LECTURE №1 2014/151

2 1. Introduction to Fluid Mechanics The Fluid mechanics The Fluid mechanics is a part of mechanics, that studies the states of motion and rest of liquids and gases, as well as the interactions with the immersed bodies.

History 2014/153 The faces of fluid mechanics Archimedes ( BC ) Euler ( ) Navier ( ) Stokes ( ) Reynolds ( ) Prandtl ( ) Bernoulli ( ) Newton ( ) Leonardo da Vinci ( )

2014/ Fluid Properties and Types : density - compressibility, normal force - pressure, tangential force – stress, viscosity – Newtonian fluids, non-Newtonian fluids, ideal fluids.

2014/155 = const. – incompressible fluid (water) const. – compressible fluid (air) water at 4 0 С air at 20 0 С relative density Fluid Mechanics Lecture №1 * density - mass per unit volume

2014/156 relative specific weight specific weight - weight per unit volume Fluid Mechanics Lecture №1

2014/157 - sound speed K water ~ 10 9 Pa K >> 1 – incompressible fluid compressibility K – modulus of elasticity (compressibility) at constant temperature Т Fluid Mechanics Lecture №1 a ≈ 300 m/s – air a ≈ 1500 m/s – water a >>1 – incompressible flow where w - volume, p - pressure

2014/158 M = U/a – Mach number М << 1 – incompressible flow М < 1 – subsonic flow М ~ 1 – sonic flow М > 1 – supersonic flow Fluid Mechanics Lecture №1

2014/159 * NORMAL FORCE F fluid – the pressure p distributes in all directions; acts normally to each surface inside the fluid solid body – the force F locally acts on the contact surface A through the pressure p Fluid Mechanics Lecture №1

2014/1510 * PRESSURE p pressure at point: dF – elementary normal force, ds – elementary surface or where is a unit normal vector to the elementary surface ds Pascal’s law (17 th century) – the outer pressure is distributed in every point of the fluid volume and does not depend on the orientation of the elementary surface ds Fluid Mechanics Lecture №1

2014/1511 * TANGENTIAL FORCE F F – drag force * VISCOSITY – inner friction  - coefficient of dynamic viscosity Fluid Mechanics Lecture №1

2014/1512 * TANGENTIAL STRESS  Fluid Mechanics Lecture №1

2014/1513 * NEWTON’S LAW FOR VISCOSITY - angular deformation, - velocity of angular deformation Fluid Mechanics Lecture №1

2014/1514 Newton's law of viscosity: The tangential stress is proportional to the angular deformation. (for most of the liquids at small temperature differences) (for gases) Fluid Mechanics Lecture №1

2014/ coefficient of kinematic viscosity NEWTONIAN FLUIDS – fulfill the Newton’s law of viscosity– water, alcohol, air, some oils; stick (non-slip) on the solid walls and are moving with the wall velocity Fluid Mechanics Lecture №1

2014/1516 * NON-NEWTONIAN FLUIDS – do not fulfill the Newton’s law of viscosity – biological solutions, blood, milk, plasma, dye solutions, cement, tooth paste, clay... * IDEAL FLUIDS – with neglected viscosity and deformation – do not exist in nature, but at some conditions every fluid could behave in such manner in the regions far away the solid surfaces, i.e., does not stick on the solid walls and does not move with their velocities. Fluid Mechanics Lecture №1

2014/1517 Coiling of a honey jet falling onto a plane: (a) Experiment (b) Numerical simulation Thin strip of a viscous fluid suspended on two supports Periodical folding of a layer of glucose syrup with 120 times bigger viscosity than that of water Viscoso-elastic fluids ( NON-NEWTONIAN FLUIDS ) Fluid Mechanics Lecture №1

2014/1518 The effect of Weissenberg Viscoso-elastic fluid (solution of a polystyrene in an organic solvent) – two successive moments of the fluid climbing on the rotation axis Coiling of the same fluid on a bobbin– application at the synthetic fibers in the textile industry Fluid Mechanics Lecture №1

 Thank you for your attention!  Till the next Tuesday at the same place and same time /1519 Fluid Mechanics Lecture №1