1.9. Dynamic and Kinematic Viscosity

Dynamic viscosity is the dimension of a fluid's resistance to flow. Highly viscous fluids like molasses or tar flow very slowly compared to less viscous fluids, such as water. In gases, viscosity is influenced by temperature and pressure, where it typically increases with higher temperature and pressure. In liquids, however, viscosity usually decreases with rising temperature.

Viscosity is a measure of a fluid's thickness or how easily it flows. Dynamic viscosity refers to this property under the influence of an applied force. For instance, a fluid like water has a low dynamic viscosity, allowing it to flow easily, while thick fluids like molasses resist flow much more. In gases, higher temperatures can cause molecules to move faster, which can increase their ability to carry momentum—this is why gases become more viscous with heat. In contrast, liquids like water start to flow more easily as they heat up, causing a decrease in viscosity.

Imagine trying to pour syrup versus water. The syrup (high viscosity) flows slowly and takes longer to move from one container to another, while the water (low viscosity) pours easily and quickly. This difference in behavior directly ties back to their respective viscosities.

Kinematic viscosity is derived from dynamic viscosity and fluid density. It is expressed as the ratio of dynamic viscosity to the density of the fluid. In units, kinematic viscosity is measured in m²/s.

Kinematic viscosity helps us understand how a fluid behaves under conditions of motion rather than just static resistance. It is calculated by dividing dynamic viscosity (which measures resistance to flow) by the fluid's density (mass per unit volume). This shows how easily a fluid flows compared to its density, making it a critical factor in fluid mechanics. Higher kinematic viscosity indicates that a fluid will have a greater resistance to flow under motion, which is important when analyzing fluid behavior in various applications.

Consider a swimming pool filled with different liquids: water, yogurt, and honey. In this scenario, honey has a higher density and higher dynamic viscosity compared to water, resulting in high kinematic viscosity. Swimmers notice they move much slower in honey than in water due to this kinematic property. Understanding kinematic viscosity helps in designing better swimming pools or guiding the behavior of fluids in pipelines.

In statics, fluids at rest show no velocity difference between layers, leading to zero shear stress. Viscosity becomes relevant in dynamics, where moving fluids have different velocities across layers, resulting in measurable shear stress.

In fluid statics (the study of fluids at rest), there is no flow, so we don’t worry about viscosity—it’s no longer a factor because the fluid is not moving and thus cannot exert shear stress. However, as soon as fluid begins to move, viscosity plays a crucial role. Viscosity causes different layers of fluid to move at varying speeds, creating shear stress that impacts how fluids flow and interact with surfaces and other fluids.

Imagine layers of different colored jelly in a dessert. If you leave the dessert untouched, the layers will stay where they are (statics). However, if someone stirs the dessert, the jelly layers begin to mix due to the shear created by the stirring action. The thicker the jelly (higher viscosity), the harder it is to mix it up, illustrating how viscosity affects fluid behavior in dynamic situations.

One standard method of measuring viscosity involves using a rotating cylinder in the fluid. The power required to turn the cylinder is related to dynamic viscosity, density, and the dimensions of the cylinder.

In experimental setups, dynamic viscosity can be measured by observing how much power is needed to turn a cylinder within a fluid at a fixed speed. The amount of resistance the fluid provides to the turning cylinder gives us direct insight into its viscosity. The relationship involves several factors, including the thickness of the fluid layer between the cylinder surfaces, the rotation speed, and the density of the fluid.

Think about stirring a thick soup with a stick. The force you feel when trying to stir it gives you an idea of its viscosity. If you had to measure how hard you are pushing to swirl the stick at a constant speed, this action could be used to calculate the soup's viscosity, just like how we measure it in scientific experiments with rotating cylinders.

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