Calculating Surface Shear Stress in a Boundary Layer with Given Velocity Profile

[exphaze]

Homework Statement

If the velocity v of the air in a boundary layer having a dynamic viscosity of
18x10^-6 kg/ms is given in terms of the distance y from the surface by v = ay + by²

where a and b are constants, calculate the surface shear stress if at 1.5 mm from the surface the velocity is 75 m/s, and at 3.0 mm from the surface it is 105 m/s.

Homework Equations

τ = μ(du/dy)

The Attempt at a Solution

 

[Chestermiller]

What have you figured out so far?

 

[exphaze]

What have you figured out so far?

I have tried the differences of the velocities and distance (du/dy) . Then multiplied it by the dynamic viscosity which came out as 0.36 N/m^2 but the answer is apparently 1.17 N/m^2.

 

[Chestermiller]

I have tried the differences of the velocities and distance (du/dy) . Then multiplied it by the dynamic viscosity which came out as 0.36 N/m^2 but the answer is apparently 1.17 N/m^2.

You need to solve for a and b from the velocity data; a is the shear rate at the wall.

 

[exphaze]

You need to solve for a and b from the velocity data; a is the shear rate at the wall.

I have worked out a = 50000 and substituted to τ*shear rate =μ and this came out as 0.9 N/m^2. I am still stuck.

 

[Chestermiller]

I have worked out a = 50000 and substituted to τ*shear rate =μ and this came out as 0.9 N/m^2. I am still stuck.

I get a = 65000/sec

 

[exphaze]

I get a = 65000/sec

I got it now, Thanks for the advice!

 

[alimoheb]

Hello
I have the same issue, but unfortunately I can't solve it.
any hind please?