Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Velocity Distribution in Parallel Plate Flow
Unlock Audio Lesson
Today, we're going to explore how fluid behaves between two parallel plates, one stationary and one moving. Can anyone describe what happens to the fluid's velocity as we move away from the stationary plate?
The fluid closest to the stationary plate will have zero velocity because of the no-slip condition!
Exactly! As we move up to the top plate, the velocity increases linearly up to V. This linear distribution is a fundamental concept we'll build upon when we discuss shear stress.
So, if we have points A and B, with A at the moving plate and B at the stationary plate, the velocity gradient is important?
Very important! The velocity gradient reflects how shear stress changes with the distance in the fluid. Remember, shear stress is like the force causing layers of fluid to slide over one another.
Can you explain the relationship between shear stress and shear strain once more?
Sure! In a linear flow, shear stress is directly proportional to the rate of strain or velocity gradient, which leads us to the concept of viscosity. Let's keep this proportion in mind.
Isn't this similar to how solid mechanics works, where stress is proportional to strain?
Precisely! However, in fluid mechanics, we deal with shear strain rate, not absolute shear strain. This distinction is key to understanding fluid behavior.
To summarize, we learned about how fluid velocity changes in parallel flow and how shear stresses relate to these changes. Both concepts are foundational for understanding the behavior of fluids.
Viscosity and Its Dependence on Temperature
Unlock Audio Lesson
Now, let's discuss viscosity. Can anyone explain how temperature affects viscosity in fluids?
I remember that increasing the temperature of liquids usually reduces their viscosity.
Correct! This is due to increased molecular motion, which weakens intermolecular forces. What about gases?
For gases, increasing temperature tends to increase viscosity.
Right again! As gas temperatures increase, molecular motion intensifies, leading to more effective collisions and a rise in viscosity. This difference between the behavior of liquids and gases is important!
How do we quantify the relationship between viscosity and temperature?
Great question! We use the Sutherland correlation. Does anyone remember the formula?
It's μ = aT^(3/2) / (T + b), right?
Close! The correct version accounts for the constants a, b, and c, which can vary by substance. Understanding this correlation is essential for fluid dynamics applications.
To recap, we looked at viscosity's dependence on temperature and introduced the Sutherland correlation. Keep these relationships in mind for your future studies!
Newtonian vs Non-Newtonian Fluids
Unlock Audio Lesson
Next, let's differentiate between Newtonian and non-Newtonian fluids. Who can describe a Newtonian fluid for me?
A Newtonian fluid exhibits a constant viscosity regardless of the shear stress applied!
Exactly! This means the shear stress is linearly proportional to the shear strain rate. And what about non-Newtonian fluids?
Non-Newtonian fluids have a variable viscosity that changes based on the shear rate!
Fantastic! They can become thicker or thinner depending on the stress and strain they experience. Can anyone give an example of a non-Newtonian fluid?
Toothpaste! It starts solid and flows when you squeeze it.
Correct! Toothpaste is a Bingham plastic, which requires a yield stress to begin flowing. Let's also not forget about shear-thinning fluids, like ketchup!
So, the behavior of the fluid really impacts how we use them in everyday applications?
Absolutely! Understanding these differences helps engineers design better systems for various industrial applications. Let's summarize: Newtonian fluids have a constant viscosity, while non-Newtonian fluids can behave unpredictably under stress.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
This section elaborates on fluid flow between parallel plates, explaining how velocity gradients relate to shear stress and introducing the Sutherland correlation for estimating dynamic viscosity as a function of temperature. It highlights the differences between fluids and their respective behaviors under changing temperature and pressure conditions.
Detailed
Sutherland Correlation
This section delves into fluid mechanics, specifically the behavior of fluids flowing between parallel plates. When observing such a flow, one plate remains stationary while the other moves with a velocity V. The resultant velocity profile across the fluid element from one plate to the other exhibits linear variation, allowing us to derive relationships critical in fluid dynamics.
The section explains how, under these parallel flow conditions, the shear stress is proportional to shear strain rate, irrespective of external factors. This conclusion is important because it sets foundational principles for understanding fluids as either Newtonian or non-Newtonian.
A thorough examination of viscosity is conducted, emphasizing its dependence on temperature. The Sutherland correlation—which offers a quantitative relationship between dynamic viscosity (μ) and temperature (T)—is discussed in depth. The correlation is defined as:
μ = aT^3 / (1 + bT)
where T denotes absolute temperature and a, b, and c are empirically determined constants. The behavior of liquids and gases under temperature and pressure changes highlights varying trends in viscosity, establishing a contrasting relationship for gases and liquids. This relationship speaks to how viscosity impacts the flow behavior of different fluids, setting the stage for practical applications and fluid dynamics models.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Fluid Flow Through Parallel Plates
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
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 a shear stress. Here what we consider that fluid element.
Detailed Explanation
In this discussion, we begin with fluid flowing between two parallel plates. One plate is stationary (at rest), represented as having a velocity of zero, while the other plate is moving with a velocity (V). This setup allows us to consider the concept of shear stress not at the molecular level but at the level of fluid elements, which are defined spaces within the fluid where we analyze characteristics like velocity and deformation.
Examples & Analogies
Imagine a thick syrup being spread on a cutting board. One side of the board is stationary, while you drag a spatula (the other plate) across the syrup. The syrup closest to the cutting board has no movement (like the stationary plate), while the syrup at the top moves with the spatula. The flow of syrup from one side to the other illustrates how fluid elements behave under the influence of movement.
Velocity Distribution and Linear Variation
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
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. That linear velocity from zero to V as the y increases, the velocity will increase it and maximum velocity will be the V.
Detailed Explanation
Due to the no-slip condition in fluid dynamics, the velocity at the stationary plate (point B) is zero, while as you move towards the moving plate (point A), the velocity gradually increases to V. This results in a linear change in velocity throughout the fluid layer, which can be visualized as a gradient. Essentially, as you move up from the stationary plate (B) towards the moving plate (A), the speed of the fluid increases proportionally.
Examples & Analogies
Think about a slide at a playground. If the bottom of the slide is against the ground (no height or velocity) and the top of the slide is where the kids gain their maximum velocity as they go down. As they slide down, they start from a stop and gradually build speed; similarly, in the fluid flow, you go from zero velocity at the lower plate to maximum velocity at the top plate.
Shear Stress and Shear Rate Clarification
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now if I consider the at the y distributions and the angular velocity distributions if I consider it I will get it the u, the velocity at these points and ratio of the distance as a linear velocity distributions concept, we can get it, √V/y.
Detailed Explanation
In fluid dynamics, we define shear stress and shear strain rate. The velocity gradient, which is the change in velocity per unit distance (here, represented as V/y), illustrates how fast the fluid's velocity is shifting as we move away from the stationary plate. This is essential for understanding how shear stress develops in the fluid, as shear stress is directly proportional to how quickly the velocity is changing at a given point in the fluid.
Examples & Analogies
Consider frosting a cake with a spatula. When you apply pressure and drag the spatula across the frosting (the fluid), the movement creates different levels of velocity at different heights of the frosting. The bottom layer (the closest to the cake) doesn't move, while the top is spread faster. This unequal distribution creates a shear effect.
Newton's Law of Viscosity
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
We remember this is what is indicating us is that the velocity gradient. If I consider this is the y directions how the velocity varies along the y directions that is the constant which is equal to the shear strain rate. The shear deformations per unit time. So we can now consider it that the shear rate strain rate and the velocity gradient is equal for these conditions.
Detailed Explanation
The relationship established indicates that the velocity gradient in the fluid (the rate at which velocity changes with vertical position) is directly tied to the shear strain rate. This connection allows us to use Newton's law of viscosity, which states that shear stress (force per area) is proportional to the shear strain rate, giving us a framework for calculating how fluids behave under stress.
Examples & Analogies
Think about honey and how it behaves when you pour it. If you pour it slowly, it flows steadily and smoothly. As you increase the speed at which you pour, the resistance (or shear stress) increases due to the honey's viscosity. The faster you try to pour, the stickier it feels. This is the shear strain rate in action!
Impact of Temperature on Viscosity
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now let us commit that how 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.
Detailed Explanation
Viscosity is also affected by temperature. As temperature increases, the energy of the molecules increases, causing them to move more rapidly and reducing the intermolecular forces holding them together. This means that typically, the viscosity of liquids decreases as temperature rises. In contrast, gases, which already have weaker intermolecular forces, can experience increased viscosity with rising temperatures due to greater molecular motion and collision frequency.
Examples & Analogies
Think about how syrup flows at room temperature—it is thick and slow-flowing. However, when heated, it becomes much thinner and flows easily. On the contrary, if you heat up some air (like when blowing up a balloon), it expands and can lead to an increase in speed, thereby affecting how it behaves under certain conditions.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Fluid Flow: The behavior of fluids moving between surfaces.
-
Velocity Gradient: The rate of change in velocity across a fluid element.
-
Shear Stress: Force per unit area acting parallel to the flow section.
-
Viscosity: The internal friction of fluids, influencing their flow behavior.
-
Sutherland Correlation: A relationship defining viscosity changes with temperature.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
The difference in viscosity between oil and water at room temperature highlights the varying flow behaviors based on molecular interactions.
-
In everyday products like toothpaste, a Bingham plastic requires an initial force to flow, showcasing non-Newtonian behavior.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
When temperatures rise and flow gets smooth, viscosity's low, it's the right groove.
📖 Fascinating Stories
-
Imagine trying to pour a thick syrup; it's hard at first, but as it warms, it flows freely.
🧠 Other Memory Gems
-
Remember 'N' for Newtonian: No change in viscosity, consistent strain rate.
🎯 Super Acronyms
VIS = Viscosity Influences Shear; it reminds you of how viscosity relates to shear stress.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Viscosity
Definition:
A measure of a fluid's resistance to flow or deformation.
-
Term: Shear Stress
Definition:
The stress component parallel to a given surface, often caused by forces acting on a fluid.
-
Term: Shear Strain Rate
Definition:
The rate at which adjacent layers of fluid move with respect to each other.
-
Term: Sutherland Correlation
Definition:
A mathematical relationship used to find the viscosity of gases as a function of temperature.
-
Term: Newtonian Fluid
Definition:
A fluid with a constant viscosity that remains unchanged regardless of the shear rate.
-
Term: NonNewtonian Fluid
Definition:
A fluid whose viscosity changes with the shear rate applied to it.