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ESO-212 Fluid Mechanics & Rate Processes
Topics covered so far (lecture-wise)
18 November 2011: Review of the salient features of the course.
16 November 2011: Diffusion in the dilute limit; Derivation of the unsteady diffusion equation; boundary conditions for mass transfer;
14 November 2011: Mass transfer: discussion on diffusion, definition of fluxes of species, Fick's law of diffusion;
11 November 2011: Non-dimensionalisation of the convective heat transfer equation (5.7, 5.8); Nusselt number as the dimensionless heat transfer coeffeicient in fluids; Dimensionless correlations for Nusselt number as a function of Reynolds number and Prandtl number (5.12);
09 November 2011: Transient conduction in a semi-infinite solid: Physical interpretation of the similarity solution; diffusion length and its meaning (3.7.5); Convective heat transfer: Illustraion by a simple 1-D example (transpiration cooling) (5.3);
04 November 2011: Completed heat transfer in a fin; effectiveness factor for fins; Transient conduction (Section 3.7) in a slab; Heissler charts for a slab; Significance of Biot number (3.7.3); Transient heating of bodies with negligible internal resistance (3.7.4);
02 November 2011: Conduction in cylindrical geometry: resistance of an annular cylindrical shell; Critical thickness of a cylindrical insulation (Section 3.3.3); Started heat transfer enhancement by fins (Section 3.5).
31 October 2011: Nondimensionalization of the unsteady heat conduction equation -- Biot number and its significance; Steady conduction in slabs; Conduction in a slab with convective BC (Sec 3.2.2); Thermal resistance of a composite slab (Sec 3.2.3); Interpretation of Biot number in terms of thermal resistances (3.2.4);
28 October 2011: Derivation of unsteady conduction equation; discussion of boundary conditions for heat transfer (Sections 2.4, 2.5, 2.6 of V. Gupta); Convective boundary condition at a solid-liquid interface; introduction to heat transfer coefficient;
24 October 2011: Review of I and II law of thermodynamics; introduction to heat transfer; heat and mass transfer as rate processes; Modes of heat transfer: conduction, convection and radiation; Fourier's law of heat conduction (Chap. 1; Section 2.1, 2.2 of Gupta)
Fluid Mechanics part ends
21 October 2011: Discussion on drag force past bluff bodies like a sphere; effect of roughness in inducing turbulence; Physics of swing bowling: fluid mechanical explanation of out-swing, in-swing and reverse swing of cricket balls.
19 October 2011: Integral momentum equation for boundary layer flows: Expression for shear stress in terms of displacement thickness and momentum thickness. Illustration for uniform flow past a flat plate; variation of boundary layer thickness with flow direction; derivation of expression for skin friction coefficient;
17 October 2011: Scaling of boundary layer thickness with Reynolds number from re-scaling Navier-Stokes equation; Integral momentum equation for obtaining the shear stress on a solid surface.
12 October 2011: Potential flow past a rotating cylinder: Magnus - Robin effect. Boundary layers: Motivation from flow past bluff bodies; separation; stream-lining; origin of boundary layers;
10 October 2011: Derivation of velocity potential and stream function for a doublet; Flow past a Rankine half body; Potential flow past a cylinder by superposition of a doublet and uniform flow;
28 September 2011: Potential flows in 2-D: Derivation that stream function also satisfies Lapalce equation for 2-D irrotataional flows; Proof that stream lines and equipotential lines are orthogonal to each other for potential flows; Stream function and velocity potential for (1) uniform flow; (2) line source/sink; (3) line vortex. Principle of superposition of simple flows to generate new potential flows.
27 September 2011: Derivation of Bernoulli equation from the Euler equation; Applicability of Bernoulli equation; Inviscid and Irrotational flows; Velocity potential; (Section 11.5 of Gupta & Gupta; Chapter 12 of Gupta & Gupta; Chapter 6 of Fox & McDonald)
26 September 2011: Major and minor losses; loss coefficients; Energy balance for a pipeline network with minor losses and pumps/compressors (Gupta & Gupta, Chap. 10; Fox and McDonald, Chap. 8; White, Chap. 6); Fluid flow at high Reynolds number; Euler equation for Inviscid flows;
23 September 2011: Pipe flows and losses in pipe fittings; laminar and turbulent flows in a pipe; Non-dimensionalization of the pipe flow problem: the concept of friction factor; Friction factor vs Reynolds number charts (Moody diagram) for smooth and rough pipes in laminar and turbulent regimes; relation between wall shear stress in a pipe and friction factor; Major and minor losses (Gupta & Gupta, Chap. 10; Fox and McDonald, Chap. 8; White, Chap. 6).
21 September 2011: Nondimensionalisation of Navier-Stokes equations: emergence of dimensionless groups such as the Reynolds number, Froude number, and their physical interpretation; Discussion on similitude; geometric, kinematic and dynamical similarity.
19 September 2011: Dimensional analysis and Similitute: Motivation for doing dimensional analysis; Buckingham's Pi theorem to reduce a functional relationship among dimensional variables to a functional relationship among (smaller number of) dimensionless groups; Example: drag force on a sphere (Chapter 7 of Fox and McDonald; Chapter 5 of White).
9 September 2011: Further discussion on pipe flow problem and its validity and assumptions involved; Started motivating Dimensional analysis.
7 September 2011: Boundary conditions for solving Navier-Stokes equations (Section 6.6 of Gupta & Gupta); Steady, fully-developed flow between two parallel plates driven by wall motion as well as pressure gradient: derivation of the velocity profile by solving the Navier-Stokes equations (Example 6.1 of Gupta & Gupta); Validity of laminar flow profiles in channels and tubes; Derivation of velocity profile for pipe Poiseuille flow from Navier-Stokes equations; Derivation of flowrate-pressure drop relation (Hagen-Poiseuille equation) for laminar flow in a pipe.
5 September 2011: Completed the derivation of Navier-Stokes equations for an incompressible Newtonian fluid; Shear stresses in a viscous fluid: Newton's law of viscosity (Section 1.3 of Gupta & Gupta; Section 2.4 of Fox & McDonald); Constitutive relation for a Newtonian fluid (Section 6.2-6.5 of Gupta & Gupta; Section 5.4 of Fox & McDonald)
2 September 2011: Derivation of differential momentum balance; State of stress in a fluid on an element of arbitrary orientation: the notion of the stress tensor and its meaning; (Sections 6.1, 6.2 of Gupta & Gupta; Section 5.4 of Fox & McDonald); To be continued.
29 August 2011: Derivation of Differential mass balance (continuity equation); Continuity equation in Rectangular (Cartesian) and cylindrical coordinates; Continuity equation for an incompressible fluid; Criterion for incompressible flow based on Mach number; Stream function for 2-D flows; Illustration that stream lines are lines where stream function is a constant; relation between volumetric flow rate across two stream lines and difference between stream function values (section 4.3 of Gupta & Gupta; Section 5.2 of Fox & McDonald).
26 August 2011: Application of Bernoulli equation to flow measurement: restriction flow meters such as orifice and venturi meteres; derivation of expression for mass flow rate using discharge coefficient; Static and stagnation pressures; Pitot tube for measurement of local fluid velocity. (section 8.7 of Gupta & Gupta, sections 6.3 and 8.10 of Fox & McDonald); Differential balances: Started derivation of differential mass conservation;
24 August 2011: Steady mechanical energy balance with losses written in the form of various "heads"; Kinetic energy correction factor for flows with non-uniform velocity profiles; Relation between energy balance with the Bernoulli equation; Bernoulli equation and its validity (Chapter 7); Started application of Bernoulli equation to flow measurement;
19 August 2011: Integral energy balance for a CV: contd from previous lecture. Discussion on shaft work, work done by normal stresses, shear stresses etc.; Viscous dissipation of energy (Chapter 7) Simplified forms of integral energy balance with assumptions of steady flow, incompressible flow, uniform flow approximation etc.;
17 August 2011: Example illustrating the Integral momentum balance: force due to a jet of liquid on a solid surface; brief discussion on the first law of thermodynamics; Integral energy balance for a CV from the first law of thermodynamics (Chapter 7);
12 August 2011: Completed discussion on integral momentum balance for a CV; Discussed body and surface forces on a CV; uniform flow approximation and its validity for free jets; Momentum correction factor for flow in pipes (section 5.3); Calculation of momentum correction factor for laminar and turbulent flows in pipes of circular cross-section;
10 August 2011: Integral balances: Conservation of mass for a CV using Reynolds transport theorem (sections 4.1,4.2). Simplified forms of mass balance for (a) incompressible fluids and (b) steady flows; simplification for uniform flows in entry and exit to CVs; introduction of (cross-section) average velocity. Started derivation of integral momentum balance for a CV (section 5.1 and 5.2).
8 August 2011: Analysis of fluid motion: System (control mass) vs control volume; Derivation of Reynolds transport theorem (section 3.8 of Gupta & Gutpa; section 4.2 of Fox and McDonald); Conservation of mass for a CV using Reynolds transport theorem (sections 4.1,4.2);
5 Aug 2011: Steady vs unsteady flows; Graphical description of flows: path lines, streak lines and stream lines (section 3.4); Derivation of equation for streamlines; Worked out example on how to derive the equation describing a streamline; Showed video clips from Eulerian & Lagrangian Description and Flow visualization of Shapiro videos (MIT).
3 Aug 2011: Kinematics: Description of fluid motion; Lagrangian and Eulerian descriptions of fluid flow (Section 3.1); Substantial derivative: relation between Eulerian (local) and Lagrangian (material) rates of change (Section 3.2).
1 Aug 2011: Hydrostatic forces on planar and curved submerged surfaces (Sec 3.5 of Fox and McDonald; 7th ed); Buoyancy (Sec 2.7 of Gupta & Gupta)
29 July 2011: Proof that pressure at a point in a static fluid is a scalar (Sec 2.1 of Gupta & Gupta); Pressure force on a fluid element (Sec 2.2 of Gupta & Gupta); Basic equation of fluid statics (Secs 2.3, 2.4 of Gupta & Gupta);
27 July 2011: Continuum Approximation and its validity; Body and Surface forces in fluid mechanics; Pressure as the normal force per unit area in a static fluid;
25 July 2011: Course policies; Introduction to fluid mechanics and rate processes; Distinction between fluids and solids;