HYDRODYNAMICS
Paper Code:
MAT225
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
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:
- Theoretical Hydrodynamics: Milne Thomson, Macmillan.
- Text book of Fluid Dynamics : Chorlton F.CBS Publications, New Delhi.
- Fluid Dynamics : Goyal & Gupta, Pragati Prakasha
- Fluid Dynamics : Dr. H.K.Pathak, Shiksha Sahitya Prakashan
References:
- Fluid Dynamics, Schaum’s series.
-
Batchelor, C.K., An Introduction to Fluid Mechanics, Cambridge University Press.
Academic Year:
