3.2. Viscosity

Now let us go to the very interesting concept, the Newton's laws of viscosities, okay, which is very simplified, simple common laws of viscosity which we use for solving many of the problems in laminar and also approximate for other flow conditions.

This section introduces viscosity as a fundamental concept in fluid mechanics related to the flow of fluids. Viscosity demonstrates how fluids respond when they are subjected to deformation or flow, reflecting the internal friction among their molecules. Newton's laws of viscosity act as guidelines for understanding fluid behavior in various scenarios, such as laminar or turbulent flow.

Imagine trying to push a heavy object across a surface. The resistance you feel is similar to viscosity in fluids; it represents the internal resistance flowing molecules have against each other. Just as harder surfaces require more force to move objects over them, fluids with higher viscosity require more force to flow.

As we know it that whenever we have the fluid flow conditions, we will have the no-slip conditions. That means, at these locations I will have the velocity zero. At these locations the contact of the fluid particles on the solid surface will give a velocity equal to the velocity of the plate.

The no-slip condition is a fundamental assumption in fluid mechanics that states fluid at a solid boundary moves at the same velocity as the boundary itself. This means that when a fluid flows over a surface, the layer of fluid molecules directly in contact with that surface does not slip – they have zero velocity at the boundary. This condition is critical for accurately modeling fluid flow and predicting how fluids will behave when in contact with solid surfaces.

Consider a slow-moving river where the water at the edges is almost stationary because it sticks to the riverbank. The water flowing faster in the center lets you visualize the no-slip condition; the water at the edges is not slipping past the riverbank, just as fluid molecules do not slip past a solid boundary.

If you look it that you have the plate, okay. If you can look it which is at the rest conditions and you have in the top another plate is there, where you are applying a force F and the velocity V is it is moving this plate.

This segment discusses how the application of force creates layers of fluid flow. When one plate moves while the other is still, the fluid layer in contact with the moving plate experiences a velocity, causing adjacent layers of fluid to move as well. The interaction between these layers generates shear stress, a measure of how much force is applied over a specific area between these layers, affecting how the fluid flows.

Think of it as layers of frosting on a cake; if you apply a light pressure on the top layer, it begins to slide over the layers beneath it, creating friction between each frosting layer. This friction is akin to the shear stress in fluid mechanics, showcasing how different layers of fluid interact through applied force.

After certain time maybe these two velocity is coming to equilibrium. That means they will be the same order, same value. So looking these the mass exchange and the momentum exchange of the molecules at this the artificial interfaces between two packets of the fluid packets.

When the two fluid packets (layers) eventually reach the same velocity, they establish a consistent flow pattern. The relationship between shear stress and velocity gradient is described by Newton's law of viscosity, where the shear stress is directly proportional to the rate of change of velocity between layers. The viscosity serves as the proportionality constant, varying between different fluids based on molecular structure and interaction.

Imagine stirring honey with a spoon; the slower the movement of the spoon, the thicker and more resistant the honey feels due to its viscosity. In contrast, water flows easily without much resistance. This difference showcases how varying viscosities result in differing responses to applied forces.

And that proportionality is known as the coefficient of viscosity or dynamic of viscosity.

The coefficient of viscosity is a measure of a fluid's internal resistance to flow, reflecting its viscosity. It quantifies how shear stress relates to the velocity gradient, providing valuable insights into how different fluids behave under similar conditions. This coefficient varies depending on the fluid type due to molecular properties.

If you have a collection of liquids, like water, oil, and syrup, pouring them will result in different flow rates. This variance represents their coefficients of viscosity; the thicker the fluid, like syrup, the higher its viscosity and the slower it flows compared to water.

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