Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today, we will explore how fluids behave when they flow between two parallel plates. Imagine one plate is stationary while the other moves. What do you think happens to the fluid in between?
I think the fluid closer to the moving plate will move faster than the one near the stationary plate.
Exactly! That's called a velocity gradient. As we move away from the stationary plate toward the moving one, the fluid's velocity increases linearly. Can anyone explain what we mean by 'linear' here?
It means that the velocity increases consistently without any sudden changes!
Perfect! Now, remember this as we discuss shear stress, which is related to these velocities.
Let’s talk about shear stress and shear strain rate. Who can tell me how they're related?
Isn't shear stress proportional to the velocity gradient?
Yes! The equation is τ = μ (du/dy). Here, τ represents the shear stress, μ is the viscosity, and (du/dy) is the velocity gradient. Can someone expand on what viscosity represents?
Viscosity measures the internal friction of the fluid, right? It shows how resistant a fluid is to flow.
Exactly! And this relationship defines Newtonian fluids. Viscosity remains constant across the shear rate for these fluids. Let's remember to differentiate between this and non-Newtonian fluids later!
Now let's compare fluid mechanics to solid mechanics. How is shear stress treated differently in fluids compared to solids?
In solids, shear stress relates to the amount of deformation, while in fluids, it relates to how quickly the fluid is deforming, right?
Exactly! In fluid mechanics, shear stress is proportional to the shear strain rate rather than the absolute strain. Why do we think this distinction is important?
It helps us understand fluid behaviors in various applications, like in pipes or when painting!
Exactly! Different behaviors mean different engineering approaches.
Next, let’s examine how temperature influences viscosity. What happens to viscosity as we heat a liquid?
I think it decreases because the molecules move faster and have less intermolecular attraction.
Right on! That's why heating oil can reduce its viscosity. In contrast, what happens with gases as we increase temperature?
For gases, viscosity actually increases because the increased thermal energy leads to more collision between molecules.
Correct! Understanding these differences helps us manage fluids in industries, like refining processes.
Let's wrap up by discussing Newtonian and non-Newtonian fluids. Who can give me an example of each?
Water is a Newtonian fluid, and ketchup is a non-Newtonian fluid!
Great examples! Newtonian fluids have a constant viscosity, while non-Newtonian fluids' viscosity changes with the rate of shear. Why is this distinction critical in engineering?
Because it affects how we design systems to handle different fluids!
Exactly! Knowing how these fluids behave allows for better designs and practical applications.
The pressure experienced by a fluid layer due to forces acting tangentially.
A constant that represents a fluid's resistance to shear, crucial for determining flow behavior.
An essential factor determining how fluid velocity changes with respect to distance.
Fluids that showcase a linear relationship between shear stress and shear rate.
Fluids with complex flow properties where shear stress does not have a direct linear relationship with shear rate.
Viscosity tells how thick or thin, Under stress, flow lets in.
Imagine a river flowing; some is thick mud while others are smooth pebbles. The mud represents a high viscosity, while the pebbles represent low viscosity fluid, illustrating how different flows experience shear stress.
SHED - Shear Stress, Hydrostatic pressure, Elastic modulus, Dynamic viscosity help remember the key fluid mechanics terms.
VASE - Viscosity And Shear Effects, to remember that viscosity is crucial in understanding shear effects in fluids.
Term
What is shear stress?
Click to flip
Term
Define dynamic viscosity.
Click to flip
The force per unit area exerted by a fluid parallel to the plane of interest.
The property of a fluid that measures its resistance to flow and deformation.
The change in velocity with respect to distance from a stationary plate in fluid flow.
A fluid whose viscosity remains constant regardless of the shear rate.
A fluid whose viscosity changes with the shear rate, exhibiting complex flow behavior.
This section discusses the concepts of fluid flow through parallel plates and the relationship between shear stress, shear strain rate, and viscosity as described by Newton's laws.
The section delves into the behavior of fluids under shear stress, particularly in parallel plate flow, illustrating how velocity gradients are related to shear strain rates. It also highlights the crucial distinction between solid mechanics and fluid mechanics, emphasizing that shear stress in fluids is proportional to shear strain rate, which is a defining feature of Newtonian fluids.
This section introduces the fundamental principles behind Newton’s laws of viscosity, focusing on fluid flow between two parallel plates. When one plate is stationary and the other moves with a velocity V, an interesting phenomenon arises: a linear velocity gradient develops from rest to the moving plate. As the distance from the stationary plate increases, the fluid's velocity increases proportionally until it reaches the moving plate's velocity.
The key mathematical relationship derived here is the direct proportionality between shear stress and shear strain rate, characterized by the equation:
τ = μ (du/dy)
where τ represents shear stress, μ is the dynamic viscosity, and (du/dy) denotes the velocity gradient perpendicular to the flow direction.
A crucial differentiation is made between the concepts within fluid mechanics and solid mechanics, as the shear stress in fluids correlates to shear strain rate (a change over time), rather than absolute strain as in solids. This section also discusses how viscosity varies with temperature and pressure, examining experimental findings that illustrate how these factors influence fluid properties.
Finally, a profile of different fluid types is introduced, including Newtonian and non-Newtonian fluids, categorized based on their responses to shear forces. The nuanced behavior of these fluids in response to changes in viscosity highlights the complexity of fluid behavior and the significance of Newton’s laws of viscosity.