Hi there. Our solid bodies in the previous session We found that the dynamics of the equation, We have reached a wave equation, including in one dimension and in three dimensions. Continuous media solids and We have divided the fluid as before, liquid fluids and We divide them into gases. But all this is a continuum in There are common side of the conservation of mass, conservation of momentum there. Equations, the main equations are the same but applications their physical behavior to reflect the simplification is going studies. Fluid physical spots are very Great place are changing flow going through it anyway, gas is flowing in the flowing liquid, solid staying near a point at objects, of particles of a given space They move around the vicinity, the place is small change for him based on equations have achieved. Now we come to the liquid. I remind liquids less remarkable change in volume, thus idealized A zero will be considered in the equation that is incompressible, No change in intensity does not change. If this change in gas volume The most important features of the subject. Now you're starting from liquids. First, we have the conservation of mass equation. This continuum for all For gases for the solids this review will be the same but different. If you changed ro fluids idealized definition of the ideal incompressible case, ie the definition of constant density means that rode hard, The first term thus falls ro of the time derivative. If ron ron divergence is constant here turns out, means that the divergence times ro v is equal to zero, that is not zero ro v is equal to zero by the divergence coming. v the velocity of the fluid port, This creates a vector field. Our momentum equation was as follows, here again a constant speed of ro derivative with a mass of momentum gives i.e. when multiplied thereof that they all came from Newton's equation we have seen derived from Newton's equations. In the latter term the total derivative, v is full derivative with respect to t We have seen that come due. Now liquids to solids As there is a difference based. Once you have a pressure whereby density does not change its place The density of a density bilinmeyenk turns out to be unknown any given When a value that remains constant, but Does a pressure unknown. This is a tensor that sigma matrix essential that a magnitude We said, therefore, pressure in the pressure p in English from the first letter of the word everywhere an accepted form of representation. Unit matrix by multiplying here We create a matrix. v is the velocity, velocity gradient was giving a matrix, Taking transposed thereof and still more of a matrix thus consists of a symmetric matrix, it multiply by a factor called a m. Now where I come from, the place where the latter term molecules in the liquid collisions with each other so show lost momentum. This significant periods observations As a result of an agreed outcome. Do you see it is zero coefficient This means that there is no loss of momentum hence we call it perfect fluid, We call frictionless fluid. It does this friction coefficient for showing the features noted friction coefficient or Turkish is used in the West the viscosity of the languages Showing the term. With this observation from nature an equation which is its theoretical There are also basic, but that's enough for us that such a structure. Newton in solid bodies, Pardon Young elasticity which replaced the coefficients a in the nature of constitutive equations. See if we took this place sigma divergence to be here. Sigma as follows from the divergence p happens at the end of the gradient vector will be released. p numerical functions, gradient vector thereof. v vector, Laplacian digital processor thus a vector gene and here are the acceleration term. This equation Navier-Stokes It's called the equation, See how easily we have achieved. This is the world of mathematics in 2000, collected Association for the next hundred years, important problems were listed, among them Waiting for a solution of the Navier-Stokes equations Among the main problems is announced to the world, and the world's most time spent on the computer from the equation is one of the Navier-Stokes equation, because all the ships and even aircraft The movement of the car of the equation requires solutions, Or a flow of liquid through the machine, the gene that produces a plastics factory flow of polymers such as plastics. Here it's a bit of this equation additional terms may be required, but more This is the main equation. If you perfect fluid friction then only the pressure of the term sigma, where there are less of us this is our definition of whereas we are assuming pressure plus against a force that minus As you can see because it comes Navier-Stokes equation for this mu'l fall term only remains following sections. This was examined before Euler equation called the Bernoulli equation. This is very interesting solutions of the equation An equation is much easier because there are. For example, in meteorology or something that used equations from the sea, This equation of wave motion in rivers are resolved to a large extent, it works by. Water, air, fluids, such as water less momentum loss In the case that equation but used also important friction There are cases where the same water time you got to use the Navier-Stokes. But honey, petroleum liquids, such as fluids such as plastics awesome There is friction, then this do not fit the definition of a perfect fluid. Now here I want to take a break then the third kind of continuum We will now, this will be the dynamics of the gas. You'll see there the same slightly different equations reviews Because the gas requires the physical We need to use the feature. Goodbye until we meet again.