Testing the Theory of Practopoiesis Using Closed Loops

This is an extended version of the preprint,4 based on the lectures given at Cargese Summer School and Chernogolovka Summer School in 1993. The incompressible fluid dynamics is reformulated as dynamics of closed loops C in coordinate space. We derive explicit functional equation for the pdf of the circulation PC (Γ) which allows the scaling solutions in the inertial range of spatial scales. The pdf decays as exponential of some power of Γ3/A2, where A is the minimal area inside the loop.

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THE PROBLEM OF IDENTIFICATION OF HYDRAULIC RESISTANCE COEFFICIENTS IN MAKISTRAL GAS PIPELINE

EurasianUnionScientists ◽

10.31618/esu.2413-9335.2021.1.89.1428 ◽

2021 ◽

pp. 6-11

Author(s):

G. Gasymov

Keyword(s):

Hydraulic Resistance ◽

Group Identification ◽

Numerical Approach ◽

Transportation Systems ◽

Gas Pipeline ◽

Closed Loops ◽

Hydraulic Network ◽

Resistance Coefficients ◽

Operating Regimes

A numerical approach, based on obtaining design formulas for the determination of hydraulic resistance coefficients of sites in pipeline transportation systems in the presence of the results of observations over a gas pipeline operating regimes, is proposed. The representation of the hydraulic network in the form of a directed graph allows to essentially reduce the number of equations in the system down to the number of closed loops. In the software implementation of the method described, for the solution of practical problems, group identification of the hydraulic resistance coefficients is provided for every eventuality.

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Efficient Dynamic Analysis Method for Multibody Systems With Constraint Violation Stabilization Method

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8255 ◽

1999 ◽

Author(s):

Apiwat Reungwetwattana ◽

Shigeki Toyama

Keyword(s):

Dynamic Analysis ◽

Multibody Systems ◽

Analysis Method ◽

Stabilization Method ◽

Kinematic Constraint ◽

Constraint Violation ◽

Closed Loops ◽

Constraint Stabilization ◽

Constraint Equations ◽

Crank Mechanism

Abstract This paper presents an efficient extension of Rosenthal’s order-n algorithm for multibody systems containing closed loops. Closed topological loops are handled by cut joint technique. Violation of the kinematic constraint equations of cut joints is corrected by Baumgarte’s constraint violation stabilization method. A reliable approach for selecting the parameters used in the constraint stabilization method is proposed. Dynamic analysis of a slider crank mechanism is carried out to demonstrate efficiency of the proposed method.

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RANGE OF ALLOWABLE OPERATING CONDITIONS FOR FFTF CLOSED LOOPS.

10.2172/4731753 ◽

1969 ◽

Author(s):

D.L. Koreis ◽

C.E. Leach

Keyword(s):

Operating Conditions ◽

Closed Loops

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Two Efficient Methods for Gas Distributive Network Calculation

10.20944/preprints201808.0277.v1 ◽

2018 ◽

Author(s):

Dejan Brkić

Keyword(s):

Pressure Drop ◽

Thermodynamic Properties ◽

Gas Flow ◽

Flow Distribution ◽

Gas Pipeline ◽

Gas Flow Rate ◽

Closed Loops ◽

Loop Method ◽

Hardy Cross ◽

Flow Through

Today, two very efficient methods for calculation of flow distribution per branches of a looped gas pipeline are available. Most common is improved Hardy Cross method, while the second one is so-called unified node-loop method. For gas pipeline, gas flow rate through a pipe can be determined using Colebrook equation modified by AGA (American Gas Association) for calculation of friction factor accompanied with Darcy-Weisbach equation for pressure drop and second approach is using Renouard equation adopted for gas pipeline calculation. For the development of Renouard equation for gas pipelines some additional thermodynamic properties are involved in comparisons with Colebrook and Darcy-Weisbach model. These differences will be explained. Both equations, the Colebrook’s (accompanied with Darcy-Weisbach scheme) and Renouard’s will be used for calculation of flow through the pipes of one gas pipeline with eight closed loops which are formed by pipes. Consequently four different cases will be examined because the network is calculated using improved Hardy Cross method and unified node-loop method. Some remarks on optimization in this area of engineering also will be mentioned.

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