Fluid Mechanics - Basic mathematical derivations from Udemy

This introductory course in Fluid Mechanics deals with the basic concepts of fluid statics, fluid kinematics, fluid dynamics, flow measurement and similitude. First section introduces the Fluid Statics to the beginners. This is followed by a kinematics approach to the mechanics of fluids in the Section-2 comprising of an introduction to laminar, turbulent, rotational, irrotational flows, the continuity equation in three dimensions. Comparative study of velocity potential function versus stream function is also carried out in this section. Next to this in Section-3, the author derived the mathematical derivations for Bernoulli’s equation, momentum equation and its applications for fluid flow in a pipe bend and reaction of a fluid jet. Also the concepts of vortex flow are discussed in detail. The last section provides an insight into flow measurement and similitude with detailed mathematical derivations of orifice meter, venturimeter, pitot tube, hotwire anemometer, flow through nozzles, notches and weirs.

A fundamental mathematical derivative approach is followed which helps the students to gain the fundamental concepts of mechanics of fluids. A step-by-step and detailed derivations of the various mathematical formulae is traced in this basic course work on fluid mechanics. This course shall help the undergraduate students to prepare themselves for the basic assessment in the area of fluid mechanics. On the whole, this course tastes better for the beginners of the engineering graduation program.

What's inside

Learning objectives

Understand of the concepts in fluid statics
Infer the mathematical derivations and concepts confirming to the field of fluid kinematics

Interpret the mathematical derivations pertaining to fluid dynamics
Develop an understanding on fluid flow measurement aspects

Understand of the concepts in fluid statics
Infer the mathematical derivations and concepts confirming to the field of fluid kinematics
Interpret the mathematical derivations pertaining to fluid dynamics
Develop an understanding on fluid flow measurement aspects

Syllabus

Stream Function

Fluid Statics

Density, Specific gravity and Viscosity

Dynamic viscosity, kinematic viscosity and Newton's law of viscosity

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Provides a strong foundation in fluid mechanics, which is essential for many engineering disciplines such as mechanical, civil, and chemical engineering

Focuses on fundamental mathematical derivations, which helps students build a solid understanding of the underlying principles of fluid mechanics

Covers a wide range of topics, including fluid statics, kinematics, dynamics, flow measurement, and similitude, providing a comprehensive overview of the field

Includes detailed mathematical derivations of various formulae, which can be beneficial for students who prefer a rigorous, analytical approach to learning

Prepares students for basic assessments in fluid mechanics, making it a useful resource for exam preparation and reinforcing core concepts

Requires a strong foundation in mathematics, which may pose a challenge for students who are not comfortable with calculus and differential equations

Reviews summary

Fluid mechanics basic mathematical derivations

Based solely on the provided course description and syllabus, 'Fluid Mechanics - Basic mathematical derivations' is designed as an introductory course for beginners, particularly undergraduate engineering students. It focuses on understanding fundamental fluid mechanics concepts through a step-by-step approach to their mathematical derivations. Key areas covered include fluid statics, kinematics, dynamics (Bernoulli's, Momentum), fluid flow measurement, and similitude laws. The course aims to prepare students for basic assessments in the field. However, no learner reviews or their rating distribution were provided for analysis. Consequently, this summary is limited to outlining the course's stated content and objectives and cannot incorporate actual student feedback, experiences, specific strengths, weaknesses, or overall satisfaction levels as perceived by learners who have completed the course. A comprehensive evaluation requires access to student reviews.

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Fluid Mechanics - Basic mathematical derivations with these activities:

Review Calculus Fundamentals

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Strengthen your understanding of calculus concepts, which are essential for deriving and applying fluid mechanics equations.

Browse courses on Differential Equations

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Review differentiation and integration techniques.
Practice solving differential equations.
Work through problems involving vector calculus.

Create a Fluid Mechanics Cheat Sheet

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Consolidate your understanding by creating a cheat sheet of key formulas, concepts, and definitions from the course.

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Review your notes and identify key information.
Organize the information into a concise format.
Include relevant diagrams and examples.

Read 'Fluid Mechanics' by Frank White

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Supplement your learning with a comprehensive textbook that provides detailed explanations and examples of fluid mechanics principles.

View Melania on Amazon

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Read chapters related to fluid statics and kinematics.
Work through example problems in the book.
Refer to the book for clarification on difficult concepts.

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Solve Bernoulli's Equation Problems

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Reinforce your understanding of Bernoulli's equation by solving a variety of problems with different boundary conditions.

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Find practice problems online or in textbooks.
Solve problems involving different flow scenarios.
Check your answers and review the solution process.

Explore 'Schaum's Outline of Fluid Mechanics'

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Use a Schaum's Outline to get additional practice problems and reinforce your understanding of key concepts.

View Schaum's Outline of Fluid Mechanics, Second... on Amazon

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Review the outline for relevant topics.
Work through the solved problems.
Attempt the practice problems and check your answers.

Create a Flow Visualization Video

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Deepen your understanding of fluid flow by creating a video that visualizes different flow patterns and phenomena.

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Choose a flow phenomenon to visualize.
Use simulation software or physical experiments to capture footage.
Edit the footage and add explanations.

Design a Venturi Meter

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Apply your knowledge of fluid mechanics to design a Venturi meter for a specific application, considering factors like flow rate and pressure drop.

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Define the specifications for the Venturi meter.
Calculate the dimensions of the meter using fluid mechanics principles.
Create a detailed design and consider manufacturing constraints.

Career center

Learners who complete Fluid Mechanics - Basic mathematical derivations will develop knowledge and skills that may be useful to these careers:

Hydraulic Engineer

A career as a Hydraulic Engineer involves designing systems to manage and control water resources. This often includes designing pipelines, dams, and other structures that efficiently and safely transport or store water. This course, focusing on fluid mechanics, helps build a foundation for understanding fluid behavior, pressure, and flow rates, which are crucial aspects of hydraulic system design. The course's exploration of Bernoulli's equation, momentum equation, and flow measurement techniques help hydraulic engineers analyze and optimize hydraulic systems. The detailed mathematical derivation approach in this course makes it particularly relevant for aspiring hydraulic engineers who need a solid understanding of the fundamental equations governing fluid behavior.

See salaries and explore the career path for Hydraulic Engineer

Aerospace Engineer

An Aerospace Engineer designs, develops, and tests aircraft and spacecraft. Understanding fluid mechanics is essential, as it governs the aerodynamic forces acting on these vehicles. This course, covering fluid kinematics and dynamics, helps in understanding airflow patterns, lift, drag, and other critical parameters. The course's sections on laminar and turbulent flows, Bernoulli's equation, and vortex flow help aerospace engineers analyze and optimize the aerodynamic performance of aircraft and spacecraft. Additionally, the exploration of similitude prepares aerospace engineers for wind tunnel testing and scale model analysis. The detailed mathematical derivations will be helpful to the Aerospace Engineer.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

Mechanical Engineers design, develop, and test mechanical devices and systems. Many of these systems involve fluid flow, such as pumps, turbines, and heat exchangers. This course provides fundamental concepts of fluid mechanics. The course's coverage of fluid statics, kinematics, and dynamics helps mechanical engineers analyze fluid flow behavior in these systems. The sections on Bernoulli's equation, momentum equation, and vortex flow are particularly helpful in designing and optimizing fluid machinery. The discussion of similitude is relevant for testing and scaling up designs. A Mechanical Engineer will be more effective with the knowledge gained from this course.

See salaries and explore the career path for Mechanical Engineer

Wind Energy Engineer

The Wind Energy Engineer designs wind turbines and wind farms to generate electricity. Understanding fluid mechanics, specifically aerodynamics, is essential for optimizing turbine performance. This course, covering fluid kinematics and dynamics, helps in understanding airflow patterns around turbine blades, lift, drag, and other parameters. The course's sections on laminar and turbulent flows, Bernoulli's equation, and vortex flow helps wind energy engineers analyze and optimize turbine blade designs. Additionally, the exploration of similitude is beneficial for wind tunnel testing and scale modeling. The detailed mathematical derivations will be helpful to the Wind Energy Engineer.

See salaries and explore the career path for Wind Energy Engineer

Computational Fluid Dynamics Engineer

A Computational Fluid Dynamics Engineer utilizes software to simulate fluid flow and heat transfer. This role often requires an advanced degree. This course provides a solid understanding of the underlying principles and mathematical formulations used in computational fluid dynamics codes. The course's coverage of fluid statics, kinematics, dynamics, and flow measurement techniques helps CFD engineers interpret and validate simulation results. The detailed mathematical derivations equip CFD engineers with the ability to understand the numerical methods used in these simulations. Aspiring Computational Fluid Dynamics Engineers may find this course quite useful.

See salaries and explore the career path for Computational Fluid Dynamics Engineer

Civil Engineer

Civil Engineers design and oversee the construction of infrastructure projects, many of which involve fluid mechanics principles. Projects like water distribution systems, sewage treatment plants, and drainage systems require a solid understanding of fluid behavior. This course helps build a strong base in fluid statics, kinematics, and dynamics. The course's exploration of Bernoulli's equation, momentum equation, and flow measurement techniques assists civil engineers in designing and analyzing these systems. The course's sections on flow through nozzles, notches, and weirs are particularly relevant for designing drainage and irrigation systems. This course may be useful for aspiring Civil Engineers.

See salaries and explore the career path for Civil Engineer

Research Scientist

A Research Scientist in fluid mechanics conducts experiments and develops models to understand and predict fluid behavior. This career role typically requires an advanced degree. This course provides a solid foundation in the fundamental principles and mathematical derivations essential for research in this area. The course's detailed coverage of fluid statics, kinematics, dynamics, and flow measurement techniques provides a strong starting point for conducting advanced research. The course's emphasis on mathematical derivations helps research scientists develop and validate their own models. This course may be useful for a Research Scientist.

See salaries and explore the career path for Research Scientist

Environmental Engineer

Environmental Engineers work to protect the environment and human health through the design of solutions to environmental problems. Many of these problems involve the movement and treatment of water and air. This course helps understand the fundamentals of fluid mechanics, which is crucial for designing effective environmental solutions. The course's coverage of fluid statics, kinematics, and dynamics helps environmental engineers analyze the flow of pollutants in rivers, groundwater, and the atmosphere. The sections on flow measurement and similitude are particularly useful for designing and optimizing water and wastewater treatment plants. This course may be useful for aspiring Environmental Engineers.

See salaries and explore the career path for Environmental Engineer

Process Engineer

A Process Engineer develops, designs, and optimizes industrial processes. Many of these processes involve the movement and transformation of fluids. This course provides a fundamental understanding of fluid mechanics, which is essential for designing efficient and safe processes. The course's coverage of fluid statics, kinematics, and dynamics helps process engineers analyze fluid flow in pipes, reactors, and other equipment. The sections on flow measurement and Bernoulli's equation are particularly useful for designing and optimizing fluid handling systems. This course may be useful for those who perform the job of Process Engineer.

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Naval Architect

Naval Architects design and oversee the construction of ships and other marine vessels. Understanding fluid mechanics is essential, as it governs the hydrodynamic forces acting on these vessels. This course, covering fluid kinematics and dynamics, helps in understanding water flow patterns around ship hulls, drag, and stability. The course's sections on laminar and turbulent flows, Bernoulli's equation, and vortex flow help naval architects analyze and optimize hull designs. Additionally, the exploration of similitude prepares naval architects for tank testing and scale model analysis. This course may be useful to a Naval Architect.

See salaries and explore the career path for Naval Architect

Energy Engineer

An Energy Engineer works to improve energy efficiency and develop sustainable energy solutions. Understanding fluid mechanics enables the design of more effective energy systems. This course provides a solid grounding in fluid behavior. The course's coverage of fluid statics, kinematics, and dynamics helps energy engineers analyze flow in pipelines, heat exchangers, and other energy-related equipment. The sections on Bernoulli's equation, momentum equation, and flow measurement techniques help optimize energy system performance. The Energy Engineer may find this course useful.

See salaries and explore the career path for Energy Engineer

Water Resource Manager

A Water Resource Manager plans and manages water resources to ensure sustainable use. This involves understanding water availability, demand, and quality. This course helps build a foundation in fluid mechanics, which is essential for understanding how water moves through rivers, aquifers, and other systems. The course's coverage of fluid statics, kinematics, and dynamics helps water resource managers analyze water flow patterns and predict the impact of various management strategies. The sections on flow measurement and similitude are useful for monitoring water resources and developing effective management plans. This course may be useful for those who perform the job of Water Resource Manager.

See salaries and explore the career path for Water Resource Manager

Reservoir Engineer

Reservoir Engineers manage the flow of oil and gas in underground reservoirs. Understanding fluid mechanics is important for optimizing production and predicting reservoir performance. This course helps understand the fundamentals of fluid flow, pressure, and permeability. The course's coverage of fluid statics, kinematics, and dynamics helps reservoir engineers analyze the movement of oil and gas through porous media. The sections on Bernoulli's equation and momentum equation are useful for understanding pressure gradients and flow rates in reservoirs. This course may be useful to a Reservoir Engineer.

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Biomechanics Engineer

Biomechanics Engineers apply engineering principles to biological systems. Fluid mechanics plays a role in understanding blood flow, respiration, and other physiological processes. This course may be of some assistance in understanding the behavior of fluids within the human body. The course's coverage of fluid statics, kinematics, and dynamics helps biomechanics engineers analyze blood flow patterns and develop medical devices. One who is a Biomechanics Engineer may find the sections on Bernoulli's equation and momentum equation useful for understanding pressure gradients and flow rates in the circulatory system.

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Climate Modeler

Climate Modelers develop and use computer models to simulate the Earth's climate system. Understanding fluid mechanics is important for modeling atmospheric and oceanic circulation. This course may be of some assistance in learning the fundamentals of fluid flow. The course's coverage of fluid statics, kinematics, and dynamics may in time help climate modelers understand the movement of air and water in the climate system. This will take additional training. The sections on Bernoulli's equation and momentum equation may be used to analyze pressure gradients and flow rates in the atmosphere and oceans.

See salaries and explore the career path for Climate Modeler

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Fluid Mechanics - Basic mathematical derivations.

Schaum's Outline of Fluid Mechanics, Second Edition

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This Schaum's Outline provides a concise and focused review of fluid mechanics principles, with numerous solved problems. It is an excellent resource for students who need extra practice and reinforcement of the concepts covered in the course. It is particularly helpful for exam preparation and quick review.

Schaum's Outline of Fluid Mechanics, Second Edition...

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Fluid Mechanics - Basic mathematical derivations

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Fluid mechanics basic mathematical derivations

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