What is the Relationship Between Shear Stress and Density for Fluids?

[womfalcs3]

Homework Statement

I have an empirically-derived equation for the shear stress of a fluid on a surface, given by the equation below.

I am supposed to take the derivative of density with respect to distance, and I must use this equation to find an expression for density.

Delta = Boundary layer thickness.
Nu = Kinematic Viscosity
u = Velocity
Rho = Density

Homework Equations

The Attempt at a Solution

I know the definition of shear stress for fluids (The second equation above). I've tried to equate it to the empirical formula, knowing that dynamic viscosity, mu, is just density*kinematic viscosity.

The density variables cancel though.

I can't have a tau term in the density expression, so I can't just algebraically manipulate the first equation to equal density.

 

[Delphi51]

I don't know anything about this topic, but it appears you have
sheer stress = a(b/u)^4 = c*du/dy and want to find the formula relating u and y.
I'm using a, b, c to save wear and tear on the keyboard.
If so, you can write it as a/c*b^.25*dy = u^.25*du
Integration yields a/c*b^.25*y = u^1.25 + D

 

[womfalcs3]

Thanks, but that's not what I'm looking for.

I need to take the derivative of density with respect to y, and I need to use the shear stress to take the derivative. So I need to find a relationship between density and stress.

I've tried using the Newtonian definition suggested by Stokes. I tried using Reynolds Number to relate density and velocity, so that I can use the velocity relation to find an expression of density in terms of shear stress, but no luck.