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.