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Welcome, everyone! Today, we will explore the no slip boundary condition. Can anyone tell me what happens when fluid flows past a solid surface?
I think the fluid sticks to the surface?
Exactly! This phenomenon is known as the no slip boundary condition. It states that fluid velocity in contact with a solid boundary is equal to the velocity of that boundary. For a stationary surface, this means the fluid velocity is zero at that point.
So, what happens further away from the surface?
Great question! The fluid velocity gradually increases away from the boundary until it reaches the free-stream velocity. This variation creates a velocity gradient within a thin region known as the boundary layer.
Can we visualize how this boundary layer forms?
Absolutely! Imagine a flat plate submerged in a flowing fluid. Near the plate, the fluid drags along with it due to viscosity, creating the boundary layer. As we move outwards from the wall, the flow regains its full velocity.
So, the no slip condition is essential for calculating fluid flow near surfaces?
Exactly right! The no slip condition is fundamental for understanding boundary layer behavior, and we'll see its importance in many applications.
To summarize, the no slip condition indicates that fluid velocity is zero at a stationary boundary, and the velocity increases away from the surface, forming the boundary layer.
Now, let’s delve deeper into the boundary layer. Can anyone describe what influences the thickness of this layer?
I assume that it depends on the fluid velocity and viscosity?
Precisely! The thickness of the boundary layer is influenced by the free-stream velocity, fluid viscosity, and distance from the leading edge of the surface.
Is there a specific way to measure or calculate this thickness?
Indeed! The boundary layer thickness, usually denoted as delta, grows as we move downstream from the leading edge. This gradient contributes to shear stress at the boundary.
And what role does shear stress play in fluid flow?
Shear stress represents how the velocity gradient near the solid surface affects the flow. Mathematically, shear stress is proportional to du/dy, where 'u' is the fluid velocity and 'y' is the distance from the boundary.
In summary, the boundary layer thickness increases with distance from the leading edge, driven by factors such as free-stream velocity and viscosity.
Moving on, let's differentiate between laminar and turbulent boundary layers. Can someone explain these two states?
I think laminar flows are smooth and orderly, while turbulent flows are chaotic and irregular.
Exactly! The laminar boundary layer occurs near the leading edge with streamlined flow. However, as we move downstream, an increase in Reynolds number can destabilize this layer, leading to turbulence.
What's the critical Reynolds number for this transition?
Good question! The transition from laminar to turbulent flow typically occurs at a Reynolds number of about 5 x 10^5 for flow over flat plates.
So, what implications does this have for flow around objects?
Excellent point! Understanding these transitions helps predict drag forces on structures and analyze environmental impacts in hydraulic engineering.
To summarize, we have learned that laminar flows are smooth, while turbulent flows are disordered. The transition occurs around a Reynolds number of 5 x 10^5.
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In fluid dynamics, the no slip boundary condition indicates that fluid velocity at a stationary boundary is zero. This leads to a velocity gradient that exists within a thin region near the boundary, termed the boundary layer, where viscous forces play a significant role before transitioning to the outer flow region.
In fluid mechanics, when a real fluid flows past a solid, the fluid particles adhere to the solid surface, resulting in what is known as the no slip boundary condition. This condition states that the velocity of the fluid particles adjacent to the solid surface matches the velocity of the boundary itself. For a stationary object, this means that at the boundary, the fluid velocity is zero.
As you move away from the boundary into the fluid, the velocity increases from zero (at the solid surface) to the free-stream velocity of the fluid. The region where this velocity change occurs is thin and is referred to as the boundary layer. Within this boundary layer, the fluid experiences both viscous forces and rotationality, affecting flow characteristics. At a considerable distance from the boundary, in the outer flow region, the fluid behaves as if it is inviscid, and potential flow theory applies.
The concept of no slip is crucial in understanding the development and characteristics of the boundary layer, which significantly impacts various applications in hydraulic engineering, such as sediment transport and biological interactions in aquatic environments.
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So, when a real fluid flows past a solid, the fluid particles stick to the solid surface. So, that is one of the phenomena that happens. And the velocity of the fluid particles close to the solid boundary is actually equal to the velocity of the boundary and this phenomenon is called the no slip boundary condition.
The no slip boundary condition describes how fluids behave when they come into contact with a solid surface. When a fluid, such as water, flows over a solid surface, the particles of the fluid right at the surface do not slide or slip; instead, they adhere to the surface. This means that these fluid particles have the same velocity as the solid surface, which, if the surface is stationary, is zero.
Imagine pushing a toy car on a smooth floor. The wheels of the car are in contact with the floor and do not slip against it. If you push the car, the wheels turn but they don’t slide on the floor; they move with the same speed as the car itself. Similarly, in fluid flow, the molecules closest to the surface of a solid adhere to it and do not slip.
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So, actually this is the most commonly used no slip boundary condition that we use in a viscous fluid flow. What is viscous fluid flow? A small detail which we have already talked about before but will look into more details in the upcoming lectures in coming weeks.
In viscous fluid flow, the fluid’s viscosity plays a crucial role in determining how the fluid behaves near surfaces. The no slip condition is essential because it indicates that the fluid's velocity gradually changes from zero (at the solid boundary) to the free stream velocity (the speed of the fluid further away from the surface). This change in velocity is the result of the fluid particles experiencing drag due to viscosity, as they interact with the solid surface.
Imagine stirring honey with a spoon. Near the spoon, the honey slows down and sticks to it, while further away, the honey flows more freely. Just as the honey's movement changes near the spoon due to the forces acting on it, fluid particles slow down and stick to solid surfaces, demonstrating the no slip condition.
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Because of this phenomenon, what happens is there is a velocity variation and this gives a velocity gradient du / dy which exists in normal direction. So, in case of say, for example, this is the boundary because of no slip and this is stationary and suppose there has been a velocity coming in, so, we are not going to talk about let us say, in between now but we say, suppose here is a velocity u and this distance is y and, of course, because this is stationary at this point, the velocity is going to be zero.
The no slip boundary condition leads to the formation of a velocity gradient, which is a measure of how much the fluid velocity changes with distance from the solid surface. The notation du/dy represents this gradient, where 'u' is the velocity of the fluid and 'y' is the distance from the boundary. In a thin layer of flow near the surface, the velocity increases from zero at the boundary to the free stream velocity farther away. This thin layer, where the velocity changes significantly, is known as the boundary layer.
Think about how the wind feels stronger the further you get from a wall. If you stand right next to the wall, the air doesn't move at all (like the fluid at the wall, which is stationary). But as you step away, the wind speeds up. This change in wind speed as you move away from the wall is similar to the velocity gradient in a fluid near a boundary.
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Prandtl actually divided the flow of the fluid in the neighbourhood of the solid boundary into 2 regions, to have a more simplified look. So, one is called the boundary layer. So, it is in the immediate vicinity of the solid boundary where the viscous forces and rotationality cannot be ignored.
To simplify the analysis of fluid flow around solids, Prandtl categorized the flow into two regions. The first, the boundary layer, is the layer where the effects of viscosity and rotational movements are significant. Inside this layer, the fluid experiences shear stress due to the velocity gradient defined by the no slip boundary condition. The second region is the outer flow region, where the fluid behaves more like an ideal fluid, largely unaffected by viscosity.
Consider a moving car. The air right next to the car’s surface moves slowly, affected by the car due to the no slip condition. This is similar to the boundary layer. However, the air farther away flows freely without being slowed down by the car's presence, which is like the outer flow region. This distinction helps in understanding how different forces act at various distances from the body.
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Key Concepts
No Slip Condition: The condition stating fluid velocity equals boundary velocity near a solid surface.
Boundary Layer: A thin region where fluid velocity changes rapidly from zero at the boundary to the free-stream velocity.
Viscous Forces: Forces due to viscosity that significantly affect fluid flow near solid surfaces.
Reynolds Number: A critical value that determines the type of flow (laminar or turbulent) and influences boundary layer behavior.
See how the concepts apply in real-world scenarios to understand their practical implications.
When water flows over a parked ship, the water at the hull remains stationary relative to the ship while the flow velocity increases away from the ship's surface, illustrating the no slip boundary condition.
In a lab experiment, dye is injected into water flowing over a surface to visualize how the boundary layer forms and grows thicker downstream.
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
At the wall, fluid has to stall; no slip means it adheres to all!
Imagine a calm lake on a still day, with a boat gradually pushing the water. The water closest to the boat doesn’t move but farther away, the current flows freely, representing the no slip condition gradually giving way to the boundary layer.
B.L.V. - Boundary Layer Velocity 'vanishes' at the wall, grows freely henceforth.
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Review the Definitions for terms.
Term: No Slip Boundary Condition
Definition:
A condition where the velocity of fluid particles at a solid boundary is equal to the velocity of that boundary, often zero for stationary boundaries.
Term: Boundary Layer
Definition:
A thin region of flow near a solid boundary where velocity changes from zero at the surface to the free-stream value.
Term: Viscous Forces
Definition:
Forces acting due to the viscosity of a fluid, affecting flow characteristics within the boundary layer.
Term: Reynolds Number
Definition:
A dimensionless number that helps predict flow patterns in different fluid flow situations, particularly in determining laminar or turbulent flow.