Hi, basic conservation of nature

We saw from the law of mass conservation,

We saw the conservation of electric charge, We saw the conservation of heat energy.

With these numerical functions conservation of the specified size.

Then, the magnitude of the vector We saw momentum conservation.

Conservation of momentum, Newton's mass times the same as the acceleration equals force law.

The continuous media in the practice of the

We saw solid objects applications.

Here iii theory Remove the equation, we

where the wave propagation equations have achieved.

Then in fluid mechanics passed to the application.

Fluids, liquids and gases We were divided into two.

We have obtained the equations of fluid,

We will now obtain the equations of gas and we will see some applications.

Now gases with liquids Not very big difference between.

Roots of equations, basic terms.

Conservation of mass and momentum conservation equations having the same validity.

but araların-

There is a difference in this important difference but it's not a big difference.

The only difference in numerical terms, There is a difference that is composed of two stages.

He can not be compressed media status liquids were saying.

Media can be compressed, We called them gas.

Then density constant kalınıyo-

was staying.

And a pressure of unknown meant that instead.

If the environment can be compressed then it's going gases,

intensity variable is going on, therefore comes as an unknown.

Furthermore, the pressure no longer independent not an unknown,

a function of concentration turns out to be.

Body fluids other than these two differences and momentum conservation equations are the same.

If summer is here and so dörtyüzellialt

Fifty-seventh on pages Equations of the same shape as the liquid.

Because these fluids always available for all.

The only difference will occur without sig this is a variable ron

will be composed of.

The behavior of gases equation as follows: Again, this tension, stress,

which showed a pressure and friction therefore we show mü'l terms.

Where i is a unit vector, the identity matrix.

Sigma already tensor matrix that we call In terms of the nature of mathematical matrix,

to specify the physical properties We call for tensor.

A vector gradient.

V is multiplied together with a gradient without any mark,

it is a dietetic, We have seen that a matrix.

This matrix also taking iiii Creating a symmetric matrix.

This is the same, the only difference I said before pressure as a function of ro.

Of course, a wide variety of gases, ideal gases, but we also

in many cases the most basic providing information in case of gas

commitment to this p ro that is linearly

pressure in proportion to the intensity going.

As density increases, the pressure is rising or pressure in the arteries increases the density contrast

shares a. We also know that,

şişerirk bicycle tire pump-yi Suppose that when you press the volume change.

Very little change in the tire.

Pressure increases, but you The density of the air inside the

sent because the volume is increasing as for the amount of air that is worth noting.

Now take them To put momentum

equation goes like this: It had the right sigma, sigmoid

There was divergence of sigma, instead of this magnitude coming.

See also in this liquid In this way it sounded.

This equation for gases We call Navier Stokes equations.

Here there are mass conservation equation.

Here you have an unknown ro.

There are three components of v is also unknown, There are thus four unknown.

There are three equations in the equations herein.

Because there is a vector for the first for component, the second component,

three for the third component Here comes the equation,

There are also a conservation of mass equation, four fourth equation.

So the four unknown ro and v is and correspondingly three of the three components

momentum equation one too comes from mass conservation equations.

Now one of them If we look at ways to simplify,

How excellent in the liquid We have talked about liquid.

Excellent internal friction of the fluid means thus interconnected particles

multiplying their lost hence momentum

consisted of the viscosity term.

If the viscosity at zero, This ideal defines a perfect gas.

Which means perfect gases See the right side was simplified.

This is the equation of conservation of mass.

As here, it should be studied

Of course this equation sediments just that easy

As alone do not work together on a simplified Or have a situation where a simplified,

so that acoustic sound waves.

I'm talking to you here my voice, My voice is creating pressure waves,

I'm changing the intensity of this air standing in front of me, out of my mouth

I'm starting and producing these sounds, we call this acoustic sound science.

Now we take this equation.

Single similar

im urethritis when you talk

tic waves in a bomb explodes Remove the large amplitudes are not the same.

I small amplitude changes I am doing so in rome

is smaller changes ro where yu can be as hard.

Eventually this divergence is staying there.

Yet here in rome rodin do not change.

ron itself may be small can be great but it is important

ron changes.

ro is changing over time and gradyand With space as the subject is changing.

We are second in the equation second change is very small

If he throws the first equation Let us take the derivative with respect to t,

by ron t in the second equation Once this time derivative of this term plus ro

See derivatives with respect to t has always been here Longitudinal changes will be minor.

ron derivative with respect to t a change in ro.

This change in there.

Both are nonlinear terms are dropped.

But once rode in the dV dt time derivative of the future.

If we take the divergence here, See here diverjans-

I received one of the future and that iii two terms have collected already here

here's why we take the divergence To create the same term.

By subtracting these two dt du roi square frames will be on the left.

These two terms will cancel each other out.

Will be on the right iii ron, We will have to remove the plus sign.

And finally, the following equation We're coming:EUR before it

we encounter such a wave equation.

Iii there in the wave equation, equal, There are the second derivative with respect to time.

Taking the simplest type thereof, i.e., in a dimension in a space dimension

Instead iii simplified structure second derivatives with respect to x is coming.

Where x is normally y ro The only x's and z's fonksiyonuyk

Upon receiving this function this one-dimensional happening.

See in this case the first term of stays the same, but instead of iii

According to the coordinates where the second derivative, I gave it earlier numbers

we have seen in the pages of one-dimensional, traditional, wave equation.

This is the kind of hyperbolic therefore, we have seen solid

same here as well as in body, We have come to the same wave equation.

Different qualities, One solid objects one air-

vibrations that may occur in a gas.

But we have seen come into the equation.

Generally, the sound in the gases waves examined by this equation

is entertainment. If there are problems in one dimension

Or that can be done very In size it is like here.

Now here's the pauses

I want to make me,

because it will change the nature of the problem then we examine.

Remember again, we looked solid objects, as a continuum.

Fluids were divided into two: Fluid is incompressible,

We have examined the liquid.

Finally, compressible fluids and gases were analyzed.

Classical physics, then the third we go to the field, electromagnetism.

The first field manual.

The second area of thermodynamics.

There we found the heat conduction equation and that such a parabolic

We have seen that equation.

Now electromagnetism we see again that the vector equation

to processes, with the gradient process We will learn how to obtain.

Also of Gauss and Stokes' theorem We will see the usage.

Please goodbye for now.