4.4.2. Gas and Liquid Viscosity Variations

If I consider the same fluid flow through a parallel plate, okay. One of the plate the velocity is zero which is at the rest conditions and other the top plate is moving with a velocity V. So as a microscopic point of view I am not talking about the molecular motions or exchange of the molecular motions or the momentum flux that what is resulting in a shear stress. Here what we consider is that fluid element. That means, I consider some space of A, B, C, D, this is what the fluid element. That means, whatever the fluids are there that reasons, I am defined as a fluid element. As you know it that at the A point we will have the velocity V as the no-slip conditions. At the B point we will have velocity zero. So velocity assuming it, it will have a linear velocity variation from B to A.

This chunk explains the concept of fluid flow between two parallel plates. One plate is stationary (velocity = 0), while the other moves at a velocity V. The velocity of the fluid layers between the plates varies linearly from zero to V, illustrating the no-slip condition where fluid in contact with a surface does not slip past it. This setup helps understand how velocity gradients create shear stress within the fluid.

Imagine spreading peanut butter on bread. The peanut butter closest to the knife (moving plate) gets smeared around faster than the peanut butter resting on the bread (stationary plate). Just like the fluid layers, the velocities increase smoothly from one point to another.

That linear velocity from zero to V as the y increases, the velocity will increase it and maximum velocity will be the V. If it that the conditions now if you look at the point which is the y distance from the plate which is at the rest conditions you will have velocity U, okay. So as a linear proportionality we can find out what is the velocity of that point.

The chunk details how the velocity of the fluid changes linearly with the distance from the stationary plate. As you move from the stationary plate upward, the fluid's velocity increases proportionately until reaching its maximum value V at the moving plate. This concept is crucial for calculating shear stress in the fluid by examining the velocity gradient.

Consider how quickly you can run while going uphill; the higher you climb, the more effort (velocity) is needed. Similarly, in this fluid case, the farther you are from the stationary surface, the faster the fluid flows.

If as a linear velocity distribution as you assume it as we got it some of the parallel flow conditions after ∆t time these fluid element will be deformed as angular deformations will happen at this point is θ. Similar way the θ at this point. So consider a very simple geometry of these problems. I can consider these distance of AE is V into delta t divide by l will be the constant.

The chunk discusses how, over a small time interval, the fluid element experiences angular deformations due to the linear velocity variation. The angular deformation is denoted as θ, and by using simple geometry, you determine the distances involved. This understanding helps in calculating shear strain rates in future steps.

Think of a rubber band stretched at one end. As you pull it over time, it will change shape, resembling the angular deformations happening within the fluid elements during flow.

So now we are coming to the exactly the solid mechanics concept the stress having the proportionality with the strain. But here, we are talking about the stress is proportionality to the strain rate. That means the change of the shear strain rate with respect to time, not the absolute value of the shear strain. That is the basic difference between fluid mechanics and solid mechanics.

This section highlights the fundamental difference between fluid and solid mechanics. While stress is proportional to strain in solids (which is a measure of deformation), in fluids, stress is proportional to strain rate, which describes how fast the deformation occurs. This behavior is captured in Newton's law of viscosity, which is essential for understanding fluid dynamics.

Consider making pasta; when you push the dough slowly, it spreads gently (low shear rate). But when you push it hard and fast, it flattens out quickly (high shear rate). The stress on the dough increases with how quickly you push—similar to how shear forces increase in fluids.

Now let us commit that how does the temperature effect on the coefficient of the viscosity. Now we have to look at the molecular levels okay. So if you look at this molecular levels, when you talk about the liquids, they will have a molecular bonding forces between two molecules okay. But that is much weaker when talk about the gases.

This chunk discusses how temperature affects viscosity at the molecular level. In liquids, molecules are held together more strongly, leading to lower viscosity than gases, where molecular forces are weak. As temperature rises, the kinetic energy and motion of the molecules increase, causing a decrease in viscosity for liquids due to weakened intermolecular forces.

Think about honey versus water. When warmed, honey flows more easily, analogous to how increasing temperature reduces viscosity since faster-moving molecules can change positions more freely.

If you increase the temperature which manifests to the molecular motions to sustain that temperatures. In that conditions what it will happen it will reduce the binding force, the intermolecular binding force between two molecules. Because of that, there will be a decreasing trend of coefficient of viscosity.

This section focuses on how different fluids react to temperature changes. For liquids, increasing temperature results in a decrease in viscosity due to weaker intermolecular forces. Conversely, in gases, as the temperature increases, viscosity actually increases. Understanding these trends is crucial for fluid mechanics applications in engineering and science.

Consider a car engine; as it heats up, the oil inside thins, making it flow easier (decreasing viscosity). In contrast, gases like air might get 'thicker' as the temperature increases, affecting how they behave in various conditions.

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