# Fluid Dynamics

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# Code(Credit) : CUTM1527 (3-0-1)

## Course Objectives

To introduce the foundations of fluid dynamics, various formulations of governing equations and their mathematical properties in order to establish a firm basis for other modules.

## Course Outcomes

 COs Course outcomes Mapping Cos with POs (High-3, Medium-2, Low-1) CO1 Distinguish and analyse the governing equations of fluid dynamics in various formulations for compressible and incompressible viscous and inviscid flows. PO1(3), PO2(2) CO2 Estimate the impact of different physical phenomena based on dimensional analysis. PO2(2), PO4(2) CO3 Examine mathematical properties of governing equations and be able to critically evaluate correct boundary/initial value problems for various flows. PO5(2), PO9(2)

## Course Syllabus

MODULE – I

Kinematics of Fluids, Methods describing Fluid motion, Lagrangian and Eulerian Methods, Translation, Rotation and Rate of Deformation, Streamlines, Path lines and Streak lines.

PROJECT 1: A Report on Steady vs Unsteady Flow, Compressible vs incompressible Flow, Laminar vs Turbulent Flow, Newtonian vs Non-Newtonian Flow, Invisid vs Viscous Flow, Rotational vs Irrotational Flow. (Definition, Comparative Study & Examples)

MODULE – II

Fundamental equations of the flow of viscous compressible fluids: Equations of continuity, motion and energy in Cartesian coordinate systems, The equation of state, Fundamental equations of continuity, motion and energy in Cylindrical & Spherical coordinate systems.

MODULE – III

2-D and 3-D inviscid incompressible flow: Basic equations and concepts of flow, Circulation theorems, Velocity potential, Rotational and Irrotational flows, Bernoulli’s Equation.

PROJECT 2: A study on Stokes Circulation Theorem

MODULE – IV

Laminar Flow of Viscous Incompressible Fluids: Flow between parallel flat plates, Couette flow, Steady Flow in pipes, Hagen-Poiseuille flow, Unsteady motion of a flat Plate.

PROJECT 3: A study on plane Poiseuille flow.

PROJECT 4: A report on steady flow of viscous incompressible fluid between two porous parallel plates.

PROJECT 5: A study on laminar flow between two coaxial circular cylinders (i.e. an annulas).

PROJECT 6: A report on unsteady flow of a viscous incompressible fluid over an oscillating plate.

MODULE – V

The Laminar boundary layer Flow: Properties of Navier-Stokes equations, Boundary layer equations in 2-D flow, Similarity of Flows, Reynold’s Number, The boundary layer along a flat plate, Boundary layer on a surface with pressure gradient.

MODULE – VI

Momentum Integral theorems for the boundary layer, Von karman-Pohlhausen method, Separation of boundary layer flow, Boundary layer control.

MODULE – VII

The origin of Turbulence, Reynold’s modification of the Navier-Stokes equations for Turbulent flow, Reynold’s stresses, Prandtl’s mixing length theory.

BOOK PRESCRIBED

1 S. W. Yuan, “Foundations of Fluid Mechanics”, Prentice – Hall of India

Chapters: 3 (3.1 to 3.4), 5 (5.1 to 5.6), 7 (7.1 to 7.5), 8( 8.1 to 8.4, 8.7 to 8.8) ,9, 10(10.1 to 10.3(a))

BOOK REFERENCE

1 J. L. Bansal , “Viscus Fluid Dynamics”, IBH Publication, Joypur.

2 M. D. Raisinghania, "Fluid Dynamics with Complete Hydrodynamics", S. Chand & Company Ltd, New Delhi.

## Session 2

Methods describing Fluid motion, Lagrangian and Eulerian Methods

## Session 3

Translation, Rotation and Rate of Deformation

## Session 5 & 6

PROJECT 1: A report on steady vs unsteady flow, compressible vs incompressible flow, laminar vs turbulent flow, Newtonian vs non-Newtonian flow, inviscid vs viscous flow, rotational vs irrotational flow (Definitions, Comparative Study & Examples).

## Session 7

Fundamental equations of the flow of viscous compressible fluids: Equations of continuity

## Session 8

Fundamental equations of the flow of viscous compressible fluids: Equations of motion

## Session 9

Fundamental equations of the flow of viscous compressible fluids: Equation of energy in Cartesian coordinate systems

## Session 11

Fundamental equations of continuity, motion and energy in Cylindrical & Spherical coordinate systems.

## Session 12

2-D and 3-D inviscid incompressible flow: Basic equations and concepts of flow

## Session 14

Velocity potential, Rotational and Irrotational flows

## Session 16 & 17

PROJECT 2: A study on Stokes circulation theorem.

## Session 18

Laminar Flow of Viscous Incompressible Fluids: Flow between parallel flat plates

## Session 20

Steady Flow in pipes: Hagen-Poiseuille flow

## Session 21

Unsteady motion of a flat Plate

## Session 22 & 23

PROJECT 3: A study on plane Poiseuille flow.

## Session 24 & 25

PROJECT 4: A report on steady flow of viscous incompressible fluid between two porous parallel plates.

## Session 26 & 27

PROJECT 5: A study on laminar flow between two coaxial circular cylinders (i.e. an annulas).

## Session 28 & 29

PROJECT 6: A report on unsteady flow of a viscous incompressible fluid over an oscillating plate.

## Session 30

The Laminar boundary layer Flow: Properties of Navier-Stokes equations

## Session 31

Boundary layer equations in 2-D flow

## Session 32

Similarity of Flows, Reynold’s Number,

## Session 33

The boundary layer along a flat plate

## Session 34

Boundary layer on a surface with pressure gradient

## Session 35

Momentum Integral theorems for the boundary layer

## Session 36

Von karman-Pohlhausen method

## Session 37

Separation of boundary layer flow

## Session 38

Boundary layer control

## Session 40

Reynold’s modification of the Navier-Stokes equations for Turbulent flow

## Session 41

Reynold’s stresses

## Session 42

Prandtl’s mixing length theory

## Case Studies

### Dr. Goutam Kumar Mahato

##### Teaching
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Received M.Sc. (Mathematics) from Vinoba Bhave University, Hazaribag and B.Ed. from Ranchi University, Ranchi in the year of 2006 and 2008 respectively. Awarded PhD, in the year of 2013, from Indian School of Mines, Dhanbad. Published 22 research papers in different journals of international repute. Participated and presented 16 research papers in various National and […]