Hydraulic Calculation Principle and Todini Formulation Algorithm Analysis

Abstract:

The Todini formulation is effectively a type of Q–H equation formulation and it has an extremely efficient approach to the inversion of the Jacobian matrix by partitioning the governing equations in a smart way. The advantage of the Todini formulation is that the Jacobian matrices are symmetric. The aim of this paper is to study the hydraulic calculation principle and analyze the relationship between physical parameters and hydraulic calculation for each step. The comprehensive resistance factor (r) is affected by the loss coefficient along the tracks (λ), and the loss coefficient along the tracks (λ) is affected by the Reynolds number (Re), the Reynolds number (Re) is affected by the kinematic viscosity (), and the kinematic viscosity () is affected by the temperature (T). The coupling of hydraulic characteristics and thermal properties of the fluid can be got by modifying the physical parameters, and this article provided evidences for the further study.

• Periodical: Applied Mechanics and Materials (Volumes 675-677)
• Pages: 927-933
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.675-677.927
• Online since: October 2014
• Authors: Xin Zhao, Qi Fen Li, Jing Jing Xu, Li Fei Song, Lin Hui Zhao, Jia Lin Zhao, Lei Zhang
• Keywords: Algorithm Analysis, Hydraulic Calculation Principle, Todini Formulation

References

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[3] A.R. Simpson and S. Elhay. Formulating the water distribution system equations in terms of heads and velocity., 10th Annual Symposium on Water Distribution Systems Analysis, American Society of Civil Engineers, Kruger National Park, South Africa, 17-20 August(2008).

DOI: 10.1061/41024(340)68