difficulty in interpreting certain formulas

[snaroz]

Hello everyone, I have a huge need for your help. I've been stuck on physical formulas for months and I can't move on anymore.

on the book of technical physics of yunus cengel, in the chapter entitled "analysis of the volumes of control according to the conservation of the mass and the conservation of energy", Chapter 6 p. 184, there is formula 6.2, which I attach as an image not knowing how to write the formulas. My problem is that I don't understand what they're "emme bet", "rò", "w_n" and "a". They should be variables, right? But exactly? Thank you!

 

[meccanicamg]

I think you have Italian issues. if you read about the text before the formula there is written what the symbols are. says that the infinitesimal element of the mass flow (m point) is equal to density (ro) multiplied the normal velocity (wn) evaluated in the infinitesimal area (a).

then integrated into the pass section etc. you will get the formula of common mortals:

♪

there is written everywhere, on every book and on all the dispensers. just look for the same topic and find everything

 

[snaroz]

I think you have Italian issues. if you read about the text before the formula there is written what the symbols are. says that the infinitesimal element of the mass flow (m point) is equal to density (ro) multiplied the normal velocity (wn) evaluated in the infinitesimal area (a).

then integrated into the pass section etc. you will get the formula of common mortals:

♪

there is written everywhere, on every book and on all the dispensers. just look for the same topic and find everything

hello mechanicalmg, first of all thank you for answering me. So, let's go calmly. in that formula, as in many others, there is the letter "d", which should represent the differential. as in analysis it defines the differential of a variable, or the differential of a function of certain variables, I conclude that the letters that stand "d" are variable (or functions of certain variables), right?
Is the density of what? and is a function of what? wn is the normal speed of what? and to is the area of a flat surface or in general curve? m point should be the mass flow through to, right?
thank you very much mechanicalmg, please answer me because I must absolutely clarify these doubts hello and good evening.

 

[meccanicamg]

hello mechanicalmg, first of all thank you for answering me. So, let's go calmly. in that formula, as in many others, there is the letter "d", which should represent the differential. as in analysis it defines the differential of a variable, or the differential of a function of certain variables, I conclude that the letters that stand "d" are variable (or functions of certain variables), right?
Is the density of what? and is a function of what? wn is the normal speed of what? and to is the area of a flat surface or in general curve? m point should be the mass flow through to, right?
thank you very much mechanicalmg, please answer me because I must absolutely clarify these doubts hello and good evening.

Then let's see. you have explained everything na can't understand. derivatives do cool and serve to complicate life. we mechanical ing need numbers to multiply or divide.

we are talking about a generic surface where there is a generic flow with speed w in transit.
the formula says that: the mass flow therefore kg/s is given by the density or specific weight of the fluid that is transiting I will multiply at normal speed to the wn surface multiplied the passage area.
read well what I wrote that there is everything.

these topics are dealt with in:
- fluid mechanics
- technical physics
- energy and turbomachine systems

if you look for the dispensers find everything explained.

density is function of temperature and pressure

 

[volaff]

I think you have Italian issues. if you read about the text before the formula there is written what the symbols are. says that the infinitesimal element of the mass flow (m point) is equal to density (ro) multiplied the normal velocity (wn) evaluated in the infinitesimal area (a).

then integrated into the pass section etc. you will get the formula of common mortals:

♪

there is written everywhere, on every book and on all the dispensers. just look for the same topic and find everything

I don't know.
Maybe we put some units of measurement to guide us better.

ro: density (kg/m^3);
wn: perpendicular fluid speed component to the area (m/s) of passage
a: passage area (m^2)

the product wn*s= (m^3/s) is the volumetric flow, multiplied by density = (kg/m^3), represents the mass flowing through the passage section (a) in the time unit.

do not let you be frightened by that d (from and to point): is only an elegant way to speak of infinitesimal mass and infinitesimal area.

 

[snaroz]

hi, then to stand for area of any surface considered, m point stands for mass flow through the supposed sup., rho stands for density of the fluid on and wn stands for module of the normal component of the vel. up from?

 

[Ing Italy]

from=area element of the section on which you will calculate the mass flow (it is an engineering writing to indicate that you will have to make the integral of that element of area "infinity")
dm'= indicates that the mass flow you are calculating is related to an infinitesimal area
rho=density of the fluid calculated in relation to the passage section on which you will integrate
wn=perpendicular component to the area element from the fluid speed vector

advice: leave the differential in the mathematical sense, 99% of the writings of this type are from the point of view of a senseless mathematician; engineering is about infinitesimal area to indicate that something is very small, nothing to do with really mathematical notions so try not to miss too much on these formalities.

Bye!

 

[snaroz]

Hi, I don't know if you'll want to read what I'll write, I hope so!
I have already given all mathematical examinations of mechanical engineering, so analysis1-2 and linear geometry/algebra. I also press that I am a lover of mathematics and logic, which has for years been merging on mathematics to understand it all the way and I have made very important progress in this regard. to understand the evolution of mathematics I am also reading books of history of mathematics (boyer, kline morris etc...) which I think are fundamental to understand the logical historical development of this discipline. Finally, I have been waiting for years that I have noticed that mathematics using physics and engineering is not exactly what is studied on the analysis books and is at least 2 years that I sink on formulas of the type d=dm/dv etc.... trying to solve the inconsistencies that there are with what is written in the current books of mathematics........after this long preamble, I arrived at this conclusion.






Mathematics used in elementary physics (mechanical, thermodynamic), and in engineering, is not that written on current analysis books. as stated by ing. italy, those forms interpreted in modern perspective do not make any sense. In physics, for example, differentials are often integrated, and this is meaningless, since in modern analysis that make you study today is defined as the integral of a function and not of a differential.

studying the history of mathematics we realize that the typical concepts of analysis such as derivatives, differentials and integrals have had a slow and constant evolution: were born around 1700 by leibniz basically, and then they underwent various changes/modifications until they arrived on our books of mathematics. the analysis today studied is formulated with the concept of limit. I'll explain. derivatives and integrals today are defined as particular limits, and the concept of limit was introduced by a certain karl weierstrass around 1850 to make rigorous the foundations of analysis. before weierstrass reprocessing, in the analysis dominated the concept of infinitesimal or infinitely small, differentials were infinitesimal variations, and integrals were the opposite of differentials. the infinitesimals etc... It's all things that shebnitz invented. most of the physical and engineering laws have been written using the analysis of leibniz, and their form has remained unchanged until our group. the concept of infinitesimal to leibniz, instead, for logical problems has been banned and has reformulated everything in terms of limits. the point is that the already written formulas of physics and engineering have not been rewritten with the new mathematics, and qesto is why the engineering or physics student who after opening the analysis book opens that of physics or technical physics remains flattened. I hope you enjoyed this little digression and I hope you agree with my point of view. I'm sorry if I wrote a little bit with the wedge but I was in a hurry. Bye!

 

[Ing Italy]

Mathematics used in elementary physics (mechanical, thermodynamic), and in engineering, is not that written on current analysis books. as stated by ing. italy, those forms interpreted in modern perspective do not make any sense. In physics, for example, differentials are often integrated, and this is meaningless, since in modern analysis that make you study today is defined as the integral of a function and not of a differential.

I allow you to notice that differential is nothing but a function!
Moreover the concept of infinitesimal has been rigorously arranged in the non-standard analysis of robinson.
However at his time (being a discreet avid of fluid dynamics) I too have penetrated enough in physical mathematics and how mathematics in engineering is not "true" mathematics. if you are interested try to study non-standard analysis and read these resources. I had saved many more on a computer that I now have no more, but on the net there are many news about it and others you can find them independently.
http://digilander.libero.it/leo723/materiali/analisi/fermat_newton_leibniz.pdfhttp://www.batmath.it/matematica/0-appunti_uni/differenziale.pdfhttp://www.fioravante.patrone.name/...iali_a_variabili_separabili_e_urang-utang.pdfFortunately, engineering must not worry about such matters hello!

 

[Fulvio Romano]

Forgive me snaroz but I think you're pretty bad.

The mathematics used by engineers is exactly the same as mathematics used by mathematicians.
exactly as the light of a rainbow is the same as white light, only presented differently. But you have to know her to understand that you are talking about the same thing.

the 'from' symbol indicates a variable of integration. and the 'd' means that that function is differentiable exactly in that variable, something not to be taken for granted in general. and this teaches us the mathematical riemann, and not the engineer riemann.

the difference between the mathematics presented in an engineering text and that presented a text of mathematics is simply that in the first case not repeated every time the hypothesis of classical work, because they are always the same. but not for this reason we must forget them.

I'm sorry if I treat you a little bit rough, but I think I can do it because we've known each other for a long time. what you write in your last post is simply delusional. where have you ever seen a differential supplement? is not that you are confusing the integrals defined with the undefined integrals? are two concepts that have in common only the word "integral" and nothing more. in fact the first return a number, the second a function.
"integrating from" is the contracted form of "following a double integral of the 1*da function extended to the domain a, assuming it has the dense field characteristics in r to 2". see that so you understand why 1 is constant, take it out of the integral that remains self-defined as a. you have not integrated a differential at all.

By the way, with the point above the letters it commonly means the derivative of that variable compared to time. so mpoint = dm/dt... Did I write it well? no, instead of 'd' it would take the non-exact differential symbol (a 6 mirrored compared to a vertical axis) that you can't put here. Why? to you the answer.

 

[snaroz]

Hello fulvio, I have spent times worsexd......I would like to write so many things but now I can't because I am with the water at the throat.......cmq we see to ourselves.....my physics book defines pressure or normal effort the quantity dfn/ds...... Would you tell me what the "d", "fn", "s"? thank you very much and sorry x accents but I write from a somewhat strange keyboard!

 

[Fulvio Romano]

Hello fulvio, I have spent times worsexd......I would like to write so many things but now I can't because I am with the water at the throat.......cmq we see to ourselves.....my physics book defines pressure or normal effort the quantity dfn/ds...... Would you tell me what the "d", "fn", "s"? thank you very much and sorry x accents but I write from a somewhat strange keyboard!

Orpo.. .
the pressure is a force f divided a surface s. on this we are? in reality only affects the component of the force that is perpendicular to the surface, therefore fn (normal). Right?

and if the force is not constant on the surface? then we reduce the size of the surface we are analyzing. ever smaller, ever smaller, until it becomes infinitesimal. the force on this piece of surface is constant, because the surface has become so small that it makes no sense to imagine differences of strength.

then the surface became 'ds'. consider it for now as a symbol to mean a very small surface. the force will be 'dfn' because it is the force (constant) on that piece of surface.

Now. the force "which varies" along the surface can be seen as a function fn = fn(x, y) with (x,y) belonging to the set s (open, for now, otherwise it becomes a casino). so that a pressure can be defined this f must not have jumps, holes, discontinuity, etc. in a word, it must be differentiable. Moreover if the fn function has an explicit dependence on x and y, or if there were also other variables (for example time) these were frozen without effects on x and y, then the dx and dy differentials are exact differentials (and therefore you can write 'd').

we know that the normal force = pressuremedia * surface. if we differentiate we obtain that dfn = dpm * ds. attention that the differential of the average pressure is the pressure at one point, then:

p * ds = dfn

integrate member to member and see that you are.


I wrote it so because I know that you are pignolo and I wanted to avoid the ambiguity of dfn / ds writing, which can mean both "derived of force compared to the point", and "forza infinitesima divided infinitesima surface". However, you will understand that the two locutions actually coincide, because if you write the derivative as limit of the incremental relationship, you get the relationship between the two infinitesimal quantities.

Clear?

 

[snaroz]

Hello fulvio, first of all thank you for answering me. in these hours I have made a lot of progress and I am convinced that my theory about the use of analysis in applications is out of place, since if you were right I would not explain why they make you do 2 years of math courses!

I also press that I have given a read to your above intervention, but there is still something that is not clear to me and I prefer to think about it over another little.



I wanted to reason on this other formula, very similar to that in the opening of the post and taken from the book of physics.

My book says these words:
"experimentally, it is found that the amount of dp heat that passes through the unit of time a ds area inside a solid material is proportional to the ds surface and the derived temperature in the direction orthogonal to the surface itself:

dp=-lambda*ds*derived partial t compared to x.

Now you said that physicists and engineers use the same math as mathematicians, and that's what makes you study at the aun. so you should agree that the letters "d" appearing in the formula I reported are the same as the definition of "differential of a function" which is given in mathematical analysis. Right?

in mathematical analysis, we define the "differential of a function", which is indicated with d(function) precisely. It also defines the partial derivative of a function. So I expect that in that formula p, s, and t are functions. It didn't happen to be otherwise. If those "d" are meant in the same sense as the analysis, then the objects written immediately to the right of the "d" must be functions.

I ask you, then: "p", "s", and "t" what do they represent?

thank you so much and sorry if I look a little heavy but I want to understand it for good!!!! ! !

 

[Fulvio Romano]

I have never known anyone more stubborn than you to try to pull out the truth from every single letter of a text. And that's why I give you my most vivid compliments. you are the antithesis of this world that makes of approximation and of any kind a chimera to be chased. (He wanted to be a compliment... he understood? )

if in a solid body each point has a certain temperature, it is possible to define the function t=t(x, y, z, t), real function of four real variables defined on the domain [corpo solido]? This is the temperature of that body. same thing for all other sizes, except heat that not being a function of state can not depend on x, y and z (I think... It's late, I think better tomorrow.

was that the question?

 

[Fulvio Romano]

ah... the "derivata of the orthogonal temperature to the surface", would be the projection of the temperature gradient compared to the surface.
the gradient would be that carrier whose components are the partial derivatives of the function compared to the coordinated axes. the gradient is independent from time, so you have to work by dissecting function t at a time t*.

Did you run ii?

 

[snaroz]

hello fulvio, thank you for your trust first. I'm still in meditation, but I think I've solved my doubts. I will soon write a detailed answer to the question (according to my point of view, which I hope is correct).