What do stress terms like p and \scriptstyle \boldsymbol{\mathsf{T}}mean to you?

[rwjefferson]

welcome to my wormhole.iii

def: topspin

the side rolling into the relative headwind!

 

newton.001

def: n

a measure of force and mass acceleration

syns: i and m and a and g

 

bernoulli.007

fluent flowing faster over a horizon means lower pressure and vice versa

Airmass streams downwards behind slippery shiny topspinning bowling balls.

Does lower pressure over accelerate fluent airmass downwards?

 

newton.102

fluent airmass departing upwards forces spinning ball mass down

Topspinning stitches and dimples drag airmass around and under and upwards.

Do satin surfaced underspinning ping~pong balls demonstrate lift?

 

inertial pressure differential.001

newton in~verse bernoulli

As inertial and pressure differential are relatively equivalent and streamlines depart straight and level.

How much grit must be glued around a slippery shiny topspinning ball before airmass departs straight and level; no matter spin?

 

navier stokes.001

[math]\rho \left( \frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v} \right) = - \nabla p + \nabla \mathbf{T} + \mathbf{b}[/math]

 

navier stokes.101

The stress terms p and [math]\scriptstyle \boldsymbol{\mathsf{T}}[/math] are yet unknown, so the general form of the equations of motion is not usable to solve problems. Besides the equations of motion—Newton's second law—a force model is needed relating the stresses to the fluid motion.

 

What do the stress terms p and [math]\scriptstyle \boldsymbol{\mathsf{T}}[/math] mean to you? Can you prove it? Really?

 

ItS

peace

ron

 

when the legend tells better

tell the legend

Edited July 30, 2013 by swansont
fix math tags

[imatfaal]

!

Moderator Note

Moved to speculations - mainly because it is so difficult to know what the point of debate is actually meant to be.

[swansont]

!

Moderator Note

And if this is another example of asking a question so you then then pontificate, it will be locked. You have been warned about this.

[studiot]

If you are going to invoke the Navier Stokes equations, please note they are plural.

 

The other half of the pair to the version you have quoted is

[math]\nabla .v = 0[/math]

Please also note that the one you have used is for incompressible flow.

However the other material in your post suggests you are continuing your investigation of airborne phenomena.

You should therefore ensure that incompressible conditions apply in any such use of these NS equations, which sometimes happens in airflow, but not always.

 

As to the apparent specific question

The p terms refer to normal stresses, the T terms to tangential (shear) stresses.

Edited July 30, 2013 by studiot

[Bignose]

The p terms refer to normal stresses, the T terms to tangential (shear) stresses.

Right, and we propose constitutive models for the shear stress (often invoking Newton's viscosity as one example). The set of equations solve for the velocity field and pressure.

 

rwjefferson,

 

I would entreat you to please read any of the many, many books about fluid mechanics. These are basic questions that are typically answered in the first chapter or two. If you would like recommendations, I would be happy to give you some.

 

But, I, like swansont, am afraid that this thread will be your typical ask 12 random questions and then a 'gotcha!' when you think you've won a point.

 

I don't mind helping share knowledge on a subject I really enjoy -- fluid mechanics. But I'm not here to play games.

 

Do satin surfaced underspinning ping~pong balls demonstrate lift?

Yes. This happens almost anywhere there is a physical boundary. Quite simply, the solid structure of the ball can support shear stresses whereas the fluid does not.

Edited July 30, 2013 by Bignose

[studiot]

 

Quite simply, the solid structure of the ball can support shear stresses whereas the fluid does not.

 

 

Many folks misinterpret this statement and imagine it means that there is no shear stress in a fluid.

 

This is far from the case.

 

A solid can 'support' shear stresses without deformation, in which case it is totally rigid.

Or it deflects a certain amount, but no more, under a given shear stress, in which case one of the responses -elastic, or some other applies.

 

On the other hand

 

The shear stress in a fluid at rest is zero.

 

But the response of a fluid to imposed shear stress is movement.

A fluid in motion suffers shear stress.

Edited July 30, 2013 by studiot

[Bignose]

Many folks misinterpret this statement and imagine it means that there is no shear stress in a fluid.

Good point.

 

In short, I think it best to reiterate that the OP would be well advised to consult an introduction to fluid mechanics book. It is a subject with an extensive literature.

[rwjefferson]

Are normal and shear stresses more likely a function of inertial pressure differential or curvature or something different? And what does the state of matter have to do with it?

really

peace

ron

[Bignose]

Are normal and shear stresses more likely a function of inertial pressure differential or curvature or something different? And what does the state of matter have to do with it?

really

The 'pressure differential' is the grad p term. And the shear stresses are in the grad T term. Mathematically, you can add the two terms together, and call it something like a 'total stress'.

 

But the equation shows how the two are related to one another.

 

Example #1: a cylindrical pipe with high pressure at one end and low pressure at the other. The shear stresses form because of the pressure drop.

 

Example #2: two infinite parallel planes have a fluid between them. The 1st plane is held steady, but the second moves at a constant velocity. In this case, the moving surface forms the shear stress, and a pressure differential forms because of the shear.

 

So, neither is really a 'function' of the either. They are just related by the N-S equations.

 

And the state of the matter depends on what constitutive equations you use for the shear stress. A Newtonian fluid has different constitutive equations than a non-Newtonian pseudo-plastic. And a solid doesn't obey the N-S eqns. They have a similar conservation of momentum equation, but it isn't the same.

[rwjefferson]

standing against trolls~20.13.08.12,08;141

def: pi

what's force got to do width it.viii

def: current wiki

yesterday's best understanding

Del, or nabla, is an operator used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

Is total stress (by any other Name) a function of initial inertial differential or bang~entropy or curvature or something even more magical than existence?

thanks

ron

as horizon lowers pressure declines over time

[Bignose]

 

Is total stress (by any other Name) a function of initial inertial differential or bang~entropy or curvature or something even more magical than

Where do you get any of that from?!?

 

I tried to tell you above that I wasn't going to play games like this, where you take things out of context or try a gotcha. Total stress is just the sum of the grad p and the grad T terms.

[rwjefferson]

its a curse of course.iIi

def: r~bvious

not from what authority tells you so

syn: those that fear truth blame context or messenger

Is gravity a state of force or a relatively equivalent mathematical construct? Will maths experts ever admit alphanumeric models and other images sometimes deceive? When will a maths expert calculate the drag of weakly interactive particles gravitating toward mass? Do maths experts know how to put a genie back into the bottle?

Is gravity a state of force or an alphanumeric construct?

def: dogma

what authority tells you so

r

[Bignose]

Is gravity a state of force or a relatively equivalent mathematical construct? Will maths experts ever admit alphanumeric models and other images sometimes deceive? When will a maths expert calculate the drag of weakly interactive particles gravitating toward mass? Do maths experts know how to put a genie back into the bottle?

What does any of this have to do with the N-S equations?

[Unity+]

To be honest, I can't tell if I can't read his sentences correctly or if they are actually just gibberish.

 

 

 

standing against trolls~20.13.08.12,08;141

As if this has any relevance to the discussion.

[swansont]

 

its a curse of course.iIi

def: r~bvious

not from what authority tells you so

syn: those that fear truth blame context or messenger

Is gravity a state of force or a relatively equivalent mathematical construct? Will maths experts ever admit alphanumeric models and other images sometimes deceive? When will a maths expert calculate the drag of weakly interactive particles gravitating toward mass? Do maths experts know how to put a genie back into the bottle?

Is gravity a state of force or an alphanumeric construct?

def: dogma

what authority tells you so

r

 

 

!

Moderator Note

This is off topic, and also personal commentary about another poster, both of which are against the rules.

[rwjefferson]

What might stress terms like p and T really mean?

stress tensor.001

Are stress and pressure and tension states of force?

Are stress terms like p and T alphanumeric symbols and grads or fields or curvature?

Or might stress terms like p and T also mean functions and derivatives of pressure and tension?

welcome to my wormhole.007

def: byLaw

whereas 'that is the most ridiculous nonsense ever posted' is construed not an ad hominem attack or personal commentary

bad dogma.101

My goal is to contribute to science and evolution. That the (un?)intended consequence of your game is to thwart and obfuscate and hijack is not necessarily the simple truth you should so readily reveal.

Does the relatively rough surface of topspinning balls accelerate air mass around and under and upwards?

Does airmass forced around and over and downwards drag and lift underspinning ballmass back and up?

If you so fear to admit basic truth, just turn away and hold your peace and let me speak mine own.

peace

ron

those that fear truth condemn the messenger

[Bignose]

If you so fear to admit basic truth, just turn away and hold your peace and let me speak mine own.

I have no fear to admit the basic truth that you really ought to go and read an introduction to fluid mechanics book. Because if you really wanted the answers to these questions, they are discussed in many numerous texts.

 

It is also a basic truth that I am very, very hesitant to answer because I think there is an extraordinary chance you'll just use the words out of context or deliberately misunderstand in order to fit your personal agenda. Again, please go and read an introductory fluid mechanics text. If you want recommendations, I will provide that, and if you have questions from the text, I'll answer those.

 

You have had over a month since this thread was started; you can find many cheap fluid mechanics books on used book websites; you really don't have much of an excuse not to have looked over a basic fluid mechanics text by now, if and only if you really sought answers to these questions. I suspect that you are playing games, again, though.

Edited September 2, 2013 by Bignose

[rwjefferson]

Are stress terms like p and T functions of pressure and tension?

newton.001

mass in motion means constant vector and velocity unless forced

your nose grows every time you post.viii

truth is out of context only under the cloak of dogma

Cite the Book and Chapter and Verse that proves curvature is more than a reaction to force.

hypervalent_ion:

In some forums it is considered polite to answer the OP's questions.

Are alphanumeric terms like stress and p and T functions of force?

Cite the context of your answer if you so fear universal truth.

peace

ron

a good teacher learns from all students

[Bignose]

whatever dude.

 

http://www.abebooks.com/servlet/BookDetailsPL?bi=10716162191&searchurl=kn%3Dintroduction%2Bfluid%2Bmechanics%26amp%3Bsts%3Dt