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A short class with Sarah and her students. The other ways are under More.
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Welcome, class! Today, we'll explore how fluids behave under the influence of shear stress, particularly when flowing between parallel plates. Let's start with the no-slip condition. Can anyone remind me what that means?
It means that the fluid at the surface of the stationary plate has zero velocity.
Exactly! And what about the fluid adjacent to the moving plate?
That fluid moves at the velocity V.
Correct! So, as we move from point B to point A, there is a linear increase in fluid velocity. Now, why do you think this gradient is important?
I guess it relates to how shear stress develops in the fluid.
Right! The velocity gradient indicates how quickly the fluid is deforming and leads us to the concept of shear stress. Let's remember the term 'velocity gradient' as VG—understand its role in shear stress formation.
Got it! VG for velocity gradient.
Great! As we continue, let's also think about how these concepts relate to viscosity.
Now that we've established the velocity gradient, let's discuss shear stress. Can someone define shear stress for us?
Shear stress is the force per unit area acting parallel to the surface.
Exactly! And how does this relate to viscosity in fluids?
I think viscosity is a measure of a fluid's resistance to flow, right?
Yes! According to Newton's law of viscosity, shear stress is proportional to the shear strain rate. If we represent the shear strain rate with the symbol 'du/dy', how would we express this relationship mathematically?
It would be τ = μ * (du/dy), where τ is shear stress and μ is viscosity.
Well done! Understanding this equation—τ = μ * du/dy—helps us grasp fluid dynamics better. Just remember the acronym 'TSV' for shear stress, viscosity, and velocity gradient.
TSV, nice! It helps to remember those key relationships.
Alright! Let’s move on to temperature effects on viscosity. What happens to a fluid’s viscosity when you increase the temperature?
I believe it decreases for liquids because the intermolecular forces become weaker.
Exactly! Lower binding forces lead to lower viscosity. And what about gases?
For gases, viscosity increases with temperature due to greater molecular movement.
Right again! Let's summarize our findings: the key term to remember here is 'temperature effect.' For liquids, increasing temperature leads to decreased viscosity, while for gases, it leads to increased viscosity. We can remember this by the mnemonic 'LiTe-Visc'—Lower viscosity for Liquids with Temperature increases, and Viscosity increases for gases.
Got it, LiTe-Visc!
So far, we’ve focused on Newtonian fluids. What do we call fluids that don't follow the simple rules of Newtonian flow?
Those are called non-Newtonian fluids!
That's right! Can anyone give me an example of a non-Newtonian fluid?
Toothpaste is a good one; it behaves differently under different forces.
Perfect example! Non-Newtonian fluids can have varying viscosity depending on the shear rate, making them more complex to study. Let’s use the acronym 'NNP' for Non-Newtonian Properties to remind ourselves of this complexity.
NNP stands for Non-Newtonian Properties!
Finally, how are these concepts related to practical applications? For instance, why is understanding viscosity important in engineering?
It affects how fluids are transported in pipelines and manufacturing processes.
Exactly! The efficiency of pumping, mixing, and applying fluids depends heavily on their viscosity. We can summarize this by remembering 'Visc-PUMP'—Understanding Viscosity is crucial for PUMPing efficiency!
Visc-PUMP is a neat way to remember!
I’m glad you find it helpful! By linking theory to applications, you'll better understand the significance of these principles in real-world scenarios.
The force that causes layers of fluid to slide past each other, essential for understanding fluid flow.
A property that quantifies a fluid's internal resistance to flow and affects applications in engineering.
Important in fluid mechanics, denoting that there is no motion of fluid along stationary surfaces.
Represents how rapidly velocity changes within a fluid and is crucial for the calculation of shear stress.
Fluids that do not have a constant viscosity; their properties change under different shear rates.
If your fluid’s slow and thick, viscosity is the trick!
Imagine a river flowing gently through rocks. At one point it’s calm, but as you reach a narrow passage, it speeds up and flows easily. This is much like how viscosity changes with shear stress.
Remember 'TSV' for Shear stress, Viscosity, and Velocity gradient—these are the relationships we must connect!
LiTe for liquids—Increasing Temperature, Lower viscosity!
Term
What is viscosity?
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Define shear stress.
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What happens to viscosity as temperature increases for liquids?
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What is the no-slip condition?
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What distinguishes a non-Newtonian fluid?
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The force per unit area acting parallel to the surface of a material.
A measure of a fluid's resistance to flow, influenced by intermolecular interactions.
The rate of change of velocity with respect to distance; crucial for determining shear stress.
A fluid whose viscosity changes with the shear rate, unlike Newtonian fluids.
A condition where fluid velocity at a solid boundary is zero.
An empirical relationship that connects dynamic viscosity with temperature for gases.
This section explores the microscopic perspective of fluid flow between parallel plates, emphasizing shear stress and viscosity.
Focusing on fluid behavior at a microscopic level, particularly in parallel plate systems, this section examines how shear stress is developed due to velocity gradients and how viscosity relates to temperature and pressure conditions. It also touches on how different fluids respond under various shear forces.
In this section, we delve into the microscopic perspective of fluid dynamics, particularly focusing on fluid flow between two parallel plates. We begin with the no-slip condition, where one plate remains stationary while the other moves at velocity V. As we analyze a fluid element defined by points A, B, C, and D in the region between the plates, we observe a linear velocity distribution that increases from B (velocity = 0) to A (velocity = V).
As fluid flows over time, deformation occurs, leading to angular deformations in the fluid element. By considering the relationships between angular deformations, shear strain rate, and velocity gradients, we derive that shear stress is proportional to the shear strain rate based on Newton’s law of viscosity. This crucially differentiates fluid mechanics from solid mechanics, where stress correlates to strain rather than strain rate.
Next, we explore how temperature and pressure affect viscosity, highlighting that temperature increases lead to reduced intermolecular forces for liquids, thus lowering their viscosity. In contrast, gases exhibit an increase in viscosity with temperature due to enhanced molecular movement.
Finally, we discuss the relation of viscosity's temperature sensitivity, providing insights into Sutherland's correlation and its empirical constants for different fluids. This section effectively sets the groundwork for understanding how fluid behavior under various conditions affects applications in engineering and physics.