Hydrodynamics

Paper Code: 
MAT 225
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. Understand the motion of fluid and develop concept, models
  2. Understand the techniques which enable us to solve the problems of fluid flow.

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

MAT225

Hydro dynamics (Theory)

The students will be able to –

 

CO60: Distinguish the basic principles of ideal fluid, such as Lagrangian and Eulerian approach, conservation of mass etc.

CO61: Use  Euler  and  Bernoulli's  equations  and  the  conservation  of  mass  to  determine velocity and acceleration for incompressible and non-viscous fluid.

CO62: Differentiate between rotational and irrotationl  flow, stream functions, velocity potential and able to construct complex potential due to sink, source and doublets.

CO63: Analyse the motion of a fluid element, Vorticity, Body forces, Surface forces, Stress & Strain analysis, Flow and circulation, Connectivity, Irrotational motion in multiple connected space,

CO64: Distinguish the concept of Irrotational motion of a cylinder in two dimensions.

CO65: Analyse the Motion of a circular cylinder in a uniform stream and two co-axial cylinders, Streaming and circulation for a fixed circular cylinder

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, power point presentation

 

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation

 

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation, Individual and group projects

 

Unit I: 
I
15.00

Kinematics of ideal fluid, Lagrange's and Euler's methods, Equation of continuity in cartesian, cylindrical and spherical polar coordinates, Boundary surface, Stream-lines, path-lines and stream lines velocity potential irrotational motion.

Unit II: 
II
15.00

Euler's hydrodynamic equations, Bernoulli's theorem, Helmholtz equations, Cauchy's integral, Motion due to impulsive forces. 

Unit III: 
III
15.00

Motion in two-dimensions, Stream function, Complex potential, Sources, Sinks, Doublets, Images in two dimensions: image of a source with regard to a plane, image of a source with regard to a circle.

Unit IV: 
IV
15.00

Irrotational Motion: Motion of a fluid element (General and Cartesian coordinates), Vorticity, Body forces, Surface forces, Stress analysis at a point, Strain analysis, Flow and circulation, Kelvin’s circulation theorem, Connectivity, Irrotational motion in multiple connected space, Acyclic and cyclic motion, Kelvin’s minimum energy theorem.

Unit V: 
V
15.00

Irrotational motion in two dimensions: Introduction, General motion of a cylinder in two dimensions, Motion of a circular cylinder in a uniform stream, Liquid streaming past a fixed circular cylinder, two co-axial cylinders, Circulation about a circular cylinder, Blasius’s theorem, Streaming and circulation for a fixed circular cylinder, Equation of a motion of a circular cylinder.

Essential Readings: 
  • M.D. Raisinghania, Fluid Dynamics, S. Chand & Co. New Delhi, 2016. 
  • Shanti Swarup, Hydrodynamics, Krishana Prakashan, 2016.
  • K.P. Goyal and J.K. Gupta, Fluid Dynamics, Pragati Prakashan, Meerut, 2011.
  • H.K. Pathak, Fluid Dynamics, Shiksha Sahitya Prakasha, 2013.
 
References: 
  • Schaum's Outlines, Fluid Mechanics, McGraw-Hill Education, 1 edition, 2007.
  • G.K. Batchelor, An Introduction to Fluid Mechanics, Cambridge University Press, 2000.
  • F. Chorlton, Text book of Fluid Dynamics, CBS Publications, New Delhi, 2004.
  • Milne Thomson, Theoretical Hydrodynamics, Macmillan, 3rd Edition, 1955.
Academic Year: 
2023-2024
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