Thanks for the excellent reply, Ahmed... I will indeed follow the suggested reading path..

... in pressure, or lack thereof, lies the answer to the N-S singularity issues...

diaw...

Mani, you're completely right! Viscous flow is not so important and total quantites are just a definition. I cimpletely agrree with you.Luca

Sorry, but I was not able to understand your post... could you explain it better?!

why is not viscous flow important? What about the flow around thin bodies aligned with the flow?!

Mani has correctly written that in MOST CASES (I would say in some cases...) shear stresses are small when compared with normal stresses but you may have problems where shear stresses are considerable.

Regards

Renato.

Another question related to fluid-structure interaction -- how would one handle the pulsating flow of a viscous incompressible fluid in a compliant rubber hose?

If we are taliking about aircrafts on aerodynamic profiles, I'd say that pressure contributes are very large compared to viscous terms...(remember what we mean by efficiency of an aircraft for example). So in fluid-structure interaction pressure forces are larger than viscous terms. Pressure force are equal to (at least) the weight of the aircraft and drag fortunately is smaller than this term. So if you want to consider the viscous stress, you can but i'm sure your analysis will be good even without this term. What it's important is to find wing deflection along lift direction, non along grad direction. In fact wing section has the smallest intertial term along the lift direction. Hope to be clear. Luca

Thin bodies (mostly) aligned with the (attached) flow tend to have a much smaller drag than lift (several orders of magnitude difference). The drag of such bodies is mostly due to shear, the lift is mostly due to normal pressure. Hence, the major force on the body is created by normal stress, very little by shear stress, and that's why thin bodies such as airfoils are prime examples for relatively small influence of viscous effects on flutter. Of course, there is a possibility that viscosity has a significant (indirect) effect on lift through separation, shock boundary-layer interaction, or any such viscous phenomena. But even in those cases, viscosity is only important in establishing the flow, and in developing the flow instabilities. Viscous effects will change the pressure distribution, but in the integration of stresses over the wall you will often still see that the shear stress doesn't add much, compared to the normal stress. I didn't say "viscosity is not important". What I meant is that the shear stress is a far less significant contribution to the total force than the pressure. There are cases where this is not a valid assumption, but I would be primarily worried about low Reynolds number flows, where viscous forces are dominant over inertial forces.

ahmed, you should read some of the other posts to get some clarity and answers to your questions. the total pressure is not the one in question for fluid-structure dynamics. neither the absolute total pressure nor the relative total pressure.

the key question is: what pressure do you actually measure experimentally. very good question. and the answer is related to the original question of which pressure to use in fluid-structure analyses. read some of the earlier posts.

as for absolute versus relative pressure... yes, for compressible flow the absolute value matters (not so for incompressible flow). however, if you integrate the pressure over the surface of an entirely immersed body, any uniform part of the pressure will not contribute to the total force. hence, for such cases (e.g. airfoils), it doesn't matter if you integrate relative or absolute pressure for the purpose of obtaining the force.

Solve the unsteady incompressible N-S equations coupled to a structural model for the hose. The boundary conditions might give you some headache... depends on what exactly you're looking at... the hose free or clamped at the ends... the mass flow or pressure imposed externally...

You could survey what people have done for flow through blood vessels. I think it's quite an active field.

There is a version of the wind turbine with a vertical axis and two vertical, symmetric, wing-like blades. At first glance one would wonder how one could get torque out of this configuration. Indeed, it will not start turning by itself. However, once it is turning in a wind it produces torque. Supposedly, the torque is produced by the effect of drag, not by lift as in an airfoil.

I'm not so sure the turbine starts rotating because of drag...sorry. Luca

I suppose it depends on what you call drag in such a setting. And the question is: Is it pressure drag or viscous drag? Can anyone give a real example of viscous drag dominating the aerodynamic force? I know there must be such cases.

A note of thanks to Ahmed,

Since we last communicated I have had a number of research-breakthroughs in my search of the underlying meaning of the instabilities in N-S equations.

You may, or may not realise the full depth of meaning which lies behind the 'pressure' concept... but, it is indeed intricately interwoven in the search for the deep understanding of the natural phenomena so deeply contained within Newton's second law (momentum conservation).

The answers are both simple, but yet, at the same time, extremely complex - creation is a wonderful thing...

Thank you for the interesting 'thought process'...

diaw...

'instabilities' in the N-S, should read 'singularities'... although they are one & the same thing in the end...

diaw...