Sizing pipes without iterative calculus: Solutions for head loss, flow discharge and diameter

Brkić, Dejan; Stajić, Zoran; Živković, Marko

doi:10.1109/iccc57093.2023.10178917

Cited by 2 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where D is the inner pipe diameter (m); Q is the gas flow through the pipe in real conditions of pressure and temperature (m 3 /s); note that the Renouard relation, on the contrary, operates with Q st , gas flow at standard conditions; p st is the standard pressure of 10 5 Pa; u is the gas velocity (m/s); here, used for optimisation, u = 15 m/s; p is the real pressure in pipes (Pa); here, p/p st ≈ 4; π is the Ludolpf number ≈ 3.1415. Pipe diameters as part of a gas network with loops are optimised in this article, which is a different problem [88][89][90] compared to determining the diameter of a single pipe (a solution to the problem of a single pipe in particular conditions is given in [91][92][93]103]). In any case, pipes are standardised and therefore they must be chosen from the prescribed list available for sale on the market [94].…”

Section: Relation Among Gas Flow Pressure and Pipe Diametermentioning

confidence: 99%

Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops

Brkić

2024

Computation

Self Cite

View full text Add to dashboard Cite

Closed-loop pipe systems allow the possibility of the flow of gas from both directions across each route, ensuring supply continuity in the event of a failure at one point, but their main shortcoming is in the necessity to model them using iterative methods. Two iterative methods of determining the optimal pipe diameter in a gas distribution network with closed loops are described in this paper, offering the advantage of maintaining the gas velocity within specified technical limits, even during peak demand. They are based on the following: (1) a modified Hardy Cross method with the correction of the diameter in each iteration and (2) the node-loop method, which provides a new diameter directly in each iteration. The calculation of the optimal pipe diameter in such gas distribution networks relies on ensuring mass continuity at nodes, following the first Kirchhoff law, and concluding when the pressure drops in all the closed paths are algebraically balanced, adhering to the second Kirchhoff law for energy equilibrium. The presented optimisation is based on principles developed by Hardy Cross in the 1930s for the moment distribution analysis of statically indeterminate structures. The results are for steady-state conditions and for the highest possible estimated demand of gas, while the distributed gas is treated as a noncompressible fluid due to the relatively small drop in pressure in a typical network of pipes. There is no unique solution; instead, an infinite number of potential outcomes exist, alongside infinite combinations of pipe diameters for a given fixed flow pattern that can satisfy the first and second Kirchhoff laws in the given topology of the particular network at hand.

show abstract

Section: Relation Among Gas Flow Pressure and Pipe Diametermentioning

confidence: 99%

Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops

Brkić

2024

Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Combining the Colebrook's and the Darcy-Weisbach equation together with the Reynolds number Re, the problem of the unknown flow discharge Q can be solved easily in a closed-form solution [12] (this closed-form solution is available together with related numerical example in [13]);…”

mentioning

confidence: 99%

“…A short overview of previous works for solving all three types of the described problems, together with numerical examples, is given in [13].…”

mentioning

confidence: 99%

Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter

Brkić,

Praks,

Praksová

et al. 2023

Axioms

Self Cite

View full text Add to dashboard Cite

This study provides novel and accurate symbolic regression-based solutions for the calculation of pipe diameter when flow rate and pressure drop (head loss) are known, together with the length of the pipe, absolute inner roughness of the pipe, and kinematic viscosity of the fluid. PySR and Eureqa, free and open-source symbolic regression tools, are used for discovering simple and accurate approximate formulas. Three approaches are used: (1) brute force of computing power, which provides results based on raw input data; (2) an improved method where input parameters are transformed through the Lambert W-function; (3) a method where the results are based on inputs and the Colebrook equation transformed through new suitable dimensionless groups. The discovered models were simplified by the WolframAlpha simplify tool and/or the equivalent Matlab Symbolic toolbox. Novel models make iterative calculus redundant; they are simple for computer coding while the relative error remains lower compared with the solution through nomograms. The symbolic-regression solutions discovered by brute force computing power discard the kinematic viscosity of the fluid as an input parameter, implying that it has the least influence.

show abstract

Sizing pipes without iterative calculus: Solutions for head loss, flow discharge and diameter

Cited by 2 publications

References 24 publications

Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops

Two Iterative Methods for Sizing Pipe Diameters in Gas Distribution Networks with Loops

Symbolic Regression Approaches for the Direct Calculation of Pipe Diameter

Contact Info

Product

Resources

About