Hydrology without Dimensions

2021 ◽  
Author(s):  
Amilcare Porporato
Keyword(s):  
Dimension Reduction ◽  
Dimensional Analysis ◽  
Landscape Evolution ◽  
Nonlinear Models ◽  
Soil Formation ◽  
Self Similarity ◽  
Weathering Rates ◽  
Dimensionless Groups ◽  
Pi Theorem ◽  
Budyko’S Curve

<div> </div><div> <div> <div>Dimensional analysis offers an ideal playground to tackle complex hydrological problems. The powerful dimension reduction, in terms of governing dimensionless groups, afforded by the PI-theorem and the related self-similarity arguments is especially fruitful in case of nonlinear models and complex datasets. After briefly reviewing these main concepts, in this lecture I will present several applications ranging from hydrologic partitioning (Budyko's curve) and stochastic ecohydrology, to global weathering rates and soil formation, as well as landscape evolution and channelization. Since Copernicus-dot-org asks me to add at least 25 words to the abstract, I would like to thank the colleagues who supported my nomination for the Dalton medal and my many collaborators.</div> </div> </div>

Hydrology without Dimensions

2020 ◽  
Author(s):  
Amilcare Porporato
Keyword(s):  
Dimension Reduction ◽  
Dimensional Analysis ◽  
Landscape Evolution ◽  
Nonlinear Models ◽  
Soil Formation ◽  
Self Similarity ◽  
Weathering Rates ◽  
Dimensionless Groups ◽  
Pi Theorem ◽  
S Curve

<p>Dimensional analysis offers an ideal playground to tackle complex hydrological problems. The powerful dimension reduction, in terms of governing dimensionless groups, afforded by PI-theorem and related self-similarity arguments is especially fruitful in case of nonlinear models and complex datasets. After briefly reviewing these main concepts, in this lecture I will present several applications ranging from hydrologic partitioning (Budyko’s curve) and stochastic ecohydrology, to global weathering rates and soil formation, as well as landscape evolution and channelization. Since Copernicus-dot-org asks me to add at least 25 words to the abstract, I would like to thank the colleagues who supported my nomination and my many collaborators.</p><p> </p><p> </p>

Dimensional analysis revisited

2001 ◽  
Vol 215 (11) ◽  
pp. 1365-1375 ◽  
Author(s):  
R Butterfield
Keyword(s):  
Dimensional Analysis ◽  
Specific Problem ◽  
Sufficient Conditions ◽  
Optimal Number ◽  
Physical Knowledge ◽  
Dimensionless Groups ◽  
New Knowledge ◽  
Complete Set ◽  
Pi Theorem ◽  
Necessary And Sufficient

Dimensionless groups, the output of a successful dimensional analysis, are usually developed via Buckingham's pi theorem. Because this theorem provides a necessary but not sufficient condition for a solution, such a dimensional analysis may, on occasion, appear to fail. The paper presents the necessary and sufficient conditions in a simple form and builds on them to demonstrate how new physical knowledge can augment a ‘primitive’ set of dimensions to arrive at an optimal number of dimensionless groups. The formulation is used to elucidate the historical Rayleigh-Ria-bouchinsky controversy and a related thermomechanical problem is analysed to demonstrate the complete ‘new knowledge’ algorithm. Mathematica code is appended which incorporates these ideas and generates the complete set of admissible dimensionless groups for any specific problem.

scholarly journals Dimensional analysis on forest fuel bed fire spread

2018 ◽  
Vol 48 (1) ◽  
pp. 105-110
Author(s):  
Jiann C. Yang
Keyword(s):  
Dimensional Analysis ◽  
Fire Spread ◽  
Fuel Particle ◽  
Wind Condition ◽  
Spread Rate ◽  
Fuel Loading ◽  
Rate Of Spread ◽  
Dimensionless Groups ◽  
Dimensionless Correlations ◽  
Fuel Moisture Content

A dimensional analysis was performed to correlate the fuel bed fire rate of spread data previously reported in the literature. Under wind condition, six pertinent dimensionless groups were identified, namely dimensionless fire spread rate, dimensionless fuel particle size, fuel moisture content, dimensionless fuel bed depth or dimensionless fuel loading density, dimensionless wind speed, and angle of inclination of fuel bed. Under no-wind condition, five similar dimensionless groups resulted. Given the uncertainties associated with some of the parameters used to estimate the dimensionless groups, the dimensionless correlations using the resulting dimensionless groups correlate the fire rates of spread reasonably well under wind and no-wind conditions.

scholarly journals Dimensional analysis and stage-discharge relationship for weirs: a review

2017 ◽  
Vol 48 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Bijankhan ◽  
Vito Ferro
Keyword(s):  
Dimensional Analysis ◽  
Review Paper ◽  
Hydraulic Structure ◽  
Drainage Network ◽  
Self Similarity ◽  
Weir Flow ◽  
Flow Motion ◽  
Approach Channel ◽  
Rating Curves ◽  
Flow Stage

Deducing the weir flow stage-discharge relationship is a classical hydraulic problem. In this regard Buckingham’s theorem of dimensional analysis can be used to find simple and accurate formulas to obtain the rating curves of different weir types. At first, in this review paper the rectangular weir that is a very common hydraulic structure is studied. It is indicated that the crest shape, approach channel width, obliquity (angle between the weir crest and the direction normal to the flow motion) and vertical inclination (pivot weir) are the key-parameters affecting the flow over the rectangular weirs. The flow over the triangular, labyrinth, parabolic, circular, elliptical, and W-weirs are also studied using dimensional analysis and incomplete self-similarity concept. For all mentioned weirs the stage-discharge relationships are presented and the application limits are discussed. The results of this paper can be used and implemented by the irrigation and drainage network designers to simplify the procedure of weir design.

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.

Scaling Laws From Statistical Data and Dimensional Analysis

2004 ◽  
Vol 72 (5) ◽  
pp. 648-657 ◽  
Author(s):  
Patricio F. Mendez ◽  
Fernando Ordóñez
Keyword(s):  
Dimensional Analysis ◽  
Scaling Laws ◽  
Ad Hoc ◽  
Scaling Law ◽  
Engineering Systems ◽  
User Input ◽  
Backward Elimination ◽  
Dimensionless Groups ◽  
Complex Engineering ◽  
Complex Engineering Systems

Scaling laws provide a simple yet meaningful representation of the dominant factors of complex engineering systems, and thus are well suited to guide engineering design. Current methods to obtain useful models of complex engineering systems are typically ad hoc, tedious, and time consuming. Here, we present an algorithm that obtains a scaling law in the form of a power law from experimental data (including simulated experiments). The proposed algorithm integrates dimensional analysis into the backward elimination procedure of multivariate linear regressions. In addition to the scaling laws, the algorithm returns a set of dimensionless groups ranked by relevance. We apply the algorithm to three examples, in each obtaining the scaling law that describes the system with minimal user input.

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