The Pi theorem of dimensional analysis

1957 ◽  
Vol 1 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Louis Brand
Keyword(s):  
Dimensional Analysis ◽  
Pi Theorem

scholarly journals Characterization of venturi injector using dimensional analysis

2019 ◽  
Vol 23 (7) ◽  
pp. 484-491 ◽  
Author(s):  
Luiz R. Sobenko ◽  
José A. Frizzone ◽  
Antonio P. de Camargo ◽  
Ezequiel Saretta ◽  
Hermes S. da Rocha
Keyword(s):  
Dimensional Analysis ◽  
Flow Rate ◽  
Injection Rate ◽  
Operating Conditions ◽  
Functional Tests ◽  
Injection Flow Rate ◽  
Injection Flow ◽  
Hydraulic Conditions ◽  
Fluid Properties ◽  
Pi Theorem

ABSTRACT Venturi injectors are commonly employed for fertigation purposes in agriculture, in which they draw fertilizer from a tank into the irrigation pipeline. The knowledge of the amount of liquid injected by this device is used to ensure an adequate fertigation operation and management. The objectives of this research were (1) to carry out functional tests of Venturi injectors following requirements stated by ISO 15873; and (2) to model the injection rate using dimensional analysis by the Buckingham Pi theorem. Four models of Venturi injectors were submitted to functional tests using clean water as motive and injected fluid. A general model for predicting injection flow rate was proposed and validated. In this model, the injection flow rate depends on the fluid properties, operating hydraulic conditions and geometrical characteristics of the Venturi injector. Another model for estimating motive flow rate as a function of inlet pressure and differential pressure was adjusted and validated for each size of Venturi injector. Finally, an example of an application was presented. The Venturi injector size was selected to fulfill the requirements of the application and the operating conditions were estimated using the proposed models.

A Numerical Model for the Identification of the Structural Damages in Rolling Contact Bearings Using Matrix Method of Dimensional Analysis

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
I. M. Jamadar ◽  
D. P. Vakharia
Keyword(s):  
Dimensional Analysis ◽  
Matrix Method ◽  
Energy Levels ◽  
Rolling Contact ◽  
Outer Race ◽  
Operating Load ◽  
Combined Use ◽  
Dependent Parameter ◽  
Multiple Variables ◽  
Pi Theorem

The damages to the structural elements, viz., inner race, outer race, rollers, cage, etc., of rolling contact bearings if not detected in time can cause tragic failures of the machineries supported by these bearings. The operating parameters like variations in the machinery speed, unbalance, operating load, etc., can cause a bearing to vibrate at higher energy levels and consequently will accelerate its wear. An attempt is made in this study, and a generalized model is developed using matrix method of dimensional analysis (MMDA) that predicted the response and correlated the dependent parameter, i.e., response with the significant independent parameters. Combined use of response surface methodology (RSM) is made to explore the dependence of various factors such as size of the defect, unbalance, speed, and their interactions on the vibration characteristics of the bearings. It is observed from the study that the model developed based on the MMDA has provided an efficient approach in recognizing the damaged bearing state, which can be easily implemented in the condition-based preventive maintenance strategies. Also, the effectiveness of MMDA as compared to the conventional Buckingham's pi theorem in the dimensional analysis (DA) practice, especially in the problems involving multiple variables, is shown in this study.

Dimensional Analysis and the Buckingham Pi Theorem

1972 ◽  
Vol 40 (12) ◽  
pp. 1815-1822 ◽  
Author(s):  
John H. Evans
Keyword(s):  
Dimensional Analysis ◽  
Pi Theorem

scholarly journals Dimensional analysis of partial discharge initiated by a metallic particle adhering to the spacer surface in a gas-insulated system

2021 ◽  
Vol 6 (2) ◽  
pp. 91-100
Author(s):  
Firmansyah Nur Budiman ◽  
Ali Muhammad Rushdi
Keyword(s):  
Dimensional Analysis ◽  
Quantitative Information ◽  
Qualitative Reasoning ◽  
Partial Discharges ◽  
Sulphur Hexafluoride ◽  
Metallic Particles ◽  
Matrix Operations ◽  
Voltage Application ◽  
The Common ◽  
Pi Theorem

Partial discharges (PDs) constitute important phenomena in a Gas-Insulated System (GIS) that warrant recognition (and, subsequently, mitigation) as they are obvious symptoms of system degradation. This paper proposes the application of dimensional analysis, based on Buckingham pi theorem, for characterizing PDs provoked by the presence of metallic particles adhering to the spacer surface in a GIS employing SF6 (Sulphur hexafluoride). The ultimate goal of the analysis is to formulate the relationships that express three PD indicator quantities, namely current, charge, and energy, in terms of six independent quantities that collectively influence these indicators. These six quantities (henceforth referred to as the influencing, determining or affecting variables) include the level of applied voltage, the SF6 pressure, the length and position of the particle on the spacer, the duration of voltage application, and the gap between electrodes. To compute the pertinent dimensionless products, we implement three computational methods based on matrix operations. These three methods produce exactly the same dimensionless products, which are subsequently used for constructing the models depicting the relationships between each of the three PD dependent quantities and the common six determining variables. The models derived provide partial quantitative information and facilitate qualitative reasoning about the considered phenomenon.

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