How to solve this pipe flow problem

[FDS]

I try to solve a pipeflow problem but I have problems in doing so as I have no experience in this type of problem. In the first part of the sheet you will find the known variables. In the second part I try to calculate the different pressures. However, I have problems in setting up the equations. Would anyone be so kind to help me with this? The file is made with MC15

[Werner_E · Accepted solution]

1) V1, V2 need to be defined

2) All equations except the top 4 should be normal assignment above the solve block.h.exit:=..., etc.

3) You should solve for P1, P2, P3 AND P4 as well (4 equations, 4 variables to solve for)

4) You need guess values for P1 .. P4, not for other variables.

[FDS]

Thank you Werner that solved the issue

[FDS]

I have one additional question. How could I calculate "theoretical" V when forcing P1 to be 0 mmHg and by changing Pc? For clarity I have put both in purple. Sorry, for these obvious questions.

[MikeArmstrong]

P.1 is not being passed to your solve block as zero, it is -66kPa.

[FDS]

Mike, thanks for your reply but even if I change P1 in the solve block by 0 mmHg it will not solve.

[Werner_E]

FDS wrote:

I have one additional question. How could I calculate "theoretical" V when forcing P1 to be 0 mmHg and by changing Pc? For clarity I have put both in purple. Sorry, for these obvious questions.

Not sure if I understand what you'd like to achieve. You set P1 to 0 and want to solve for V1 instead of P1 in your solve block? This would be possible likewise but the problem is, that V and P have different units and can't be placed in the same vector. So you would have to make the solve block unitless by dividing all varaibles used by their unit and add the proper units later again - quite cumbersome.

[FDS]

Thanks Werner for your reply. I will try to explain a little bit better what I would like to achieve. I am draining fluid out of a collapsible system. When I use only gravity (siphon) Pc (pressure in the reservoir) would be 0 mmHg when I add also vacuum to increase drainage Pc would become negative. In the first part of the worksheet I try to define a flow were pressure at the entrance of the system would be as close as possible to 0, as this would not create collapse. It is quite cumbersome to estimate the flow in this way so I wondered if I could get a good estimate by using a solve block. What would you suggest to get this information?

[Werner_E]

Sorry, my fault. I haven't look to the end of your worksheet and stopped at the first solve block.

When you right click the red expression you get the option to trace the error and then you get the "real" reason for the solve block failing - "no solution found".

The reason is that with the values given the solution for the equation is a complax value (4.20 i m/s). Set the guess value for V1 to 1.2im/s you get that result.

What you are trying to solve is a simple single equation for just one variable. This can be done easily symbolically by hand. Of course you could use Mathcads symbolic to do so for you, but you should copy the expression to an empty sheet to do so, otherwise the values assigned would be substituted.

You get a handy expression for V1 depending on all the other variables you can play conveniently with now.

You may also turn it into a function of Pc or maybe even addtionally of P1 if this makes sense for you

[FDS]

Werner what you describe I had used first but the result in this case 4.183 m/s does not generate a P1 of 0 mmHg when used in the first part of the worksheet but a value of 31035 mmHg. That was why I got confused in the first place. I believe it has to do with the fact that the head losses are calculated using the original V and thus not adapted in the reversed approach. Can this be solved or is this caused by another reason? Appreciate you help in this matter!

[Werner_E]

I haven't checked all dependencies but I see that at least h.in is dependent on V1 and I guess other variables used in the calculation ov V1 at the and, too. So its no surprise you don't get P1=0 by simply changing the value of V1 at the top of the sheet.

Only way out I can see is turning all calculations which depend on V1 and Pc into functions of those variables and use those functions in both solve blocks instead of the variables.

[FDS]

Thank you for your suggestion. I tried it (I hope in a correct way) but at no avail. Would you be so kind to have another look?

[Werner_E]

FDS wrote:

Thank you for your suggestion. I tried it (I hope in a correct way) but at no avail. Would you be so kind to have another look?

Why do you think it doesn't work?

The last solve block yield Vel=304.718 cm/s and if I set V.1 and P.c to their appropriate values before the first solve block, I get the solution with P1=0. Could it be that you forgot to set P.c to -70 mmHg and so the solveblock used P.c=0?

[FDS]

Well, when I use Pc = -70mmHg and Q = 5.99 L/min (put in purple background now) then I obtain a P1 of -0.17 mmHg. When I use P1 = 0 and Pc = -70 mmHg in the last solve block I obtain 5.903 L/min. However putting this value in for the flow in the first part with Pc -70 mmHg will generate a P1 of -3.06 mmHg. Also when I put in different values of Pc in the last solve block, for example -40 mmHg I get a V1 of 85 cm/s higher than with a Pc of -70 mmHg so there must be something wrong I presume.

[Werner_E]

Not sure but I think you have setup a different situation here because you change Q and not just V1 as before!

All velocities are dependend on Q so all have to be functions in Q, otherwise it can't work of course. Depending on your need it may also be usefull to express V2 to V4 not as functions in Q but as functions in V.1

Some of the discrepancy might also be because of rounding errors. You use just three decimals of the result. It may be a better idea to put the last solve block which yields V1 before the first one which calculates P1 to P4, so you can use the exact result without the need for manual copy and paste.

[Werner_E]

Upon rethinkig the whole thing I guess its best to express all as functions in Q.

See attached.

[FDS]

Werner, I admire the way you support this forum. This is really helpful. I will look at it more closely tomorrow but at first sight this seems to solve all previous problems. Thanks a lot.