# Aerospace Shear stress on a moving body

1. Oct 16, 2016

### MaxKang

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!

2. Oct 17, 2016

### Staff: Mentor

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.

3. Oct 17, 2016

### MaxKang

Thank you so much! I will read up on it :)