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.
Displacement Thickness
Unlock Audio Lesson
Today, we'll examine displacement thickness. It represents how much the streamline just outside the boundary layer is pushed away from the wall due to viscosity. Can anyone tell me why this is significant?
Wouldn't it affect the overall flow rate?
Exactly! The displacement thickness impacts the effective flow area. The greater the displacement, the less flow can occur close to the surface due to viscous effects. Now, can anyone summarize what the definition of displacement thickness is?
It's the distance a streamline is pushed away from the wall by fluid viscosity.
Perfect! Remember this acronym: **D**isplacement = **D**istance due to **D**issipation. Let’s proceed to momentum thickness.
Momentum Thickness
Unlock Audio Lesson
Moving on to momentum thickness, this measures the loss of momentum flux. Anyone know why momentum flux is critical?
It helps in determining how much energy is lost due to friction!
Exactly! Momentum flux loss affects velocity profiles in boundary layers. To derive momentum thickness, we integrate the difference between the velocity distributions inside and outside the boundary layer. Who can recall that?
Is it the area under the curve difference?
Yes! Remember, [D](https://en.wikipedia.org/wiki/Momentum_flux) = mass flow rate per unit area. Let's summarize: **M**omentum = **M**ass flow loss due to **M**ixture distribution.
Energy Thickness
Unlock Audio Lesson
Finally, let’s discuss energy thickness. This accounts for the loss of kinetic energy in the fluid flow. Can anyone differentiate it from the other thicknesses we discussed?
Is it based on kinetic energy loss due to velocity defects?
Exactly! The kinetic energy is reduced due to viscosity, and we measure this with energy thickness. When we're solving problems, we relate energy thickness to the overall energy distribution. What can we remember about energy thickness?
We can say **E**nergy = **E**fficiency lost due to **E**xcess friction!
Great acronym! Let's summarize the three thicknesses we've covered today.
Applications and Problem-Solving
Unlock Audio Lesson
Now we will apply these concepts to solve practical problems. Let’s start with calculating displacement thickness for a given velocity profile. Who wants to tackle this example?
I'll give it a try! The formula is from 0 to delta of (1 - u/U) dy.
Correct! Can you explain how you would set up the integral with the velocity profile?
We substitute the velocity profile into the integral to evaluate.
Perfect! Remember to specify the limits correctly. Let’s summarize what we learned about integrating for thicknesses.
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In this section, we delve into the concepts of displacement thickness, momentum thickness, and energy thickness, critical elements of boundary layer theory in fluid dynamics. The discussion includes definitions, mathematical derivations, and comparisons to illustrate the significance of these phenomena in hydraulic engineering.
Detailed
Detailed Summary
This lecture focuses on the boundary layer theory, explaining essential concepts such as displacement thickness, momentum thickness, and energy thickness. The displacement thickness is defined as the distance by which a streamline just outside the boundary layer is displaced due to viscous effects, while momentum thickness accounts for the loss of momentum flux in contrast to potential flow. The section dives into analogous definitions and mathematical derivations for each type of thickness, comparing the effects on fluid flow due to viscosity and boundary conditions. These concepts are further explored through practical examples and problem-solving methods.
Youtube Videos
Audio Book
Dive deep into the subject with an immersive audiobook experience.
Introduction to Displacement Thickness
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Displacement thickness is the distance by which a streamline, just outside the boundary layer, is displaced away from the wall due to viscous effects on the plate.
Detailed Explanation
Displacement thickness is an essential concept in boundary layer theory. It describes how much a streamline is pushed away from a wall by viscous forces in the fluid. When a fluid flows over a flat plate, it experiences friction due to its viscosity, causing slower velocities near the plate compared to the free stream. Displacement thickness quantifies this effect and is important for understanding how much the flow is altered due to the presence of the plate.
Examples & Analogies
Imagine a large crowd of people trying to walk through a narrow doorway. As they approach the doorway, some people slow down due to congestion. The displacement thickness is analogous to how far the crowd is pushed back from the doorway. The higher the congestion (or viscosity in fluid terms), the more the crowd spreads out before reaching that doorway.
Deriving Displacement Thickness
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now, we consider the flow over a smooth flat plate, like this... The area of the strip can be given by, b into dy...
Detailed Explanation
To derive displacement thickness, we consider a flat plate with fluid flowing over it. We look at an elemental strip of thickness 'dy'. The mass flux through this strip is calculated as the product of density and velocity across that area. When we compare the mass flux in this boundary layer with that in an unrestricted flow (or uniform flow), we find the difference is due to the reduction in velocity caused by the viscous effect. This difference, when integrated across the boundary layer, gives us the displacement thickness.
Examples & Analogies
Think of water flowing through a wide pathway that narrows into a vent. As the water approaches the narrow opening, it slows down and spreads out. This 'spreading out' effect can be calculated in a similar way to how we derive the displacement thickness in fluid dynamics.
Momentum Thickness Definition
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Momentum thickness theta is the loss of momentum flux in the boundary layer, as compared to that of the potential flow.
Detailed Explanation
Momentum thickness quantifies the loss of momentum in a boundary layer compared to an ideal flow without any boundary effects. It is defined through momentum flux, which is the mass flux multiplied by velocity. As fluid flows over the boundary, some of its momentum is lost due to friction with the surface, causing a deficit that represents our momentum thickness.
Examples & Analogies
Imagine a skateboarder gliding smoothly along a flat sidewalk (ideal flow), but then transitioning onto a rougher surface like gravel (boundary layer effects). The skateboarder would lose speed and momentum due to friction with the gravel. The difference in speed they experience when gliding on gravel versus on the smooth sidewalk is akin to momentum thickness.
Energy Thickness Explanation
Unlock Audio Book
Signup and Enroll to the course for listening the Audio Book
Now, there is something called energy thickness, delta double dash. This is defined based on the reduction of the kinetic energy of the fluid flow due to the velocity defect.
Detailed Explanation
Energy thickness is another way of looking at the effects of viscosity in a fluid flow. It focuses on how the kinetic energy of a flow is reduced due to the slower speeds in the boundary layer compared to the free stream. This reduction in energy can greatly affect the energy transfer and performance in various engineering applications.
Examples & Analogies
Consider a car trying to go uphill. The car has to expend more energy to overcome gravitational forces. Similarly, when fluid flows over a surface and encounters resistance (due to viscosity), it loses kinetic energy, which we can measure as energy thickness.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Displacement Thickness: Measurement of streamline displacement due to viscous effects.
-
Momentum Thickness: Represents momentum loss in the fluid due to viscosity.
-
Energy Thickness: Indicator of kinetic energy loss in the flow.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
Analyzing flow over a flat plate to determine displacement thickness given a velocity profile.
-
Calculating momentum thickness for a fluid with known viscosity and velocity profile.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
-
When flow meets the surface, the streamline goes astray, viscous force affects it, that's displacement today!
📖 Fascinating Stories
-
Imagine water flowing over a smooth slab. As it touches the slab, it slows down, pushing the streamline away into the wider river.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Displacement Thickness
Definition:
The distance by which a streamline outside the boundary layer is displaced due to viscous effects.
-
Term: Momentum Thickness
Definition:
The measure of the loss of momentum flux in a flow compared to the free stream.
-
Term: Energy Thickness
Definition:
The measure of energy loss due to the velocity deficit in the boundary layer.