Hydrodynamics
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.
Euler's hydrodynamic equations. Bernoulli's theorem. Helmholtz equations. Cauchy's integral, Motion due to impulsive forces.
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.
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.
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.
1. Milne Thomson, Theoretical Hydrodynamics, Macmillan.
2. Chorlton F.,Text book of Fluid Dynamics , CBS Publications, New Delhi.
3. Goyal & Gupta, Fluid Dynamics, Pragati Prakashan.
4. Dr. H.K.Pathak ,Fluid Dynamics , Shiksha Sahitya Prakashan.
1. Schaum's Outlines, Fluid Mechanics, McGraw-Hill Education; 1 edition(2007)
2. Batchelor, G.K., An Introduction to Fluid Mechanics, Cambridge University Press 2000.
3. Raisinghania,M.D, Fluid Dynamics, S. Chand, 2003.
