Syllabus
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Course Code: MMATH21-301 Course Name: Fluid Mechanics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Kinematics of fluid in motion: Real fluids and ideal fluids, Velocity at a point of a fluid. Lagrangian and Eulerian methods. Stream lines, Path lines and Streak lines. Vorticity and Circulation, Vortex lines, Velocity potential, Irrotational and rotational motions. Acceleration at a point of fluid, Local and particle rates of change. Equation of continuity. Conditions at a rigid boundary, boundary surfaces. (Relevant portions from the recommended text books at Sr. No. 1 & 2) |
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| 2 | Pressure at a point in a fluid, Conditions at a boundary of two immiscible fluids. Equation of Motion : Lagrange's and Euler's equations of Motion. Bernoulli's equation, Applications of the Bernoulli Equation in one–dimensional flow problems, Steady motion under conservative body forces. Kelvins circulation theorem, Vorticity equation. Energy equation for incompressible flow. Kinetic energy of irrotational flow. Kelvins minimum energy theorem. Mean value of the velocity potential. Kinetic energy of infinite liquid. Uniqueness theorems. (Relevant portions from the recommended text books at Sr. No. 1 & 2) |
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| 3 | Axially symmetric flows. Sphere at rest in a uniform stream, Sphere in motion in fluid at rest at infinity. Equation of motion of a sphere. Kinetic energy generated by impulsive motion. Motion of two concentric spheres. Three-dimensional sources, sinks and doublets. Images of sources, sinks and doublets in rigid impermeable infinite plane and in impermeable spherical surfaces. (Relevant portions from the recommended text books at Sr. No. 1 & 2) |
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| 4 | Two-dimensional flows: Use of cylindrical polar coordinates, Stream function, Some fundamental stream functions, Axisymmetric flow, Equations satisfied by Stokes’s stream function in irrotational flow, Basic Stokes’s stream functions, Boundary conditions satisfied by the stream function. Irrotational plane flows: Complex potential, Image systems in plane flows. Milne-Thomson circle theorem. Circular cylinder in uniform stream with circulation. Blasius theorem. (Relevant portions from the recommended text books at Sr. No. 1 & 2) |
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