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Solution of overdetermined nonlinear pipe network
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Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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At present, my country Sri Lanka is undergoing its worst crisis since its independence in 1948, with severe shortage of essential items like fuel, cooking gas, electricity, medicine, milk and food items. As a result, we are compelled to be at home, while thousands are protesting in the capital city of Colombo and other major cities. So, during this period I spent some time on SMath, and attempted the attached example in the internet solved by Hardy Cross Method using EXCEL Essentially it is an overdetermined nonlinear pipe network with 22 variables {pipe flows) and 23 equations (16 Nodes + 7 Loops). The solution using SMath is based on a snippet using al_nleqsolve() posted by Viacheslav N. Mezentsev (uni) in SMath Forum. Overdetermined_Nonlinear_Pipe_Network.pdf (433kb) downloaded 77 time(s). Overdetermined_Nonlinear_Pipe_Network.sm (630kb) downloaded 80 time(s).Edited by user 14 April 2022 13:55:31(UTC)
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Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
4 users thanked ndtma for this useful post.
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on 14/04/2022(UTC), on 14/04/2022(UTC), on 14/04/2022(UTC), on 12/06/2022(UTC)
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Joined: 15/07/2010(UTC) Posts: 437 Location: Beer-Sheva Was thanked: 520 time(s) in 288 post(s)
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Hello,ndtma Fragments withal_nleqsolve() can be reduced to one line. alnlegsolve(3).sm (636kb) downloaded 47 time(s).Edited by user 14 April 2022 15:44:56(UTC)
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Originally Posted by: Ber7 Hello,ndtma Fragments withal_nleqsolve()can be reduced to one line. Hello Ber7, Thank you very much for your very valuable suggestion. It works fine. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Hi Nugegodage. I hope that the problems in your country can be solved, for the better, and that you and your family are well. Thank you for this excellent example. Your worksheet with a little different setup, using tables. No one new calc actually. alnlegsolve v2.sm (905kb) downloaded 59 time(s).Best regards. Alvaro.
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Hello Nugegodage I hope that you and your family are very well in these times of crisis in your country. I have made your example in the Epanet program, the results are shown in the graph below. For the network to be valid, Node A must have an input pressure equal to or greater than 129.4 mH2O, and Node C equal to or greater than 150.28 mH2O. Best Regards Carlos
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Hi Jean, Alvaro, Carlos and others. Thanks for expressing your sentiments and encouragement. We are safe and hope the situation will settle as early as possible.
Many thanks to Alvaro and Carlos for your suggestions on the example. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Thanks for your sample. I always like your irrigation examples. Hope crisis in your country resolves too.
Regards
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Hi overlord. Thank you for the sentiments and comments. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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The subject revisited. In my original post #1, the K values were simply computed using a given formula, and head loss in each pipe computed accordingly. In Method 1 of the attached example, friction factors (f) depend on the Reynold numbers (Re) of each pipe and computed using a given formula involving Re. In Method 2, NewtonRapson function of SMath is used for the numerical solution of the implicit Colebrook-White equation to find f. Many thanks to Ber7, Alvaro and Carlos for your earlier suggestions on the subject. Overdetermined_Pipe_Network_3 LOOPS-As per CHEGUIDE_al_nleqsolve.sm (287kb) downloaded 53 time(s). Overdetermined_Pipe_Network_3 LOOPS-As per CHEGUIDE_al_nleqsolve.pdf (582kb) downloaded 32 time(s).Edited by user 26 May 2022 11:11:11(UTC)
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Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 14/10/2015(UTC) Posts: 308
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Hello ndtmda Here are the results of your example calculated with a very old version of Pipe Flow Expert. Best Regards Carlos
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Originally Posted by: CBG Hello ndtmda
Here are the results of your example calculated with a very old version of Pipe Flow Expert.
Thank you Carlos! |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Hello Carlos Can you please explain how the marked values of gauge pressures are calculated? Thank you. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 14/10/2015(UTC) Posts: 308
Was thanked: 77 time(s) in 58 post(s)
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Hello Ndtma Originally Posted by: ndtma Hello Carlos Can you please explain how the marked values of gauge pressures are calculated? Thank you. This pressure (0.9787 bar g) is caused by the water level in the tank, which is 10 meters. The pressure of 0.6553 bar g is obtained by subtracting from the inlet pressure of 0.9787 bar g. the losses in the pipe of 0.3234 bar g (3.304 m hd) The system is not correctly resolved for the pressures, since nodes 3 and 8 have pressures below atmospheric. Best Regards Carlos Edited by user 07 June 2022 05:37:33(UTC)
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 14/10/2015(UTC) Posts: 308
Was thanked: 77 time(s) in 58 post(s)
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Hello Ndtma Originally Posted by: ndtma Thank you Carlos. You're welcome. Changing the diameter of tubes 9 and 10 from 0.25 m diameter to 0.5 m, the problem of negative pressures is solved. Another way to solve it is by increasing the level below the tank from 0m to 20m. and with the liquid level at 10 m Best Regards Carlos
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Originally Posted by: CBG You're welcome.
Changing the diameter of tubes 9 and 10 from 0.25 m diameter to 0.5 m, the problem of negative pressures is solved.
Another way to solve it is by increasing the level below the tank from 0m to 20m. and with the liquid level at 10 m
Thank you Carlos. Your contributions are very much appreciated. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Originally Posted by: CBG You're welcome.
Changing the diameter of tubes 9 and 10 from 0.25 m diameter to 0.5 m, the problem of negative pressures is solved.
Another way to solve it is by increasing the level below the tank from 0m to 20m. and with the liquid level at 10 m Hello Carlos, Can you please post the Pipe Data Table (with Pipe Number, Inner diameter, ..... Re, Friction Head loss) for the case Changing the diameter of tubes 9 and 10 from 0.25 m diameter to 0.5 m.. as I get different results for this case. Hope I am not troubling you. Edited by user 11 June 2022 06:29:25(UTC)
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Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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Rank: Advanced Member Groups: Registered
Joined: 14/10/2015(UTC) Posts: 308
Was thanked: 77 time(s) in 58 post(s)
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Hello Ndtma Originally Posted by: ndtma
Hello Carlos,
Can you please post the Pipe Data Table (with Pipe Number, Inner diameter, ..... Re, Friction Head loss) for the case Changing the diameter of tubes 9 and 10 from 0.25 m diameter to 0.5 m.. as I get different results for this case.
Hope I am not troubling you.
There is no problem. Here is the requested table Best Regards Carlos
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Rank: Advanced Member Groups: Registered
Joined: 05/06/2014(UTC) Posts: 348 Location: Colombo Was thanked: 124 time(s) in 82 post(s)
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Thank you very much Carlos. |
Look within!... The secret is inside you. Best Regards Eng. NDTM Amarasekera - Sri Lanka |
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