1.8. Role of Viscosity in Statics and Dynamics

In fluid statics, when the fluid is at rest, there is no relative motion between the layers of the fluid. This means that the velocity is zero, hence the shear stress is also zero. Therefore, fluid statics is independent of the fluid viscosity.

When we discuss fluid statics, we refer to fluids that are not in motion. In such cases, the fluid layers do not slide past each other, which implies that there is no velocity difference between these layers. Since shear stress is related to the velocity gradient (change in velocity over a distance), if the velocity is zero, the shear stress must also be zero. Consequently, viscosity does not play a role in fluid statics because there are no forces arising from fluid movement.

Imagine a calm lake. The surface of the water is perfectly still; there are no waves or currents causing any layers of water to move. Since everything is at rest, we can say that the water exhibits no viscosity effects. However, if someone were to drop a stone into the lake, the water would start moving, introducing viscosity effects associated with the layers of water interacting.

In contrast, in fluid dynamics, viscosity becomes a crucial factor as fluids in motion have different layers moving at varying velocities, leading to a velocity gradient.

In fluid dynamics, we study fluids that are in motion. Here, unlike in statics, different layers of the fluid move relative to one another at different velocities. This creates a velocity gradient, meaning that the speed of the fluid changes as you move from one layer to another. Viscosity comes into play because it quantifies the internal resistance of the fluid to flow, which impacts how easily the fluid moves and the shear stress experienced between the layers.

Think of a thick smoothie and a thin water stream. When you stir the smoothie, it resists your spoon's motion because of its high viscosity, making it harder to mix compared to stirring plain water, which flows readily with low resistance. This difference in resistance is a direct result of viscosity, with significant implications in how these fluids would behave in different applications, like in pipes or channels.

Kinematic viscosity is defined as a fluid property obtained by dividing dynamic viscosity by the fluid density. It is represented in units of m²/s and is related to Reynolds number, which is crucial for understanding fluid flow.

Kinematic viscosity (ν) relates to how a fluid flows when subjected to external forces, while dynamic viscosity (μ) is a measure of a fluid's resistance to shear. The relationship between the two is given by the equation ν = μ/ρ, where ρ is the fluid density. This relationship is important in fluid mechanics as it helps characterize flow behavior, especially in terms of laminar and turbulent flows described by the Reynolds number. The Reynolds number is a dimensionless quantity that predicts flow patterns in different fluid flow situations.

Consider how oil and water behave when mixed. Oil, which has a lower density and higher viscosity, will not mix freely with the water, creating distinct layers. The Reynolds number can be used here to predict whether the flow will mix well (laminar flow at low Reynolds numbers) or remain separate (turbulent flow at high Reynolds numbers). This analogy highlights how varying viscosities lead to different behaviors in fluid flow.

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