# Advanced Fluid Mechanics with Engineering Applications

## What you'll learn

- Introduction to Fluid Mechanics from very basic level that can engage the beginner learner to the course.
- Derivation and complete explanation of continuity equation with examples and numericals.
- Understand momentum equation and momentum equation in differential form.
- Understand Navier-Stokes Equation and applications of Navier-Stokes Equation.
- Get complete explanation about Reynolds Transport Theorem with its Derivation.
- Understand about Linear and Angular momentum equation.
- Understand about Kinematics of all types of Flow in detail.
- Understand Potential Flow and Superposition of potential flow (I, II, III)
- Explanation about Turbo Machines (Euler’s Equation, Blade Angles, Performance (I,II)
- Get Information about turbine and turbine performance.
- Understand about Boundary layer Concepts (Order Analysis over Flat plate, Turbulent flow over flat plate, Blasius solution, Displacement and Momentum thickness)
- Understand about External flow Concepts (Drag Coefficient and Drag in Vehicles)
- Explanation of Airfoil and the Performance of Airfoil
- Understand Advanced concepts about CFD and its Applications.

## Requirements

- Just Basic Knowledge of Physics and Chemistry as this course is start from the very basic level.
- As this course is designed for engineering university students so the prior knowledge is important.

## Description

Learn the fundamental principles underlying fluid dynamics; including the kinematics of deformation, hydrostatics & buoyancy, inviscid flow, the application of Bernoulli’s theorems, as well as applications of control volume analysis for more complex problems of engineering interest and in the end understand Autodesk CFD computational fluid dynamics simulation software that engineers and analysts use to intelligently predict how liquids and gases will perform.

The subject of Fluid Mechanics has a wide scope and is of prime importance in several fields of engineering and science. The present course emphasizes the fundamental underlying fluid mechanical principles and the application of those principles to solve real-life problems. Special attention is given to deriving all the governing equations starting from the fundamental principle. There is a well-balanced coverage of physical concepts, mathematical operations along with examples and exercise problems of practical importance.

After completion of the course, the students will have a strong fundamental understanding of the Principles of Fluid Mechanics and will be able to apply the Principles to analyze fluid mechanical systems.

This course is of relevance to engineers and scientists across a wide range of mechanical chemical and process industries who must understand, analyze and optimize flow processes and fluids handling problems. Applications are drawn from hydraulics, aero & hydrodynamics as well as the chemical process industries.

COURSE OUTLINE

**Lecture-1 Introduction to Fluid**

The subject of Fluid Mechanics

Laws in the scientific study

Engineering approach of problem-solving

Fluid definition

Newton’s law of viscosity

Newtonian and Non-Newtonian fluid

Problems based on Newton’s law of Viscosity

**Lecture-2 Continuity Equation**

Principle of conservation of mass

Differential and Integral approach

Eulerian and Lagrangian approach

Inventory Equation

Derivation of Continuity equation-Differential approach

Conservation and Non-Conservation forms of Continuity

Material derivative

Scalar and Vector field

Acceleration field

**Lecture-3 Momentum Equation**

Newton’s Second law of motion

Body force

Surface force

Momentum Equation in differential form

Stokes postulate

Navier-Stokes Equation

**Lecture-4 Application of Navier Stokes equation**

N-S equation as governing equation of fluid flow

Application of N-S equation for a steady and laminar fluid flow between two fixed infinitely long plates.

Velocity profile

Volume flow rate calculation from the velocity profile

Local velocity, average velocity, maximum velocity

Calculating Reynolds Number from the Velocity profile

**Lecture-5 Application of Navier Stokes equation - Couette flow**

The physical meaning of N-S equation

Fully developed flow

Application of N-S equation for a steady and laminar fluid flow between one fixed and one moving plate-Couette Flow

Applications of Couette flow

**Lecture-6 Reynolds Transport Theorem Derivation**

Control Mass (A System) and Control Volume

Lagrangian and Eulerian Approach

Extensive and Intensive property

Derivation of Reynolds Transport Theorem (RTT)

Interpretation of net flux term of RTT

**Lecture-7 Reynolds Transport Theorem - Continuity Equation**

Reynolds Transport Theorem (RTT)

Deriving Continuity Equation using RTT

Mass flow rate, volume flow rate, and Average speed

Differential and Integral form of Continuity Equation

**Lecture-8 RTT-Continuity Equation Numericals**

Continuity Equation in Integral form

Solving numerical problems using Continuity Equation

**Lecture-9 RTT- Linear Momentum Equation**

Reynolds Transport Theorem (RTT)

Deriving Momentum Equation using RTT

Resultant Forces acting on a CV

Momentum accumulation in a CV

Momentum flow through a CV

**Lecture-10 RTT- Angular Momentum Equation**

Reynolds Transport Theorem (RTT)

Deriving Angular Momentum Equation using RTT

Problem-based on Linear and Angular Momentum

RTT for Moving and Deforming CV

**Lecture-11 Kinematics of Flow-Flow types**

Fluid Flow Visualization- Classics

Streamline

Path-line

Streak-line

Time-line

Software for flow visualization (2dflowvis)

**Lecture-12 Kinematics of Flow- Irrotational Flow**

The motion of fluid Element

Transformation of a fluid element

Angular velocity vector

Vorticity Vector

Irrotational flow field

**Lecture-13 Kinematics of Flow- Stream function**

Visualizing velocity field-Java Applet

Visualizing velocity field- Maple

Stream function

Change in the value of stream function

Problem on the stream function

Stream function in polar coordinates

**Lecture-14 Kinematics of Flow- Circulation**

Circulation

Relationship between Circulation and Vorticity

Stoke’s theorem

Problem on Circulation

The physical meaning of Divergence of a vector

Circulation and Divergence in Java Applet

**Lecture-15 Potential Flow- Velocity potential function**

Velocity Potential function, φ

Potential flow

Relationship between ψ and φ

Flow net

Velocity potential function in cylindrical coordinates

Velocity Potential function in Java Applet

**Lecture-16 Potential Flow- Basic potential flows**

Uniform flow

Source and Sink flow

Vortex flow

Stream function and Velocity potential function for basic flows

**Lecture-17 Potential Flow- Superposition of potential flows-I**

Superposition of basic potential flows

Doublet

Half body

**Lecture-18 Potential Flow- Superposition of potential flow-II**

Flow around a cylinder

Flow around a cylinder-Velocity and pressure distribution

Flow around a cylinder-Drag and Lift

Rankine body

Problem on Rankine Body

**Lecture-19 Potential Flow- Superposition of potential flow-III**

Superposition of basic potential flows

Flow around a cylinder with circulation

Magnus Effect

Problem- Flow around a cylinder with circulation

**Lecture-20 Turbo-machine- Fluid Machines**

Fluid machines classification

Positive Displacement machines

Turbo-machines

Comparison of PDPs and Roto-dynamic pumps

Turbo-machine Classifications

Scope of Turbo-machines

**Lecture-21 Turbo-machine- Euler’s Equation**

One dimensional flow through an impeller

Velocity triangle

Euler’s equation of turbo-machine

**Lecture-22 Turbo-machine- Blade Angles**

Velocity triangle

Velocity triangle at inlet-assumptions

Effect of blade angle on head

Typical Characteristic curve of a centrifugal pump

Effect of blade angle on Characteristic curve

**Lecture-23 Turbo-machine- Performance-I**

Problem-Centrifugal blower

Static, Friction and System head

Pump Losses

Pump Efficiency

Pump Performance Characteristic curves

**Lecture-24 Turbo-machine- Performance-II**

Pump System Curve

Pumps in Series and Parallel

Pump Affinity laws

Pump specific speed

**Lecture-25 Turbo-machine- Turbine**

Turbine

Schematics of hydraulic turbines

Velocity triangles of Turbine

Impulse Turbine

Reaction Turbine

Degree of Reaction

**Lecture-26 Turbo-machine- Turbine Performance**

Pump and Turbine Efficiencies

General Energy Equation

Problem-Turbine

Affinity laws for Turbine

Turbine specific speed

**Lecture-27 Boundary layer- Concept**

Classification of flows

One dimensional and multi dimensional flow

Steady and Unsteady flow

Uniform and Non-Uniform flow

Inviscid and Viscous flow

Attached and Flow separation

Laminar and Turbulent flow

Prandtl-Boundary layer concept

Growth of boundary layer thickness

**Lecture-28 Boundary layer- Order Analysis over Flat plate**

Order of Magnitude or Scale Analysis

Order of Magnitude Analysis over a flat plate

Boundary layer thickness as a function of Reynold’s Number

Wall shear stress using Scale Analysis

Skin friction coefficient using Scale Analysis

**Lecture-29 Boundary layer- Blasius solution**

Laminar boundary layer on a flat plate

Blasius solution

Wall shear stress using Blasius solution

Friction coefficient using Blasius solution

Problem- Using Blasius solution

**Lecture-30 Boundary layer- Turbulent flow over flat plate**

Turbulent flow

Governing Equations in Turbulent flow

Boundary layer in Turbulent flow

The velocity profile in laminar and turbulent flow

Velocity distribution in the turbulent boundary layer

Law of wall

**Lecture-31 Boundary layer- Displacement and Momentum thickness**

Disturbance or Boundary layer thickness

Displacement thickness

Displacement thickness using Blasius solution

Momentum thickness

Momentum thickness using Blasius Solution

The relative amount of displacement and momentum thickness for laminar flow over flat plate

**Lecture-32 Boundary layer- Approximate solution**

Control Volume analysis for Boundary layer

Von Karman Solution

Von Karman Integral equation

Approximate solution to Laminar boundary layer over a flat plate

**Lecture-33 Boundary layer- Skin Friction Coefficient**

Friction Coefficient for laminar boundary layer

Local and Average skin friction coefficient

Friction Coefficient for Turbulent boundary layer

Friction Coefficient for Mixed boundary layer

Problem- Mixed boundary layer over a flat plate

**Lecture 34 Introduction to EES-Parametrics and plotting**

**Lecture-35 External flow- Introduction**

External flow- Application

Forces and Moments on arbitrary shape body

External Flow over a flat plate and cylinder

External flow- Low and High Reynolds's Number flows

Introduction to Open channel flow

External flow characteristics

**Lecture-36 External flow-Drag and Lift**

The resultant force on a body

Drag and lift Forces

Drag Coefficient

Problem-Drag coefficient

Pressure and Shear stress distribution

**Lecture-37 External flow- Drag Coefficient-1**

Drag and lift Forces-Alternate Method

The drag coefficient for slender bodies

Problem-Drag coefficient

Factors affecting drag coefficient

**Lecture-38 External flow- Drag Coefficient-2**

The drag coefficient for common geometries

Drafting

Fairing

Drag reduction in nature

Drag reduction in other applications

Experimental measurement of drag coefficient

**Lecture-39 External flow- Drag in Vehicles**

Drag Coefficient of cars-History

Drag and Rolling resistance on a Vehicle

Power required to drive a vehicle

Problem-Power-Drag and Rolling Resistance

Drag reduction in Vehicles

**Lecture-40 External flow-Introduction to Airfoil**

What is Airfoil?

Airfoil types

Airfoil Nomenclature

Aircraft terminologies

Airfoil-Potential flow theory

Minimum Flight Velocity

**Lecture-41 External flow-Airfoil Performance**

Lift and Drag on Airfoil

Airfoil-Boundary layer theory

Airfoil-Flow separation

Effect of angle of attack

Performance of different Aerofoil

Airfoil with flap

Airfoil at different Mach Number

**Lecture-42 CFD- Introduction**

What is CFD?

CFD Scope and Applications

Role of CFD in Engineering

How CFD works

Practical Steps of Solving problem in CFD

**Lecture-43 CFD- Finite Difference Method**

Numerical Techniques

Finite difference Method

Forward, Backward and Central Difference

Mixed Derivatives

Problem- Finite Difference Method

Solving problems in CFD using ANSYS-CFX

**Lecture 44 CFD-Geometry and Mesh**

**Lecture 45 CFD-Pre Solver Solution Post Process (CFX)**

## Who this course is for:

- This course is specially designed for engineering students who are interested in Fluid Mechanics and want to understand Fluid Mechanics in advanced Level
- This course is especially for automotive engineering and processing engineering students.
- This course is for those who want to learn and know how to use CFD (computational fluid dynamics simulation software)

## Instructor

**OZIS Academy** is the platform for struggling university or high school students and professionals who want to improve their skills in the work field as we provide quality and detailed courses. We offer courses from brilliant **Ph.D. Professors** from prestigious Universities who are experts in their relative fields. We have a team of well-experienced, full-time faculty and dedicated staff including talented retired and working University professors. Our mission is to impart the most qualitative education by the way of systematic methodical and scientific approaches.