Idealized Fluid: Pressure & Force Tangential to Surface

[Von Neumann]

1. The problem statement...
The textbook I am using states that an idealized fluid cannot sustain a force tangential to its surface. Can anyone expound upon this argument? This statement is an introductory exploration of pressure and is cited as the reason that the force dF exerted by its surrounding is perpendicular to the surface bounding a fluid. Therefore, this force dF is parallel to the area vector dA. The pressure is then defined to be the ratio of these two quantities. Pressure being the ratio of force per unit area makes perfect sense, but this explanation is somewhat cloudy to me.

 

[physninj]

I found this to be a helpful explanation. http://www.britannica.com/EBchecked/topic/211221/fluid

 

[Saladsamurai]

Sounds like a round about way of talking about a fluid. By definition, a fluid is a substance that cannot sustain a force tangential to its surface (i.e. a shearing force).

 

[Von Neumann]

Thanks guys!

Now this makes complete sense! I thought some particular property of fluids was responsible for this phenomenon. I wasn't aware that this is a defining feature of fluids.

 

[Chestermiller]

Sounds like a round about way of talking about a fluid. By definition, a fluid is a substance that cannot sustain a force tangential to its surface (i.e. a shearing force).

This is, of course, not correct. A viscous Newtonian fluid supports shear stresses via Newton's law of viscosity. If a fluid could not support shear stresses, the pressure drop in a straight cylindrical pipe would always be zero. For rectilinear flow, shear stress is equal to the viscosity times the shear rate.

 

[Saladsamurai]

This is, of course, not correct. A viscous Newtonian fluid supports shear stresses via Newton's law of viscosity. If a fluid could not support shear stresses, the pressure drop in a straight cylindrical pipe would always be zero. For rectilinear flow, shear stress is equal to the viscosity times the shear rate.

It cannot support a shear force means it will continually deform when subjected such. See links.

 

[Chestermiller]

It cannot support a shear force means it will continually deform when subjected such. See links.

In that sense, it cannot support a normal force either, unless the normal loading is isotropic. If the three principal stresses are unequal, a fluid will always exhibit a shear deformation.

 

[Saladsamurai]

In that sense, it cannot support a normal force either, unless the normal loading is isotropic. If the three principal stresses are unequal, a fluid will always exhibit a shear deformation.

I am not sure what you are getting at. Two links have been provided. See any fluid mechanics text for a definition of a fluid. For example:

From the point of view of fluid mechanics, all matter consists of only two states, fluid
and solid. The difference between the two is perfectly obvious to the layperson, and it
is an interesting exercise to ask a layperson to put this difference into words. The technical
distinction lies with the reaction of the two to an applied shear or tangential stress.
A solid can resist a shear stress by a static deformation; a fluid cannot. Any shear
stress applied to a fluid, no matter how small, will result in motion of that fluid.

 

[Chestermiller]

I am not sure what you are getting at. Two links have been provided. See any fluid mechanics text for a definition of a fluid. For example:

I should reveal to you that I am a guy with a lot of fluid mechanics experience. What I am getting at by what I said is that not only can a fluid not support shear stresses, it also can not support normal stresses without deforming (unless the stress tensor is isotropic). The stress tensor being isotropic means that the three principal stresses are all equal to one another. If you don't know much about the stress tensor and principal stresses, and intend to work in fluid mechanics, you need to learn something about how it works.

Chet