# Virtual University of Pakistan

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## MTH7123 : Advanced Fluid Dynamics

### Course Overview

#### Course Synopsis

This course is a survey of principal concepts and methods of advanced fluid dynamics, and emphasizes fundamental concepts and problem-solving techniques. Topics to be covered include fluid properties, fluid statics, fluid kinematics, control volume analysis, dimensional analysis, internal flows (pipe flows), differential analysis (including approximations such as creeping flow, potential flow, and boundary layers), and external flows (lift and drag); use of differential and finite control volume analysis with continuity, momentum, and energy equations, You will acquire an understanding of the essential theoretical basis of the fluid mechanic sciences and their application to a range of problems of relevance to practical engineering.

#### Course Learning Outcomes

On successful completion of this course students will be able to:

• Demonstrate their understanding of the basic principles of static and fluid systems.
• Explain the fundamental properties of fluids, including viscosity, Newtonian and Non-Newtonian rheology, and viscoelasticity.
• Grasp the basic ideas of turbulence and knowledge of laminar and turbulent boundary layer fundamentals.
• Understand the dynamics of fluid flows and the governing non-dimensional parameters.
• State the conservation principles of mass, linear momentum, and energy for fluid flow

#### Course Calendar

 Topic Lecture Resource Page Introduction, Examples of Fluid Dynamics(continued) 1 Examples and Application of Fluid Dynamics, Basic Concepts, Pressure and Fluid Statics, Fluid Kinematics, Mass, Bernoulli and Energy Equations 2 Momentum , Differential and Dimensional Analysis, Flow in Pipes,Navier-Stokes Equation, Drag and Lift, Advanced Fluid Dynamics 3 What is a Fluid? Application Areas of Fluid Mechanics, No-Slip Condition 4 Brief History , Classification of Fluid Flow, Internal vs. External Regions of Flow 5 Compressible vs Incompressible Flow,Laminar vs Turbulent Flow, Steady vs Unsteady Flow 6 One-, Two-, and Three-Dimensional Flows, System and Control Volume,Importance of Dimensions and Units 7 Accuracy, Precision and Significant Digits, Fluid Properties, Continuum,Density and Specific Gravity 8 Vapor Pressure & Cavitation, Viscosity 9 Surface Tension & Capillary Effect,Pressure and Stress ,Variation of Pressure with Depth, 10 Use of Pascal Law,The Manometer, The Barometer & Atmospheric Pressure, Buoyancy & Stability,Stability of Immersed and Floating Bodies 11 ASSIGNMENT #1 Fluid Kinematics, Lagrangian And Eulerian Descriptions,Eulerian Description, 12 Acceleration Field, Acceleration Field and Material Derivatives, Flow Visualization,Streamlines, Pathlines 13 Streaklines and Comparison,Timelines,Plot of Data,Kinematic Description, Rate of Translation & Rotation, Shear Strain Rate 14 Kinematics, Eulerian Descriptions, Steady Two-Dimensional Velocity Field, Acceleration Field 15 Examples of Acceleration Field, Material Derivative and its Examples 16 Vorticity and Rotationabilty,Comparison of Two Circular Flows, Reynolds Transport Theorem 17 ASSIGNMENT #2 Application of Leibnitz Theorem,Exercises/Examples 18 Exercises/Examples,Objectives, Conservation of Mass 19 Mass, Bernoulli , Energy Equations,Linear Momentum Equation, Mass and Volume Flow Rates, 20 Bernoulli Equation,Derivation of Bernoulli Equation, Force Balance across Streamlines 21 Static, Dynamic, and Stagnation Pressures, Limitations on the Use of the Bernoulli Equation, Hydraulic Grade Line and Energy Grade Line 22 SPECIAL ASSIGNMENT Applications of Bernoulli’s Principle(continued) 23 Applications of Bernoulli’s Principe, Newton’s Laws of Motion(continued) 24 Newton’s Laws of Motion, Forces Acting on a Control Volume(continued) 25 Forces Acting on a Control Volume,The Linear Momentum Equations, Momentum-Flux Correction Factor 26 Flow with No External Forces(continued) 27 Flow with No External Forces, Rotational Motion and Angular Momentum,The Angular Momentum Equation 28 The Angular Momentum Equation, Radial Flow Devices, Summary ,Dimensional Analysis Background 29 Dimensional Analysis, Dimensions and Units, Dimensional Homogeneity, non Dimensionalisation of Equations, Dimensional Variables 30 ASSIGNMENT #3 Nondimensional (or dimensionless) variables, Examples of Non Dimensionalisation of Equations 31 Dimensional Analysis and Similarity,Similarity between Model and Pro-type car,Nondimensionalization of Equations 32 Buckingham Pi Theorem,Differential Analysis of Fluid Flow:Prelimineries 33 Derivative of Temperature, Total Derivative,Continuity Equation its Objectives, its Derivation using Divergence Theorem 34 Derivation of The Continuity Equation Using an Infinitesimal Control Volume, its alternative forms,in Cylindrical Coordinates,its Special Cases, Examples of Application of Continuity Equation 35 Examples of Application of Continuity Equation 36 The Stream Function in Cartesian and Polar Coordinates, Compressible Stream Function, Cauchy’s Equations, Derivation using Divergence Theorem,Infinitesimal Control Volume 37 Cauchy’s Equations, Derivation using Newton’s Second Law,Navier–Stokes Equation, Newtonian and Non-Newtonian Fluids,Derivation of the Navier–Stokes Equation for Incompressible, Isothermal Flow 38 Continuity and Navier–Stokes Equation in Cylindrical Coordinates,Calculation of the Pressure Field for a Known Velocity Field and in Cylindrical Coordinates 39 ASSIGNMENT #4 Exact Solutions of the Continuity and Navier–Stokes Equations for Fully Developed Couette Flow 40 Couette Flow with an Applied Pressure Gradient, Example of Exact Solutions of the Continuity and Navier–Stokes Equations: Fully Developed Couette Flow 41 Fully Developed Flow In a Round Pipe– Poiseuile’s flow and Sudden Motion of an Infinite Plate 42 Differential Analysis of Biofluid Mechanics Flows and Fully Developed Flow in a Round Pipe with a Simple Blood Viscosity Model, Boundary Layer, Boundary Layer Thickness 43 Boundary Layer Scaling of Navier-Stokes Equations, Laminar Viscous Flow : Exact Solution, Flow on an Infinite Plate, Flow Between Coaxial Cylinder (Circular Couette Flow), Steady Flow Through a Cylindrical Pipe (Hagen-Poiseuille Flow) 44 Flow in the Entrance Region of aCircular Pipe, Nonsteady Unidirectional Flow, Impulsive Motion of an Infinite Plate, Harmonic Oscillation of an Infinite Plate,Ekman Layer Problem, Motion Produced due to a Vortex Filament, Flow Past a Rigid Sphere 45 FINAL TERM EXAMINATION