1.7. Fluid Viscosity

Some examples of highly viscous fluids are molasses, tar, if you have more concentration of oil or glycerin, these are some of the things which are highly viscous. So, what is the fundamental mechanism of viscosity in gases, it is due to the transfer of the molecular momentum.

Viscosity is the measure of a fluid's resistance to deformation or flow. Highly viscous liquids like molasses and tar flow very slowly compared to less viscous liquids like water. In gases, viscosity is primarily caused by the momentum transfer between molecules. When gas molecules collide, they transfer momentum, which creates friction that resists flow.

Think of honey pouring out of a jar compared to water. Honey is thick and flows slowly because it has a high viscosity, while water pours quickly because it has low viscosity. This difference can be likened to a race between a slow-moving turtle (honey) and a fast-moving rabbit (water).

In case of gases, the viscosity increases as temperature increases, also the viscosity increases as the pressure also increases. Liquids, it happens due to cohesion and momentum transfer and here the viscosity decreases as temperature increases. It is very important to note that it is quite different from the gases where the viscosity increases on increasing the temperature.

For gases, as the temperature rises, the kinetic energy of the molecules increases, leading to more frequent and energetic collisions, resulting in higher viscosity. Conversely, in liquids, an increase in temperature generally decreases viscosity because the molecules move faster, reducing the cohesive forces that cause resistance to flow. Pressure also affects gas viscosity but has a minimal impact on liquid viscosity.

Imagine sautéing vegetables in hot oil. As the oil heats up, it becomes less viscous (thinner) and allows the vegetables to cook more easily. However, if you were to increase the temperature of a gas, like in an air-filled balloon on a hot day, the air inside will become more viscous, making it harder for the gas to move, just like how a crowded dance floor becomes difficult to navigate as people bump into each other more frequently.

Now, one of the examples that we will talk about is used to measure the viscosity of the water. It is a very standard experiment. So, the inner cylinder in this particular case I have broken it down in form of a numerical as well. So, the inner cylinder here is 10 centimeters in diameter, there is another outer cylinder as well. So, the inner cylinder being 10 centimeters in diameter and it rotates at 10 rpm rotations per minute, the fluid layer in between those cylinders is 2 mm thick and the height at which it is 20 cm high.

In this experiment, the viscosity of water is measured using two concentric cylinders. The inner cylinder rotates at a constant speed, causing the liquid between the two cylinders to flow. The viscosity can be calculated based on the power required to maintain this rotation, the geometric dimensions of the cylinders, and the thickness of the fluid layer.

Think of a potter spinning a pot on a wheel. As the speed increases, the clay (acting as the fluid) stretches and spreads out. By measuring how hard the potter has to push down to keep the pot spinning, we can determine how thick or thin the clay is, similar to how viscosity is measured by seeing how much power is needed to spin the inner cylinder.

Now, what is the role of viscosity in statics? Its important to note that fluid at rest have no relative motion between layers of the fluid. Right? So, statics means rest. So, when the liquids do not move, there will be no velocity difference between those 2 fluids. Therefore, the shear stress is 0.

In static fluid, the absence of motion between fluid layers means that there is no shear stress, thus no resistance to flow. This contrasts with dynamic fluid situations, where viscosity plays an important role as the layers of the fluid slide past one another, creating velocity gradients and shear stress.

Imagine a calm lake where the water is motionless. There is no friction or resistance between the top layers of water and the deeper layers because they aren't moving against each other. However, if you were to create a disturbance, like throwing a stone into the lake, the water would ripple, creating motion similar to how shear stress occurs in dynamic fluids.

Kinematic viscosity also called ν is a fluid property obtained by dividing dynamic viscosity by fluid density. It is related to Reynolds number.

Kinematic viscosity provides another way to understand the flow characteristics of a fluid. By dividing the dynamic viscosity (a measure of a fluid's internal resistance) by its density, we gain insight into how the fluid behaves under flow. The Reynolds number, which relates inertial forces to viscous forces, is calculated using the kinematic viscosity.

Think of kinematic viscosity like comparing how thick a syrup is compared to how much it weighs. If you have two types of syrup, one may be thicker and denser, thus affecting how quickly it flows (the Reynolds number helps predict if it flows smoothly or creates turbulence, much like how a fat, heavy syrup would resist flow more than a light, watery syrup).

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