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Course Description
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Fundamentals: Molecular motion, continuum hypothesis, introduction to kinetic theory, Mean free path, transport phenomena, kinetic theory for transport equations, Introduction to Cartesian Tensors: Scalars, Vectors and Tensor Notation, Forces Acting on a Surface, Scalar and Vector Products, Kronecker Delta and Alternating Tensor, Gradient, Divergence and Curl Operators, Symmetric and Anti-Symmetric Tensors, Conservation Laws for Fluid Flows: Continuity equation: Mass flux, integral and differential equations, stream function. Momentum equation: Forces, stresses, symmetry of stress tensor; properties of second-order, symmetric tensors; Newtonian fluid; Derivation of momentum equations, boundary conditions; Euler equations, streamline coordinates. Energy equation: First law of thermodynamics, heat transfer, derivation of energy equation. Derivation of entropy equation, implications for transport coefficients. General form of Bernoulli equation. Potential Flows: Complex potentials, Source, Sink, Doublet, Vortex, Transformation of Flows: Conformal mapping, Solutions of the Viscous Flow Equations: Classification of solutions; Unidirectional flows; Similarity solutions; Lubrication theory; Creeping motion, Laminar Boundary Layer: Boundary layer equations; Similarity solution; Free-Shear Flows; Approximate integral solutions; Thermal boundary layer; Asymptotic solutions. Turbulent Flows: Reynolds decomposition, Reynolds stresses, Reynolds equation. Self similar free shear flows; effective viscosity. Turbulent boundary layers; mixing length hypothesis. Turbulence models.
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Course Objectives
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The course is designed to teach senior and first year graduate mechanical engineering students the fundamentals of the classical fluid mechanics at an advanced level that is beyond the scope of the first fluid mechanics course. An introduction to the Cartesian tensors and derivation of flow equations in various forms. Solutions to the flow equations using scaling and approximations. Giving a general perspective on viscous fluid flows, boundary layer theory, turbulent flows, unidirectional flows and lubrication theory with applications in engineering.
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Course Learning Outcomes
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At the end of this course, students will have a complete understanding of the following fundamental topics in engineering:
I. Be able to use Cartesian tensors to manipulate flow equations;
II. Understand the derivation and physical interpretation of the flow equations;
III. Understand and effectively use the scaling and approximations to obtain analytical solutions
IV. Understand the physical meaning and mathematical implementation of potential theory and the inviscid flows
V. Understand the boundary layer theory, derivation and solution of the boundary layer equations,
VI. Understand the lubrication theory, its limitations and applications
VII. Understand the concept of flow instability and turbulent flows,
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Textbook
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1. White, F.M., Viscous Fluid Flow, McGraw-Hill, 1994.
2. Kundu, P.K., Cohen, I.M and Dowling, D.R. “Fluid Mechanics” 5th Edition
3. Panton, L. “Incompressible Flows”, 2013, Wiley
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Other References
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1. An Introduction to Fluid Dynamics by Batchelor G.K.
2. Physical Fluid Dynamics by Tritton, D.J.
3. Boundary-layer Theory by Herrmann Schlichting, Klaus Gersten, with contributions from Egon Krause and Herbert Oertel Jr.
4. Turbulent Flows by Pope, S.B.
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