How is shear stress related to shear rate in aerodynamic applications?

In summary, the conversation is about the relationship between shear stress and shear rate in aerodynamics. The first question is asking for a molecular explanation of why they are proportional, and the second question is about computing the velocity gradient on the surface of an aircraft. The source suggests reading chapter 1 of Bird, Stewart, and Lightfoot's book "Transport Phenomena" for a quantitative explanation.
  • #1
MaxKang
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Hello everyone,

I came across this in J. Anderson's book "Fundamentals of Aerodynamics".

"For the type of gases and liquids of interest in aerodynamic applications, the value of the shear stress at a point on a streamline is proportional to the spatial rate of change of velocity normal to the streamline at that point"

1. I am aware that air is a type of Newtonian fluid where its dynamic viscosity remains constant. Could someone why the magnitude of shear stress happen to be proportional to that of the shear rate(or Velocity Gradient)? A lot of books and Youtube videos merely say this is experimental and do not quite explain why this is the case.

2. I also read "Conventional boundary layer analysis assumes that the flow conditions at the outer edge of the boundary layer are the same as the surface flow conditions from an inviscid flow analysis" so in order to find the flow velocity at the outer edge of the boundary layer, I would assume the flow is inviscid and use the velocity right on the surface for the outer edge velocity. My question is, then how do I go about computing the velocity gradient(dv/dy) right on the surface? The velocity gradient on the surface of an aircraft is not linear unlike the Couette flow so I don't think I can use the the speed at the outer edge of the boundary layer(right adjacent to free stream) to find the theoretical value of the shear stress.
I would like to know how it's done for temperature as well.

Thank you!
 
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  • #2
Can you please break this down into several threads. There are too many questions here to answer all in one place.

I will answer your first question, however. If you are asking for a quantitative molecular explanation of why the shear stress is proportional to the shear rate, see chapter 1 of Bird, Stewart, and Lightfoot, Transport Phenomena.
 
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  • #3
Chestermiller said:
Can you please break this down into several threads. There are too many questions here to answer all in one place.

I will answer your first question, however. If you are asking for a quantitative molecular explanation of why the shear stress is proportional to the shear rate, see chapter 1 of Bird, Stewart, and Lightfoot, Transport Phenomena.
Thank you so much! I will read up on it :)
 

1. What is shear stress on a moving body?

Shear stress on a moving body is the force per unit area that is applied to a body as it moves through a fluid or gas. This force is perpendicular to the direction of the body's motion and is caused by the fluid or gas exerting frictional drag on the body's surface.

2. How is shear stress calculated?

Shear stress can be calculated by dividing the force of the fluid or gas on the body by the area of the body that is in contact with the fluid or gas. It is typically measured in units of Newtons per square meter (N/m²) or Pascals (Pa).

3. What are the effects of shear stress on a moving body?

Shear stress can have both positive and negative effects on a moving body. On one hand, it can help reduce drag and improve the body's motion through the fluid or gas. However, if the shear stress is too high, it can cause damage to the body's surface and decrease its performance.

4. How can shear stress be reduced on a moving body?

There are several ways to reduce shear stress on a moving body, including changing the body's shape to reduce drag, adding a lubricating layer to the body's surface, or adjusting the fluid or gas properties (such as viscosity) to decrease friction. In some cases, shear stress can also be reduced by adjusting the body's speed or direction of motion.

5. What real-world applications involve shear stress on a moving body?

Shear stress on a moving body is an important concept in many fields, including aerodynamics, hydrodynamics, and biomechanics. It is relevant in the design of airplanes, ships, and other vehicles, as well as in understanding the movement of fluids through pipes and channels. In the human body, shear stress plays a role in blood flow and can impact the functioning of cells and tissues.

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