This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
The document provides an overview of dimensional analysis and its applications in fluid mechanics. Dimensional analysis is a tool used to correlate analytical and experimental results and predict prototype behavior from model measurements. It involves identifying the fundamental dimensions of variables (e.g. mass, length, time) and establishing dimensionless relationships between variables using methods like Rayleigh's or Buckingham's π-theorem. Dimensional analysis is important for model analysis where dynamic similarity between a model and prototype must be achieved. The document discusses different model laws used to design models for similarity based on dominant forces like viscosity, gravity, etc. It also provides scale ratios required for geometric, kinematic and dynamic similarity.
008a (PPT) Dim Analysis & Similitude.pdfhappycocoman
This document discusses dimensional analysis and similitude. It defines dimensional analysis as the study of relations between physical quantities based on their units and dimensions. Dimensional analysis involves identifying the base quantities like length, mass, time that physical quantities are measured in. Dimensional analysis is useful for checking equations for dimensional homogeneity and developing scaling laws. The document discusses Rayleigh's and Buckingham π theorem methods of dimensional analysis. It also discusses the three types of similitude required for model analysis: geometric, kinematic and dynamic similitude. Finally, it defines several common dimensionless numbers like Reynolds number, Froude number, Euler number, Weber number and Mach number in terms of dominant forces.
Dimensional analysis is a mathematical technique used to solve engineering problems by studying dimensions. It relies on the principle that dimensionally homogeneous equations will have identical powers of fundamental dimensions (mass, length, time, etc.) on both sides. There are two main methods: Rayleigh's method determines relationships between variables based on dimensional homogeneity. Buckingham's π-theorem determines the minimum number of dimensionless groups needed to describe a phenomenon with multiple variables. Model analysis uses scaled models and dimensional analysis to predict the performance of full-scale structures before being built. Complete similitude between a model and prototype, including geometric, kinematic, and dynamic similarity, allows test results from the model to accurately represent the prototype.
The document discusses dimensional analysis and dimensionless numbers. It defines dimensionless numbers as ratios of different forces that give a dimensionless quantity. Some important dimensionless numbers discussed are Reynolds number, Froude number, Euler number, Weber number, and Mach number. Equations for each of these numbers are provided showing the ratio of inertia force to viscous, gravity, pressure, surface tension, and elastic forces respectively. Methods of dimensional analysis including Rayleigh's method and Buckingham π-theorem are also summarized. Repeating variables, their selection criteria, and example problems applying Buckingham π-theorem are outlined in brief.
Dimensional analysis Similarity laws Model laws R A Shah
Rayleigh's method- Theory and Examples
Buckingham Pi Theorem- Theory and Examples
Model and Similitude
Forces on Fluid
Dimensionless Numbers
Model laws
Distorted models
The document discusses dimensional analysis, similitude, and model analysis. It provides background on how dimensional analysis and model testing are used to study fluid mechanics problems. Dimensional analysis uses the dimensions of physical quantities to determine which parameters influence a phenomenon. Model testing in a laboratory allows measurements to be applied to larger scale systems using similitude. Buckingham's π-theorem is introduced as a way to non-dimensionalize variables when there are more variables than fundamental dimensions. Rayleigh's and Buckingham's methods are demonstrated on an example of determining the resisting force on an aircraft.
This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
The document provides an overview of dimensional analysis and its applications in fluid mechanics. Dimensional analysis is a tool used to correlate analytical and experimental results and predict prototype behavior from model measurements. It involves identifying the fundamental dimensions of variables (e.g. mass, length, time) and establishing dimensionless relationships between variables using methods like Rayleigh's or Buckingham's π-theorem. Dimensional analysis is important for model analysis where dynamic similarity between a model and prototype must be achieved. The document discusses different model laws used to design models for similarity based on dominant forces like viscosity, gravity, etc. It also provides scale ratios required for geometric, kinematic and dynamic similarity.
008a (PPT) Dim Analysis & Similitude.pdfhappycocoman
This document discusses dimensional analysis and similitude. It defines dimensional analysis as the study of relations between physical quantities based on their units and dimensions. Dimensional analysis involves identifying the base quantities like length, mass, time that physical quantities are measured in. Dimensional analysis is useful for checking equations for dimensional homogeneity and developing scaling laws. The document discusses Rayleigh's and Buckingham π theorem methods of dimensional analysis. It also discusses the three types of similitude required for model analysis: geometric, kinematic and dynamic similitude. Finally, it defines several common dimensionless numbers like Reynolds number, Froude number, Euler number, Weber number and Mach number in terms of dominant forces.
Dimensional analysis is a mathematical technique used to solve engineering problems by studying dimensions. It relies on the principle that dimensionally homogeneous equations will have identical powers of fundamental dimensions (mass, length, time, etc.) on both sides. There are two main methods: Rayleigh's method determines relationships between variables based on dimensional homogeneity. Buckingham's π-theorem determines the minimum number of dimensionless groups needed to describe a phenomenon with multiple variables. Model analysis uses scaled models and dimensional analysis to predict the performance of full-scale structures before being built. Complete similitude between a model and prototype, including geometric, kinematic, and dynamic similarity, allows test results from the model to accurately represent the prototype.
The document discusses dimensional analysis and dimensionless numbers. It defines dimensionless numbers as ratios of different forces that give a dimensionless quantity. Some important dimensionless numbers discussed are Reynolds number, Froude number, Euler number, Weber number, and Mach number. Equations for each of these numbers are provided showing the ratio of inertia force to viscous, gravity, pressure, surface tension, and elastic forces respectively. Methods of dimensional analysis including Rayleigh's method and Buckingham π-theorem are also summarized. Repeating variables, their selection criteria, and example problems applying Buckingham π-theorem are outlined in brief.
Dimensional analysis Similarity laws Model laws R A Shah
Rayleigh's method- Theory and Examples
Buckingham Pi Theorem- Theory and Examples
Model and Similitude
Forces on Fluid
Dimensionless Numbers
Model laws
Distorted models
The document discusses dimensional analysis, similitude, and model analysis. It provides background on how dimensional analysis and model testing are used to study fluid mechanics problems. Dimensional analysis uses the dimensions of physical quantities to determine which parameters influence a phenomenon. Model testing in a laboratory allows measurements to be applied to larger scale systems using similitude. Buckingham's π-theorem is introduced as a way to non-dimensionalize variables when there are more variables than fundamental dimensions. Rayleigh's and Buckingham's methods are demonstrated on an example of determining the resisting force on an aircraft.
This document discusses dimensional analysis and model analysis. It begins by introducing dimensional analysis as a technique that uses the dimensions of physical quantities to understand phenomena. It then describes the two types of dimensions: fundamental dimensions like length, time, and mass, and secondary dimensions that are combinations of fundamental ones, like velocity.
It presents the methodology of dimensional analysis, which requires equations to be dimensionally homogeneous. Two common methods are described: Rayleigh's method and Buckingham's pi-theorem. Rayleigh's method can be used for up to 4 variables while Buckingham's pi-theorem groups variables into dimensionless pi-terms. Model analysis is introduced as an experimental method using scale models, and the importance of similitude or
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. Dimensional analysis relies on equations being dimensionally homogeneous with identical powers of fundamental dimensions on both sides.
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. The key concepts are that theoretical equations must be dimensionally homogeneous and empirical equations have limited applications. Dimensional analysis methods include Rayleigh's method of exponential relationships and Buckingham's Π-method of grouping variables into dimensionless terms.
- Dimensional analysis is a technique used to determine the relationship between variables in a physical phenomenon based on their dimensions and units.
- It allows reducing the number of variables needed to describe a phenomenon through the use of dimensionless parameters known as π terms.
- Lord Rayleigh and Buckingham developed systematic methods for dimensional analysis. Buckingham's π-method involves identifying all variables, their dimensions, and grouping them into as many dimensionless π terms as needed to describe the phenomenon.
The resisting force R of a supersonic plane depends on its length l, velocity V, air viscosity μ, air density ρ, and bulk modulus of air k. Using Buckingham's π-theorem with repeating variables l, V, and ρ, the relationship can be written as three dimensionless terms:
π1 = R/lVρ, π2 = μ/lV2ρ, π3 = k/lV2ρ. Equating the powers of fundamental dimensions gives the relationship between the resisting force R and the variables it depends on.
This document discusses moments, skewness, kurtosis, and several statistical distributions including binomial, Poisson, hypergeometric, and chi-square distributions. It defines key terms such as moment ratios, central moments, theorems, skewness, kurtosis, and correlation. Properties and applications of the binomial, Poisson, and hypergeometric distributions are provided. Finally, the document discusses the chi-square test for goodness of fit and independence.
Similitude and Dimensional Analysis -Hydraulics engineering Civil Zone
This document discusses similitude and dimensional analysis for model testing in hydraulic engineering. It introduces key concepts like similitude, prototype, model, geometric similarity, kinematic similarity, dynamic similarity, dimensionless numbers, and model laws. Reynolds model law is described in detail, which states that the Reynolds number must be equal between the model and prototype for problems dominated by viscous forces, such as pipe flow. An example problem demonstrates how to calculate the velocity and flow rate in a hydraulic model based on given prototype parameters and Reynolds model law.
https://utilitasmathematica.com/index
Our journal has to a fully open-access format is a significant step toward advancing the principles of open science and equitable access to knowledge. However, this transition also brings challenges, such as ensuring sustainable funding models and maintaining rigorous peer-review standards.
https://utilitasmathematica.com/index.php/Index
Our Journal has recently transitioned to becoming a fully open-access journal. This transition marks a significant shift in the landscape of academic publishing, aiming to provide numerous benefits to both authors and readers. Open access has the potential to democratize knowledge, enhance research impact, and foster greater collaboration within the academic community.
Utilitas Mathematica Journal is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.The journal publishes original research in all areas of pure and applied mathematics, statistics.
Utilitas Mathematica Journal. It's our journal publishes original research in all areas of pure and applied mathematics.Number Theory,Operations Research,Mathematical Biology,and it's the Utilitas Mathematica Journal commits to strengthening our professional .
The document discusses dimensional analysis and Buckingham Pi theorem. It begins by defining dimensions, units, and fundamental vs. derived dimensions. It then discusses dimensional homogeneity and uses examples to show how dimensional analysis can be used to identify non-dimensional parameters and reduce the number of variables in equations. The Buckingham Pi theorem is introduced as a method to systematically create dimensionless pi terms from physical variables. Steps of the theorem and examples applying it are provided. Overall, the document provides an overview of dimensional analysis and Buckingham Pi theorem as tools for understanding relationships between physical quantities and reducing complexity in experimental modeling.
The document is a report submitted by three students on surface and volume integrals and linear systems in real world problems. It discusses line, surface, and volume integrals and defines linear systems. It provides examples of applying integrals in electrostatics, magnetism, and gravity. It also discusses applications of linear systems and integrals in areas like fluid dynamics, mass continuity, and conservation of momentum. The conclusion reiterates that linear systems can have zero, one, or infinite solutions depending on consistency and independence, and methods for solving systems like graphing, substitution, and addition/subtraction are introduced.
This document provides an overview of key concepts in physics, including:
- Physics is the science that describes the basic components of the universe and forces. It underpins other sciences.
- Physical quantities have numerical values and units, and can be basic or derived. Basic quantities include length, mass, and time.
- Vectors have magnitude and direction, while scalars only have magnitude. Examples of each are provided.
- Methods for adding and subtracting vectors graphically and by components are described. Properties of vector operations are also summarized.
This document provides information about an Advanced Physics course offered at Mbeya University of Science and Technology. The course code is NS 6141 and it covers dimensions of physical quantities, atomic theory, and radioactivity. It will be taught on Fridays from 7:30-9:45am in the Sports Hall by instructor Charles Kadala. Students will be assessed based on two class tests, assignments, and an end of semester exam. The document also provides details on the concepts that will be covered related to dimensions of physical quantities, including defining, explaining, deriving formulas for, and checking formulas using dimensions.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
The document discusses physical hydraulic model testing of structures. It provides an outline for a one-day training on the topic. The training will cover:
- What hydraulic structures are and why physical testing is conducted
- The hydraulic design procedure and testing options
- Conducting a SWOT analysis of physical model testing
It will also cover the theoretical background of physical modeling, including similitude laws and dimensionless numbers. A practical exercise on computing model dimensions is included. The training will conclude with a case study of physical model testing conducted for the Diamer Basha Dam project in Pakistan.
Lagrange's Mean Value Theorem, also known as the Mean Value Theorem (MVT), is a fundamental result in calculus that describes the relationship between the slope of a tangent to a function's graph and the average rate of change of the function over an interval. It is a crucial tool in analyzing the behavior of functions and has wide-ranging applications in various areas of mathematics and science. The Mean Value Theorem states that if a function f satisfies the following conditions: 1. Establish inequalities: By comparing the slope of the tangent to the average rate of change, the Mean Value Theorem can be used to establish inequalities involving function values.
2. Prove Rolle's Theorem: Rolle's Theorem is a special case of the Mean Value Theorem that applies to functions that have zero values at the endpoints of an interval. 3. Analyze Rolle's Theorem: The Mean Value Theorem can be used to analyze the conditions for Rolle's Theorem and understand the geometric implications of the theorem.
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
Considerations on the genetic equilibrium lawIOSRJM
In the first part of the paper I willpresentabriefreview on the Hardy-Weinberg equilibrium and it's formulation in projective algebraicgeometry. In the second and last part I willdiscussexamples and generalizations on the topic
This document discusses dimensional analysis and model analysis. It begins by introducing dimensional analysis as a technique that uses the dimensions of physical quantities to understand phenomena. It then describes the two types of dimensions: fundamental dimensions like length, time, and mass, and secondary dimensions that are combinations of fundamental ones, like velocity.
It presents the methodology of dimensional analysis, which requires equations to be dimensionally homogeneous. Two common methods are described: Rayleigh's method and Buckingham's pi-theorem. Rayleigh's method can be used for up to 4 variables while Buckingham's pi-theorem groups variables into dimensionless pi-terms. Model analysis is introduced as an experimental method using scale models, and the importance of similitude or
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. Dimensional analysis relies on equations being dimensionally homogeneous with identical powers of fundamental dimensions on both sides.
Dimensional analysis is a mathematical technique used to establish relationships between physical quantities in fluid phenomena. It involves considering the dimensions of quantities and grouping dimensionless parameters to better understand flows. Dimensional analysis provides guidance for experimental work by indicating important influencing factors. It is applied to develop equations, convert between units, reduce experimental variables, and enable model studies through similitude. The key concepts are that theoretical equations must be dimensionally homogeneous and empirical equations have limited applications. Dimensional analysis methods include Rayleigh's method of exponential relationships and Buckingham's Π-method of grouping variables into dimensionless terms.
- Dimensional analysis is a technique used to determine the relationship between variables in a physical phenomenon based on their dimensions and units.
- It allows reducing the number of variables needed to describe a phenomenon through the use of dimensionless parameters known as π terms.
- Lord Rayleigh and Buckingham developed systematic methods for dimensional analysis. Buckingham's π-method involves identifying all variables, their dimensions, and grouping them into as many dimensionless π terms as needed to describe the phenomenon.
The resisting force R of a supersonic plane depends on its length l, velocity V, air viscosity μ, air density ρ, and bulk modulus of air k. Using Buckingham's π-theorem with repeating variables l, V, and ρ, the relationship can be written as three dimensionless terms:
π1 = R/lVρ, π2 = μ/lV2ρ, π3 = k/lV2ρ. Equating the powers of fundamental dimensions gives the relationship between the resisting force R and the variables it depends on.
This document discusses moments, skewness, kurtosis, and several statistical distributions including binomial, Poisson, hypergeometric, and chi-square distributions. It defines key terms such as moment ratios, central moments, theorems, skewness, kurtosis, and correlation. Properties and applications of the binomial, Poisson, and hypergeometric distributions are provided. Finally, the document discusses the chi-square test for goodness of fit and independence.
Similitude and Dimensional Analysis -Hydraulics engineering Civil Zone
This document discusses similitude and dimensional analysis for model testing in hydraulic engineering. It introduces key concepts like similitude, prototype, model, geometric similarity, kinematic similarity, dynamic similarity, dimensionless numbers, and model laws. Reynolds model law is described in detail, which states that the Reynolds number must be equal between the model and prototype for problems dominated by viscous forces, such as pipe flow. An example problem demonstrates how to calculate the velocity and flow rate in a hydraulic model based on given prototype parameters and Reynolds model law.
https://utilitasmathematica.com/index
Our journal has to a fully open-access format is a significant step toward advancing the principles of open science and equitable access to knowledge. However, this transition also brings challenges, such as ensuring sustainable funding models and maintaining rigorous peer-review standards.
https://utilitasmathematica.com/index.php/Index
Our Journal has recently transitioned to becoming a fully open-access journal. This transition marks a significant shift in the landscape of academic publishing, aiming to provide numerous benefits to both authors and readers. Open access has the potential to democratize knowledge, enhance research impact, and foster greater collaboration within the academic community.
Utilitas Mathematica Journal is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.The journal publishes original research in all areas of pure and applied mathematics, statistics.
Utilitas Mathematica Journal. It's our journal publishes original research in all areas of pure and applied mathematics.Number Theory,Operations Research,Mathematical Biology,and it's the Utilitas Mathematica Journal commits to strengthening our professional .
The document discusses dimensional analysis and Buckingham Pi theorem. It begins by defining dimensions, units, and fundamental vs. derived dimensions. It then discusses dimensional homogeneity and uses examples to show how dimensional analysis can be used to identify non-dimensional parameters and reduce the number of variables in equations. The Buckingham Pi theorem is introduced as a method to systematically create dimensionless pi terms from physical variables. Steps of the theorem and examples applying it are provided. Overall, the document provides an overview of dimensional analysis and Buckingham Pi theorem as tools for understanding relationships between physical quantities and reducing complexity in experimental modeling.
The document is a report submitted by three students on surface and volume integrals and linear systems in real world problems. It discusses line, surface, and volume integrals and defines linear systems. It provides examples of applying integrals in electrostatics, magnetism, and gravity. It also discusses applications of linear systems and integrals in areas like fluid dynamics, mass continuity, and conservation of momentum. The conclusion reiterates that linear systems can have zero, one, or infinite solutions depending on consistency and independence, and methods for solving systems like graphing, substitution, and addition/subtraction are introduced.
This document provides an overview of key concepts in physics, including:
- Physics is the science that describes the basic components of the universe and forces. It underpins other sciences.
- Physical quantities have numerical values and units, and can be basic or derived. Basic quantities include length, mass, and time.
- Vectors have magnitude and direction, while scalars only have magnitude. Examples of each are provided.
- Methods for adding and subtracting vectors graphically and by components are described. Properties of vector operations are also summarized.
This document provides information about an Advanced Physics course offered at Mbeya University of Science and Technology. The course code is NS 6141 and it covers dimensions of physical quantities, atomic theory, and radioactivity. It will be taught on Fridays from 7:30-9:45am in the Sports Hall by instructor Charles Kadala. Students will be assessed based on two class tests, assignments, and an end of semester exam. The document also provides details on the concepts that will be covered related to dimensions of physical quantities, including defining, explaining, deriving formulas for, and checking formulas using dimensions.
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
The document discusses physical hydraulic model testing of structures. It provides an outline for a one-day training on the topic. The training will cover:
- What hydraulic structures are and why physical testing is conducted
- The hydraulic design procedure and testing options
- Conducting a SWOT analysis of physical model testing
It will also cover the theoretical background of physical modeling, including similitude laws and dimensionless numbers. A practical exercise on computing model dimensions is included. The training will conclude with a case study of physical model testing conducted for the Diamer Basha Dam project in Pakistan.
Lagrange's Mean Value Theorem, also known as the Mean Value Theorem (MVT), is a fundamental result in calculus that describes the relationship between the slope of a tangent to a function's graph and the average rate of change of the function over an interval. It is a crucial tool in analyzing the behavior of functions and has wide-ranging applications in various areas of mathematics and science. The Mean Value Theorem states that if a function f satisfies the following conditions: 1. Establish inequalities: By comparing the slope of the tangent to the average rate of change, the Mean Value Theorem can be used to establish inequalities involving function values.
2. Prove Rolle's Theorem: Rolle's Theorem is a special case of the Mean Value Theorem that applies to functions that have zero values at the endpoints of an interval. 3. Analyze Rolle's Theorem: The Mean Value Theorem can be used to analyze the conditions for Rolle's Theorem and understand the geometric implications of the theorem.
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
Considerations on the genetic equilibrium lawIOSRJM
In the first part of the paper I willpresentabriefreview on the Hardy-Weinberg equilibrium and it's formulation in projective algebraicgeometry. In the second and last part I willdiscussexamples and generalizations on the topic
Similar to Open Channel Flow Dimensional Analysis.pdf (20)
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
VARIABLE FREQUENCY DRIVE. VFDs are widely used in industrial applications for...PIMR BHOPAL
Variable frequency drive .A Variable Frequency Drive (VFD) is an electronic device used to control the speed and torque of an electric motor by varying the frequency and voltage of its power supply. VFDs are widely used in industrial applications for motor control, providing significant energy savings and precise motor operation.
Generative AI Use cases applications solutions and implementation.pdfmahaffeycheryld
Generative AI solutions encompass a range of capabilities from content creation to complex problem-solving across industries. Implementing generative AI involves identifying specific business needs, developing tailored AI models using techniques like GANs and VAEs, and integrating these models into existing workflows. Data quality and continuous model refinement are crucial for effective implementation. Businesses must also consider ethical implications and ensure transparency in AI decision-making. Generative AI's implementation aims to enhance efficiency, creativity, and innovation by leveraging autonomous generation and sophisticated learning algorithms to meet diverse business challenges.
https://www.leewayhertz.com/generative-ai-use-cases-and-applications/
AI for Legal Research with applications, toolsmahaffeycheryld
AI applications in legal research include rapid document analysis, case law review, and statute interpretation. AI-powered tools can sift through vast legal databases to find relevant precedents and citations, enhancing research accuracy and speed. They assist in legal writing by drafting and proofreading documents. Predictive analytics help foresee case outcomes based on historical data, aiding in strategic decision-making. AI also automates routine tasks like contract review and due diligence, freeing up lawyers to focus on complex legal issues. These applications make legal research more efficient, cost-effective, and accessible.
Build the Next Generation of Apps with the Einstein 1 Platform.
Rejoignez Philippe Ozil pour une session de workshops qui vous guidera à travers les détails de la plateforme Einstein 1, l'importance des données pour la création d'applications d'intelligence artificielle et les différents outils et technologies que Salesforce propose pour vous apporter tous les bénéfices de l'IA.
Rainfall intensity duration frequency curve statistical analysis and modeling...bijceesjournal
Using data from 41 years in Patna’ India’ the study’s goal is to analyze the trends of how often it rains on a weekly, seasonal, and annual basis (1981−2020). First, utilizing the intensity-duration-frequency (IDF) curve and the relationship by statistically analyzing rainfall’ the historical rainfall data set for Patna’ India’ during a 41 year period (1981−2020), was evaluated for its quality. Changes in the hydrologic cycle as a result of increased greenhouse gas emissions are expected to induce variations in the intensity, length, and frequency of precipitation events. One strategy to lessen vulnerability is to quantify probable changes and adapt to them. Techniques such as log-normal, normal, and Gumbel are used (EV-I). Distributions were created with durations of 1, 2, 3, 6, and 24 h and return times of 2, 5, 10, 25, and 100 years. There were also mathematical correlations discovered between rainfall and recurrence interval.
Findings: Based on findings, the Gumbel approach produced the highest intensity values, whereas the other approaches produced values that were close to each other. The data indicates that 461.9 mm of rain fell during the monsoon season’s 301st week. However, it was found that the 29th week had the greatest average rainfall, 92.6 mm. With 952.6 mm on average, the monsoon season saw the highest rainfall. Calculations revealed that the yearly rainfall averaged 1171.1 mm. Using Weibull’s method, the study was subsequently expanded to examine rainfall distribution at different recurrence intervals of 2, 5, 10, and 25 years. Rainfall and recurrence interval mathematical correlations were also developed. Further regression analysis revealed that short wave irrigation, wind direction, wind speed, pressure, relative humidity, and temperature all had a substantial influence on rainfall.
Originality and value: The results of the rainfall IDF curves can provide useful information to policymakers in making appropriate decisions in managing and minimizing floods in the study area.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
2. Learning Objectives
1. Introduction to Dimensions & Units
2. Use of DimensionalAnalysis
3. Dimensional Homogeneity
4. Methods of DimensionalAnalysis
5. Rayleigh’s Method
4. Many practical real flow problems in fluid mechanics can be solved by using
equations and analytical procedures. However, solutions of some real flow
problems depend heavily on experimental data.
Sometimes, the experimental work in the laboratory is not only time-consuming,
but also expensive. So, the main goal is to extract maximum information from
fewest experiments.
In this regard, dimensional analysis is an important tool that helps in correlating
analytical results with experimental data and to predict the prototype behavior from
the measurements on the model.
Introduction
5. Dimensions and Units
In dimensional analysis we are only concerned with the nature of the
dimension i.e. its quality not its quantity.
Dimensions are properties which can be measured.
Ex.: Mass, Length, Time etc.,
Units are the standard elements we use to quantify these dimensions.
Ex.: Kg, Metre, Seconds etc.,
The following are the Fundamental Dimensions (MLT)
Mass kg M
Length m L
Time s T
6. Secondary or Derived Dimensions
Secondary dimensions are those quantities which posses more than one
fundamental dimensions.
1. Geometric
a) Area
b) Volume
m2
m3
L2
L3
2. Kinematic
a) Velocity
b) Acceleration
m/s
m/s2
L/T
L/T2
L.T-1
L.T-2
3. Dynamic
a) Force
b) Density
N ML/T
kg/m3 M/L3
M.L.T-1
M.L-3
7. Problems
Find Dimensions for the following:
1. Stress / Pressure
2. Work
3. Power
4. Kinetic Energy
5. Dynamic Viscosity
6. Kinematic Viscosity
7. Surface Tension
8. Angular Velocity
9.Momentum
10.Torque
8. Use of Dimensional Analysis
1. Conversion from one dimensional unit to another
2. Checking units of equations (Dimensional
Homogeneity)
3. Defining dimensionless relationship using
a) Rayleigh’s Method
b) Buckingham’s π-Theorem
4. Model Analysis
11. Rayeligh’s Method
To define relationship among variables
This method is used for determining the
expression for a variable which depends upon
maximum three or four variables only.
12. Rayeligh’s Method
To define relationship among variables
This method is used for determining the
expression for a variable which depends upon
maximum three or four variables only.
Methodology:
Let X is a function of X1 ,X2, X3 and mathematically it can be written as
X = f(X1, X2, X3)
This can be also written as
X = K (X1
a , X2
b , X3
c ) where K is constant and a, b and c are arbitrarily powers
The values of a, b and c are obtained by comparing the powers of the fundamental
dimension on both sides.
13. Rayeligh’s Method
To define relationship among variables
This method is used for determining the
expression for a variable which depends upon
maximum three or four variables only.
Methodology:
Let X is a function of X1 ,X2, X3 and mathematically it can be written as
X = f(X1, X2, X3)
This can be also written as
X = K (X1
a , X2
b , X3
c ) where K is constant and a, b and c are arbitrarily powers
The values of a, b and c are obtained by comparing the powers of the fundamental
dimension on both sides.
Problem: Find the expression for Discharge Q in a open channel flow when Q is
depends on Area A and Velocity V.
Solution:
Q = K.Aa.Vb 1
where K is a Non-dimensional constant
Substitute the dimensions on both sides of equation 1
M0 L3 T-1 = K. (L2)a.(LT-1)b
Equating powers of M, L, T on both sides,
Power of T,
Power of L,
-1 = -b b=1
3= 2a+b 2a = 2-b = 2-1 = 1
Substituting values of a, b, and c in Equation 1m
Q = K. A1. V1 = V.A
14. Rayeligh’s Method
To define relationship among variables
This method is used for determining the
expression for a variable which depends upon
maximum three or four variables only.
Methodology:
Let X is a function of X1 ,X2, X3 and mathematically it can be written as
X = f(X1, X2, X3)
This can be also written as
X = K (X1
a , X2
b , X3
c ) where K is constant and a, b and c are arbitrarily powers
The values of a, b and c are obtained by comparing the powers of the fundamental
dimension on both sides.
15. Rayeligh’s Method
To define relationship among variables
This method is used for determining the
expression for a variable which depends upon
maximum three or four variables only.
Methodology:
Let X is a function of X1 ,X2, X3 and mathematically it can be written as
X = f(X1, X2, X3)
This can be also written as
X = K (X1
a , X2
b , X3
c ) where K is constant and a, b and c are arbitrarily powers
The values of a, b and c are obtained by comparing the powers of the fundamental
dimension on both sides.
16. This method of analysis is used when number of variables are more.
Theorem:
If there are n variables in a physical phenomenon and those n variables contain m dimensions,
then variables can be arranged into (n-m) dimensionless groups called Φ terms.
Explanation:
If f (X1, X2, X3, ……… Xn) = 0 and variables can be expressed using m dimensions then
f (π1, π2, π3, ……… πn - m) = 0 where, π1, π2, π3, … are dimensionless groups.
Each π term contains (m + 1) variables out of which m are of repeating type and one is of non-
repeating type.
Each π term being dimensionless, the dimensional homogeneity can be used to get each π term.
π denotes a non-dimensional parameter
Buckingham’s π-Theorem
17. Selecting Repeating Variables:
1. Avoid taking the quantity required as the repeating variable.
2. Repeating variables put together should not form dimensionless group.
3. No two repeating variables should have same dimensions.
4. Repeating variables can be selected from each of the following
properties.
Geometric property Length, height, width, area
Flow property Velocity, Acceleration, Discharge
Fluid property Mass density, Viscosity, Surface tension
Buckingham’s π-Theorem
21. For predicting the performance of the hydraulic structures (such as dams, spillways
etc.) or hydraulic machines (such as turbines, pumps etc.) before actually
constructing or manufacturing, models of the structures or machines are made and
tests are conducted on them to obtain the desired information.
Model is a small replica of the actual structure or machine
The actual structure or machine is called as Prototype
Models can be smaller or larger than the Prototype
Model Analysis is actually an experimental method of finding solutions of
complex flow problems.
Model Analysis
22. Similitude is defined as the similarity between the model and prototype in
every aspect, which means that the model and prototype have similar
properties.
Types of Similarities:
1. Geometric Similarity Length, Breadth, Depth, Diameter,Area,
Volume etc.,
2. Kinematic Similarity Velocity, Acceleration etc.,
3. Dynamic Similarity Time, Discharge, Force, Pressure Intensity,
Torque, Power
Similitude or Similarities
23. The geometric similarity is said to be exist between the model and
prototype if the ratio of all corresponding linear dimensions in the model
and prototype are equal.
Geometric Similarity
L B D r
m m m
L
LP
BP
DP
r
2
L
AP
Am
r
3
L
VP
Vm
where Lris Scale Ratio
24. The kinematic similarity is said exist between model and prototype if the
ratios of velocity and acceleration at corresponding points in the model and
at the corresponding points in the prototype are the same.
Kinematic Similarity
VP
Vm
Vr
aP
am
ar
whereVr is Velocity Ratio where ar is Acceleration Ratio
Also the directions of the velocities in the model and prototype should be same
25. The dynamic similarity is said exist between model and prototype if the
ratios of corresponding forcesacting at the corresponding points are
equal
Dynamic Similarity
FP
Fm
Fr
where Fr is Force Ratio
Also the directions of the velocities in the model and prototype should be same
It means for dynamic similarity between the model and prototype, the
dimensionless numbers should be same for model and prototype.
26. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
It is the product of mass and acceleration of the flowing fluid and acts in the
direction opposite to the direction of acceleration.
It always exists in the fluid flow problems
27. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
2. Viscous Force, Fv
It is equal to the product of shear stress due to viscosity and surface area of the
flow.
28. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
2. Viscous Force, Fv
3. Gravity Force, Fg
It is equal to the product of mass and acceleration due to gravity of the flowing
fluid.
29. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
2. Viscous Force, Fv
3. Gravity Force, Fg
4. Pressure Force, Fp
It is equal to the product of pressure intensity and cross sectional area of
flowing fluid
30. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
2. Viscous Force, Fv
3. Gravity Force, Fg
4. Pressure Force, Fp
5. Surface Tension Force, Fs
It is equal to the product of surface tension and length of surface of the flowing
31. Types of Forces Acting on Moving Fluid
1. Inertia Force, Fi
2. Viscous Force, Fv
3. Gravity Force, Fg
4. Pressure Force, Fp
5. Surface Tension Force, Fs
6. Elastic Force, Fe
It is equal to the product of elastic stress and area of the flowing fluid
32. Dimensionless Numbers
V
Lg
InertiaForce
Gravity Force
Dimensionless numbers are obtained by dividing the inertia force by
viscous force or gravity force or pressure force or surface tension force or
elastic force.
1. Reynold’s number, Re =
2. Froude’s number, Fe =
3. Euler’s number, Eu =
e
4. Weber’s number, W =
V
p /
InertiaForce
PressureForce
InertiaForce V
SurfaceTensionForce / L
Viscous Force
Inertia Force
VL
or
VD
Inertia Force
V
Elastic Force C
37. The laws on which the models are designed for dynamic similarity are
called model laws or laws of similarity.
1. Reynold’s Model
Model Laws
Models based on Reynolds’s Number includes:
a) Pipe Flow
b) Resistance experienced by Sub-marines, airplanes, fully immersed bodies
38. The laws on which the models are designed for dynamic similarity are
called model laws or laws of similarity.
1. Reynold’s Model
2. Froude Model Law
Model Laws
Froude Model Law is applied in the following fluid flow problems:
a) Free Surface Flows such as Flow over spillways, Weirs, Sluices, Channels
etc.,
b) Flow of jet from an orifice or nozzle
c) Where waves are likely to formed on surface
d) Where fluids of different densities flow over one another
39. The laws on which the models are designed for dynamic similarity are
called model laws or laws of similarity.
1. Reynold’s Model
2. Froude Model Law
3. Euler Model Law
Model Laws
Euler Model Law is applied in the following cases:
a) Closed pipe in which case turbulence is fully developed so that viscous forces
are negligible and gravity force and surface tension is absent
b) Where phenomenon of cavitations takes place
40. The laws on which the models are designed for dynamic similarity are
called model laws or laws of similarity.
1. Reynold’s Model
2. Froude Model Law
3. Euler Model Law
4. Weber Model Law
Model Laws
Weber Model Law is applied in the following cases:
a) Capillary rise in narrow passages
b) Capillary movement of water in soil
c) Capillary waves in channels
d) Flow over weirs for small heads
41. Model Laws
The laws on which the models are designed for dynamic similarity are
called model laws or laws of similarity.
1. Reynold’s Model
2. Froude Model Law
3. Euler Model Law
4. Weber Model Law
5. Mach Model Law
Mach Model Law is applied in the following cases:
a) Flow of aero plane and projectile through air at supersonic speed ie., velocity
more than velocity of sound
b) Aero dynamic testing, c) Underwater testing of torpedoes, and
d) Water-hammer problems
42. If the viscous forces are predominant, the models are designed for dynamic
similarity based on Reynold’s number.
Reynold’s Model Law
p
P P
P
m
m m
m V L
ρ
V L
ρ
V
L
t r
r
r
TimeScaleRatio
Velocity, V = Length/Time T = L/V
t
a
r
Vr
r
Acceleration ScaleRatio
Acceleration, a = Velocity/Time L = V/T
R Re
e p
m
43.
44.
45. Problems
1. Water flowing through a pipe of diameter 30 cm at a velocity of 4 m/s. Find the
velocity of oil flowing in another pipe of diameter 10cm, if the conditions of
dynamic similarity is satisfied between two pipes. The viscosity of water and oil
is given as 0.01 poise and 0.025 poise. The specific gravity of oil is 0.8.
46. If the gravity force is predominant, the models are designed for dynamic
similarity based on Froude number.
Froude Model Law
Lr
Tr
ScaleRatioforTime
g Lm g LP
m p
Vm
Vp
Lr
Vr
VelocityScaleRatio
F Fe
e p
m
Tr
Scale Ratio for Accele ration 1
2.5
Qr
Scale Ratio for Discharge Lr
3
Fr
Scale Ratio for Force Lr
Fr
Scale Ratio for Pressure Intensity Lr
3.5
Pr
Scale Ratio for Power Lr
47.
48.
49.
50.
51.
52.
53. Problems
1. In 1 in 40 model of a spillway, the velocity and discharge are 2 m/s and 2.5
m3/s. Find corresponding velocity and discharge in the prototype
2. In a 1 in 20 model of stilling basin, the height of the jump in the model is
observed to be 0.20m. What is height of hydraulic jump in the prototype? If
energy dissipated in the model is 0.1kW, what is the corresponding value in
prototype?
3. A 7.2 m height and 15 m long spillway discharges 94 m3/s discharge under a
head of 2m. If a 1:9 scale model of this spillway is to be constructed,
determine the model dimensions, head over spillway model and the model
discharge. If model is experiences a force of 7500 N, determine force on the
prototype.
54. Problems
4. A Dam of 15 m long is to discharge water at the rate of 120 cumecs under a
head of 3 m. Design a model, if supply available in the laboratory is 50 lps
5. A 1:50 spillway model has a discharge of 1.5 cumecs. What is the
corresponding discharge in prototype?. If a flood phenomenon takes 6 hour to
occur in the prototype, how long it should take in the model