Advanced Fluid Mechanics & Computational Fluid Dynamics
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Dive deep into the intricate world of Fluid Mechanics and experience the aweinspiring symphony of fluidic behavior that powers our natural and engineered systems. From the foundational concepts of Newton’s laws applied to fluids to the complex calculations needed for engineering problemsolving, this course offers a comprehensive understanding of fluid motion and its critical role in both natural phenomena and manmade inventions. Grasp the nuances of continuity equations, momentum conservation, and the beauty of NavierStokes’ equations, as they govern fluid flow.
Embark on a journey through the intricacies of turbomachines, exploring their classifications, working principles, and applications. Delve into the dynamics of boundary layers, from their genesis to their effect on the bodies in flow. Engage in the fascinating realm of external flow, uncovering the principles behind drag, lift, and the magnificent designs of airfoils. Finally, stands at the forefront of technological advancement with an introduction to Computational Fluid Dynamics (CFD), exploring the realm of numerical simulations that push the boundaries of engineering capabilities.
This course isn’t just about learning theories but bridging the chasm between theory and realworld application. By the end, you will not only understand the mathematics behind fluid motion but will gain a profound appreciation for its relevance in shaping the world around us. Whether you aspire to design advanced aerostructures, engineer efficient transportation systems, or merely satiate an academic curiosity, this course is a key milestone in your journey of discovery and innovation.
Reference books for this course:

Fluid Mechanics by Yunus A. Cengel, John M. Cimbala

Fundamentals of Fluid Mechanics, 6th Edition By Munson
COURSE OUTLINE
Lecture1 Introduction to Fluid

The subject of Fluid Mechanics

Laws in the scientific study

Engineering approach of problemsolving

Fluid definition

Newton’s law of viscosity

Newtonian and NonNewtonian fluid

Problems based on Newton’s law of Viscosity
Lecture2 Continuity Equation

Principle of conservation of mass

Differential and Integral approach

Eulerian and LaGrange’s approach

Inventory Equation

Derivation of Continuity equationDifferential approach

Conservation and NonConservation Forms of Continuity

Material derivative

Scalar and Vector field

Acceleration field
Lecture3 Momentum Equation

Newton’s Second Law of Motion

Body force

Surface force

Momentum Equation in differential form

Stokes postulate

NavierStokes Equation
Lecture4 Application of Navier Stokes equation

NS equation as governing equation of fluid flow

Application of the NS 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
Lecture5 Application of Navier Stokes equation – Couette flow

The physical meaning of the NS equation

Fully developed flow

Application of NS equation for a steady and laminar fluid flow between one fixed and one moving plateCouette Flow

Applications of Couette flow
Lecture6 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
Lecture7 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
Lecture8 RTTContinuity Equation Numericals

Continuity Equation in Integral Form

Solving numerical problems using Continuity Equation
Lecture9 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
Lecture10 RTT Angular Momentum Equation

Reynolds Transport Theorem (RTT)

Deriving Angular Momentum Equation using RTT

Problembased on Linear and Angular Momentum

RTT for Moving and Deforming CV
Lecture11 Kinematics of FlowFlow Types

Fluid Flow Visualization Classics

Streamline

Pathline

Streakline

Timeline

Software for flow visualization (2dflowvis)
Lecture12 Kinematics of Flow Irrotational Flow

The motion of fluid Element

Transformation of a fluid element

Angular velocity vector

Vorticity Vector

Irrotational flow field
Lecture13 Kinematics of Flow Stream function

Visualizing velocity fieldJava Applet

Visualizing velocity field Maple

Stream function

Change in the value of the stream function

Problem with the stream function

Stream function in polar coordinates
Lecture14 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
Lecture15 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
Lecture16 Potential Flow Basic potential flows

Uniform flow

Source and Sink flow

Vortex flow

Stream function and Velocity potential function for basic flows
Lecture17 Potential Flow Superposition of potential flowsI

Superposition of basic potential flows

Doublet

Half body
Lecture18 Potential Flow Superposition of Potential flowII

Flow around a cylinder

Flow around a cylinderVelocity and pressure distribution

Flow around a cylinderDrag and Lift

Rankine body

Problem with Rankine Body
Lecture19 Potential Flow Superposition of Potential flowIII

Superposition of basic potential flows

Flow around a cylinder with circulation

Magnus Effect

Problem Flow around a cylinder with circulation
Lecture20 Turbomachine Fluid Machines

Fluid machines classification

Positive Displacement machines

Turbomachines

Comparison of PDPs and Rotodynamic pumps

Turbomachine Classifications

Scope of Turbomachines
Lecture21 Turbomachine Euler’s Equation

Onedimensional flow through an impeller

Velocity triangle

Euler’s equation of turbomachine
Lecture22 Turbomachine Blade Angles

Velocity triangle

Velocity triangle at inletassumptions

Effect of blade angle on the head

Typical Characteristic curve of a centrifugal pump

Effect of blade angle on Characteristic curve
Lecture23 Turbomachine PerformanceI

ProblemCentrifugal blower

Static, Friction, and System head

Pump Losses

Pump Efficiency

Pump Performance Characteristic curves
Lecture24 Turbomachine PerformanceII

Pump System Curve

Pumps in Series and Parallel

Pump Affinity laws

Pump specific speed
Lecture25 Turbomachine Turbine

Turbine

Schematics of hydraulic turbines

Velocity triangles of Turbine

Impulse Turbine

Reaction Turbine

Degree of Reaction
Lecture26 Turbomachine Turbine Performance

Pump and Turbine Efficiencies

General Energy Equation

ProblemTurbine

Affinity laws for Turbine

Turbine specific speed
Lecture27 Boundary layer Concept

Classification of flows

Onedimensional and multidimensional flow

Steady and Unsteady flow

Uniform and NonUniform flow

Inviscid and Viscous flow

Attached and Flow Separation

Laminar and Turbulent flow

PrandtlBoundary layer concept

Growth of boundary layer thickness
Lecture28 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
Lecture29 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’s solution
Lecture30 Boundary layer turbulent flow over a 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
Lecture31 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 a flat plate
Lecture32 Boundary layer Approximate solution

Control Volume analysis for Boundary layer

Von Karman Solution

Von Karman Integral equation

An approximate solution to Laminar boundary layer over a flat plate
Lecture33 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 EESParametric and plotting
Lecture35 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
Lecture36 External FlowDrag and Lift

The resultant force on a body

Drag and lift Forces

Drag Coefficient

ProblemDrag coefficient

Pressure and Shear stress distribution
Lecture37 External flow Drag Coefficient1

Drag and Lift ForcesAlternate Method

The drag coefficient for slender bodies

ProblemDrag coefficient

Factors affecting drag coefficient
Lecture38 External flow Drag Coefficient2

The drag coefficient for common geometries

Drafting

Fairing

Drag reduction in nature

Drag reduction in other applications

Experimental measurement of drag coefficient
Lecture39 External flow Drag in Vehicles

Drag Coefficient of carsHistory

Drag and Rolling Resistance on a Vehicle

Power required to drive a vehicle

ProblemPowerDrag and Rolling Resistance

Drag Reduction in Vehicles
Lecture40 External FlowIntroduction to Airfoil

What is Airfoil?

Airfoil types

Airfoil Nomenclature

Aircraft terminologies

AirfoilPotential flow theory

Minimum Flight Velocity
Lecture41 External FlowAirfoil Performance

Lift and Drag on Airfoil

AirfoilBoundary layer theory

AirfoilFlow separation

Effect of angle of attack

Performance of different Aerofoil

Airfoil with flap

Airfoil at different Mach Number
Lecture42 CFD Introduction

What is CFD?

CFD Scope and Applications

Role of CFD in Engineering

How CFD works

Practical Steps of Solving Problems in CFD
Lecture43 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 ANSYSCFX
Lecture 44 CFDGeometry and Mesh
Lecture 45 CFDPreSolver Solution Post Process (CFX)
Unlock the secrets of the fluid world and propel your understanding to new heights. Enroll today and embark on an unparalleled journey into the heart of Fluid Mechanics!

4Lecture4 Navier Stokes equationVideo lesson
NS equation as governing equation of fluid flow
Application of NS equation for a steady and laminar fluid flow between two fixed infinitely long plates.
Velocity profile
Volume flow rate calculation from velocity profile
Local velocity, average velocity, maximum velocity
Calculating Reynolds Number from Velocity profile

5Lecture5 Application of Navier Stokes equation  Couette flowVideo lesson
Physical meaning of NS equation
Fully developed flow
Application of NS equation for a steady and laminar fluid flow between one fixed and one moving plateCouette Flow
Applications of Couette flow

6Lecture6 Reynolds Transport Theorem DerivationVideo lesson
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

7Lecture7 Reynolds Transport Theorem  Continuity EquationVideo lesson
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

8Lecture8 RTTContinuity Equation NumericalsVideo lesson
Continuity Equation in Integral form
Solving numerical problems using Continuity Equation

9Lecture9 RTT Linear Momentum EquationVideo lesson
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

10Lecture10 RTT Angular Momentum EquationVideo lesson
Reynolds Transport Theorem (RTT)
Deriving Angular Momentum Equation using RTT
Problem based on Linear and Angular Momentum
RTT for Moving and Deforming CV

11Lecture11 Kinematics of Flow Flow typesVideo lesson
Fluid Flow Visualization Classics
Streamline
Pathline
Streakline
Timeline
Software for flow visualization (2dflowvis)

12Lecture12 Kinematics of Flow Irrotational FlowVideo lesson
Motion of fluid Element
Transformation of fluid element
Angular velocity vector
Vorticity Vector
Irrotational flow field

13Lecture13 Kinematics of Flow Stream functionVideo lesson
Visualizing velocity fieldJava Applet
Visualizing velocity field Maple
Stream function
Change in the value of stream function
Problem on stream function
Stream function in polar coordinates

14Lecture14 Kinematics of Flow CirculationVideo lesson
Circulation
Relationship between Circulation and Vorticity
Stoke’s theorem
Problem on Circulation
Physical meaning of Divergence of a vector
Circulation and Divergence in Java Applet

15Lecture15 Potential Flow Velocity potential functionVideo lesson
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

16Lecture16 Potential Flow Basic potential flowsVideo lesson
Uniform flow
Source and Sink flow
Vortex flow
Stream function and Velocity potential function for basic flows

17Lecture17 Potential Flow Superposition of potential flowsIVideo lesson
Superposition of basic potential flows
Doublet
Half body

18Lecture18 Potential Flow Superposition of potential flowIIVideo lesson
Flow around a cylinder
Flow around a cylinderVelocity and pressure distribution
Flow around a cylinderDrag and Lift
Rankine body
Problem on Rankine Body

19Lecture19 Potential Flow Superposition of potential flowIIIVideo lesson
Superposition of basic potential flows
Flow around a cylinder with circulation
Magnus Effect
Problem Flow around a cylinder with circulation

20Lecture20 Turbomachine Fluid MachinesVideo lesson
Fluid machines classification
Positive Displacement machines
Turbomachines
Comparison of PDPs and Rotodynamic pumps
Turbomachine Classifications
Scope of Turbomachines

21Lecture21 Turbomachine Euler’s EquationVideo lesson
One dimensional flow through an impeller
Velocity triangle
Euler’s equation of turbomachine

22Lecture22 Turbomachine Blade AnglesVideo lesson
Velocity triangle
Velocity triangle at inletassumptions
Effect of blade angle on head
Typical Characteristic curve of a centrifugal pump
Effect of blade angle on Characteristic curve

23Lecture23 Turbomachine PerformanceIVideo lesson
ProblemCentrifugal blower
Static, Friction and System head
Pump Losses
Pump Efficiency
Pump Performance Characteristic curves

24Lecture24 Turbomachine PerformanceIIVideo lesson
Pump System Curve
Pumps in Series and Parallel
Pump Affinity laws
Pump specific speed

25Lecture25 Turbomachine TurbineVideo lesson
Turbine
Schematics of hydraulic turbines
Velocity triangles of Turbine
Impulse Turbine
Reaction Turbine
Degree of Reaction

26Lecture26 Turbomachine Turbine PerformanceVideo lesson
Pump and Turbine Efficiencies
General Energy Equation
ProblemTurbine
Affinity laws for Turbine
Turbine specific speed

27Lecture27 Boundary layer ConceptVideo lesson
Classification of flows
One dimensional and multi dimensional flow
Steady and Unsteady flow
Uniform and NonUniform flow
Inviscid and Viscous flow
Attached and Flow separation
Laminar and Turbulent flow
PrandtlBoundary layer concept
Growth of boundary layer thickness

28Lecture28 Boundary layer Order Analysis over Flat plateVideo lesson
Order of Magnitude or Scale Analysis
Order of Magnitude Analysis over flat plate
Boundary layer thickness as a function of Reynold’s Number
Wall shear stress using Scale Analysis
Skin friction coefficient using Scale Analysis

29Lecture29 Boundary layer Blasius solutionVideo lesson
Laminar boundary layer on a flat plate
Blasius solution
Wall shear stress using Blasius solution
Friction coefficient using Blasius solution
Problem Using Blasius solution

30Lecture30 Boundary layer Turbulent flow over flat plateVideo lesson
Turbulent flow
Governing Equations in Turbulent flow
Boundary layer in Turbulent flow
Velocity profile in laminar and turbulent flow
Velocity distribution in turbulent boundary layer
Law of wall

31Lecture31 Boundary layer Displacement and Momentum thicknessVideo lesson
Disturbance or Boundary layer thickness
Displacement thickness
Displacement thickness using Blasius solution
Momentum thickness
Momentum thickness using Blasius Solution
Relative amount of displacement and momentum thickness for laminar flow over flat plate

32Lecture32 Boundary layer Approximate solutionVideo lesson
Control Volume analysis for Boundary layer
Von Karman Solution
Von Karman Integral equation
Approximate solution to Laminar boundary layer over flat plate

33Lecture33 Boundary layer Skin Friction CoefficientVideo lesson
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 flat plate

35Lecture35 External flow IntroductionVideo lesson
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

36Lecture36 External flowDrag and LiftVideo lesson
Resultant force on a body
Drag and lift Forces
Drag Coefficient
ProblemDrag coefficient
Pressure and Shear stress distribution

37Lecture37 External flow Drag Coefficient1Video lesson
Drag and lift ForcesAlternate Method
Drag coefficient for slender bodies
ProblemDrag coefficient
Factors affecting drag coefficient

38Lecture38 External flow Drag Coefficient2Video lesson
Drag coefficient for common geometries
Drafting
Fairing
Drag reduction in nature
Drag reduction in other applications
Experimental measurement of drag coefficient

39Lecture39 External flow Drag in VehiclesVideo lesson
Drag Coefficient of carsHistory
Drag and Rolling resistance on a Vehicle
Power required to drive a vehicle
ProblemPowerDrag and Rolling Resistance
Drag reduction in Vehicles

40Lecture40 External flowIntroduction to AirfoilVideo lesson
What is Airfoil?
Airfoil types
Airfoil Nomenclature
Aircraft terminologies
AirfoilPotential flow theory
Minimum Flight Velocity

41Lecture41 External flowAirfoil PerformanceVideo lesson
Lift and Drag on Airfoil
AirfoilBoundary layer theory
AirfoilFlow separation
Effect of angle of attack
Performance of different Aerofoil
Airfoil with flap
Airfoil at different Mach Number
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