# Understanding the rigorous meaning of fluid.

I'm taking my first course on Fluid Mechanics. My book (my books means the book which I'm reading not the one I have written ) says that the definitions of fluids like Fluid is something that flows or Anything apart form solid is a fluid are somewhat vague and therefore the rigorous definition of a fluid is

A substance that deforms continuously when acted on by a shearing stress of any magnitude.

I'm having problem in understanding the meaning of deform here, as from my study of Elasticity is concerned deform means change of shape, but my book tries to convey the idea of flow by using the word deform (I have attached an image of that page). I want to know how is that? I mean how deformation and flow are connected?

The second problem is shearing stress of any magnitude . I can't understand why only shearing stress is mentioned over here and any magnitude is emphasized over here.

I would prefer if you write your own understanding of these things, I mean the way you have understood these things. This is because I have found you people much more helpful, comprehensible, genial, friendly.

Thank you.

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I have done few editing therefore it seems to me that this site is not allowing me anymore edits and hence I need edit my question by writing out here.

The image is not clear because only small size images are allowed and I have tried almost everything. Therefore, I'm just writing the paragraph whose image I have attached

Although the difference between solids and fluids can be explained qualitatively on the basis of molecular structure, a more specific definition is based on how they deform under the action of an external load. Specifically, a fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. A shearing stress (force per unit area) is created whenever a tangential force acts on a surface as shown by the figure in the margin. When common solids such as steel or other metals are acted on by a shearing stress, they will initially deform (usually a very small deformation), but they will not continuously deform (flow). However, common fluids such as water, oil, and air satisfy the definition of a fluid - that is, they will flow when acted on by a shearing stress.

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#### DarnItJimImAnEngineer

Put a steel block on a surface and tilt the surface. The weight will pull it downwards, while friction holds it up. This produces shear which will (imperceptibly) deform the block. The deformation is static, though (i.e., not time-dependent).

Put a sheet of water on a surface (ignore for now how the ends stay in place) and tilt the surface. The weight will pull it downwards, while the no-slip condition (friction) holds the lower surface in place. The shear will pull the upper surface down, deforming the water. It won't stop, though. The water will keep deforming (flowing). The intermolecular bonds in a liquid or gas are weaker than in a solid; they have enough energy to break away and temporarily bond to other molecules.

From a mathematical point of view, shear stress in a solid is directly related to strain,
$\displaystyle \tau \propto \frac{\partial x}{\partial y}$,
while shear stress in a fluid is related to a strain rate,
$\displaystyle \tau \propto \frac{\partial u_x}{\partial y}$.

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Put a steel block on a surface and tilt the surface. The weight will pull it downwards, while friction holds it up. This produces shear which will (imperceptibly) deform the block. The deformation is static, though (i.e., not time-dependent).

Put a sheet of water on a surface (ignore for now how the ends stay in place) and tilt the surface. The weight will pull it downwards, while the no-slip condition (friction) holds the lower surface in place. The shear will pull the upper surface down, deforming the water. It won't stop, though. The water will keep deforming (flowing). The intermolecular bonds in a liquid or gas are weaker than in a solid; they have enough energy to break away and temporarily bond to other molecules.

From a mathematical point of view, shear stress in a solid is directly related to strain,
$\displaystyle \tau \propto \frac{\partial x}{\partial y}$,
while shear stress in a fluid is related to a strain rate,
$\displaystyle \tau \propto \frac{\partial u_x}{\partial y}$.
I have understood that deformation gonna happen forever because the strain angle gonna increase and increase as the bottom layer is fixed. Am I correct? Is the change of strain is called deformation ?

#### DarnItJimImAnEngineer

I have understood that deformation gonna happen forever because the strain angle gonna increase and increase as the bottom layer is fixed. Am I correct?
That is correct.

Is the change of strain is called deformation ?
Strain is the deformation itself. For example, we define axial (linear) strain as $\varepsilon_x = \frac{\Delta L}{L}$ ($L$ is the length of a control volume in the $x$ direction). Shear strain is, in essence, $\gamma_{xy} = \theta \approx \frac{\Delta x}{y}$, or the "angle of deformation."

Shear stress in a solid causes it to exhibit a certain strain (angle). Shear stress in a fluid causes it to exhibit strain that changes at a certain rate. As you continue the course, you will learn more about viscosity and the stress tensor in fluids.

You will also learn about non-Newtonian fluids (such as Bingham plastics -- materials that behave like solids at low stress and fluids at high stress), which can stretch the definition a little bit.

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