Physics of Life
Soft and Living Matter Group
Fluid Mechanics lectures:
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Books:
1. Physical hydrodynamics: Oxford publications
4-Authors: E. Guyon, J.P Hulin, L. Petit, C.D Mitescu,
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2. Fluid Mechanics : Elsevier publications.
Authors: P. Kundu, I.Cohen, D. Dowling.
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3. David Tong Lectures
http://www.damtp.cam.ac.uk/user/tong/fluids.html
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Week -1
Fluid mech applications, examples fluid flow.
Fluid Dyn. Laws : just a solution of 3 PDEs ?!!?
Fluid element, Knudsen number, Mathematical preliminaries
Viscous vs. convective transport of mass, momentum,energy
Week-2
Kinematics: Eulerian/Lagrange reference frames
https://www.youtube.com/watch?v=3OYOfuWXwy8&t=632s
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Stream-Path-Streak lines.
Velocity grad tensor =>
( symmetric + anti-symmetric -> vol. change + deviatoric + rotational)
Large and small deformation,
Conservation of mass eqn., incompressible flow (div. V=0)
Stream function for various kinds of flow.
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Week-3 (Euler flows)
Mass conservation equation.
Momentum Conservation equation, Momentum current
Euler equation for inviscid flows.
Bernoullis eqn for ideal flows. What is vorticity ? Vorticity equation.
Do all circular flow have vorticity ?
When are Euler flows valid or relevant ?
Does Planar shear flow or Couette flow have vorticity ?
Velocity potential for planar/ source/ sink/ dipole flows.
Vortex flow, Flow around (spinning) cylinder or sphere, Magnus force.
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QUIZ on 14th Sept, 2022
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Week-4 (mass and momentum eqn: Navier Stokes)
Stress tensor properties,
Expressing stress tensor in terms of : pressure terms +
deviatoric + dilation parts of the vel. gradient tensor
Navier Stokes equation
Properties of viscosity are different for liquid and for gas.
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https://www.whoi.edu/cms/files/adoucette/2006/4/Pedlosky_12.800_Ch3%2706_9199.pdf
section 3.6 onwards
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https://web.mit.edu/2.25/www/pdf/viscous_flow_eqn.pdf
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Week-5 ( Navier Stokes to Stokes, Reynolds number)
Lec-1 Lec-2
Lec1: Bernouli eqn valid for STEADY (no explicit time dependence) of flows along streamline.
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Brief intro to boundary layer,
Momentum diffusion and feel of other numbers.
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Week-6 (Incompressible flows and Boussinesq apprx, microscopic origins of viscosity and conductivity, dimensionaless numbers characterizing flows)
Lec-1 Lec-2 Lec-3 Lec4
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Week-7 (low Reynolds number flows)
Lec-1 Lec-2 Lec-3 Lec4
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Week-8 (compressible flow)
Lec-1 Lec-2 Lec-3 Lec4
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