case 2: P_top = 90 Bar (a) & P_bot = 110 Bar (a) + rho x g x h x 10^-5

 

              Avg Pressure : > 100 Bar (a)

 

              Where h is increase in the height of coil.

Edited by samayaraj, 13 October 2015 - 04:00 AM.

[Bobby Strain]

Not a very good description of the system. So, back to square 1. Let's see your PhD friends analysis, but not with Olga.

 

Bobby

[jamese]

I don't really want to annoy him anymore, since I asked him a question and he gave me his answer, the bit in my mail in quotes in my last mail above on October 13th  was part of his response.

 

To me it is starting to make more sense, since how can the total energy of the system change if the system is closed and we don't add anything.

If the bottom pressure increases without the upper pressure decreasing we have got something for free.

 

ie imagine the pipe rotates at its middle point.

Edited by jamese, 19 October 2015 - 07:01 AM.

[Bobby Strain]

Ah, but you do add something. You add the energy to elevate the pipe and its contents. That results in higher pressure at the bottom. You can go to Bernoulli's equation and it will become obvious to you.

 

Bobby

[jamese]

If the pipe is rotated at the middle point then nothing is added.

 

ie if the pipe is horizontal and then rotated 90 degrees at a point half way down its length

Edited by jamese, 20 October 2015 - 05:54 AM.

[samayaraj]

I don't really want to annoy him anymore, since I asked him a question and he gave me his answer, the bit in my mail in quotes in my last mail above on October 13th  was part of his response.

 

To me it is starting to make more sense, since how can the total energy of the system change if the system is closed and we don't add anything.

If the bottom pressure increases without the upper pressure decreasing we have got something for free.

 

ie imagine the pipe rotates at its middle point.

 

If the pipe is rotated at the middle point then nothing is added.

 

ie if the pipe is horizontal and then rotated 90 degrees at a point half way down its length

Could not understand what your are trying to say. We were talking about vertical coil.

 

For horizontal pipe, there wont be any pressure change if there is no change in volume and density while increasing the length of coil/ rotating it anywhere.

[jamese]

Hi Samayara,

 

Yes the scenario changed, to allow the problem to be better visualized;

 

Imagine a water filled pressurized closed horizontal pipe (a closed system) which can rotate half way down its length.

Again in this imaginary example there is no change in pipe volume as the pipe is rotated 90 degrees from the horizontal orientation to the vertical.

 

The pressure will increase at the bottom and drop at the top, the difference between top and bottom will be as per rho x g x h

 

The average pressure in the pipe remains the same, ie the pressure in the pipe when it is horizontal is the same as the pressure in the vertical midpoint of the pipe after it has been rotated.

Edited by jamese, 20 October 2015 - 08:53 AM.

[Bobby Strain]

Jamese,

      You have doubters, and I am among them. Maybe you can conduct an experiment and share the results.

 

Bobby

[breizh]

Jamese ,

 

a simple sketch ( drawing) will save hundred of words ! Really difficult to visualize your project .

 

Breizh

[samayaraj]

Jamese,

 

Find attached the excel sheet. I hope I made the right sketch what you are saying.

 

As bobby said, make a simple experiment at you home using a hose. Take a sufficient length of hose (preferably 15m) and fill it with water. Attach pressure gauges at both the ends. Keep it in the ground (horizontal elevation). You can observe the pressure in both points will be same. Keep the one end down and raise the another end of hose to top of your terrace and fix it at about 10m. You will see small pressure changes in top due to shrinking of hose. Water will compress to a limit but you cannot see much variation. In the bottom, pressure will be raised by about .981 bar. If the hose is rigid and if there is no change in volume, the top end pressure will remains same.

 

 

If the bottom pressure increases without the upper pressure decreasing we have got something for free.

 

Since you are adding head to pipe and this adds the pressure to the bottom and the average pressure of the system will increase. You are not getting something free. You are adding some energy to system by raising the pipe height. Try to look at Bernoulli or make an experiment as I said above.

Attached Files

•  pressure variation.xlsx   11.63KB   23 downloads

Edited by samayaraj, 20 October 2015 - 11:03 PM.

[jamese]

But in the example I used the pipe is rotated from horizontal to vertical at the mid point of its length.

 

Hence one end is raised and one end is lowered, by equal amounts.

 

Hence, no energy is added.

 

(The experiments you encourage me to perform would have to be extremely controlled, since even an infinitesimally small change in volume can give a loss of pressure, ie elongation of hose as it deployed into vertical position. So it is probably best to stick to the theory.

 

After my colleague stated what we are all struggling to believe, he ran an Olga model and the results of it displayed exactly what he stated)

Edited by jamese, 21 October 2015 - 01:29 AM.

[jamese]

@ breizh

 

Pressurized freshwater filled horizontal pipe closed at either end, 100m long. 

Assume 100 bar initial pressure.

 

Pipe is rotated to vertical, at a point midway down its length.

Assume no change in pipe volume as it is rotated.

Assume pipe is a closed system

 

A.

My colleague with physics PHD and 30 years in fluid dynamics tell me:

Pressure at bottom end of pipe will be 105 bar

Pressure at top end of pipe will be 95 bar

Olga model also shows this.

 

Average pressure in a closed system must stay the same, otherwise where did the extra pressure come from if no energy is added (ie still 100 bar at mid point of pipe)

 

B.

Most people want to believe pressure at top end of pipe stays at 100 bar, whilst pressure at bottom increases to 110 bar.

Average pressure is now 105 bar

 

How did average pressure increase?

Edited by jamese, 21 October 2015 - 02:39 AM.

[samayaraj]

Jamese,

 

Without giving sketch its difficult to understand for us. I hope this sketch is correct. See the attached excel.

 

The top end pressure will not change unless it is down the mid line where as the bottom pressure will increase if it is coming down the mid line. The mid point pressure will vary according to orientation.

Attached Files

•  pressure variation R1.xlsx   15.92KB   27 downloads

Edited by samayaraj, 21 October 2015 - 03:31 AM.