Laminar to turbulent flow transition?

[BlueCB]

Homework Statement

Consider the flow of air over an aerofoil.
The critical Reynolds number marking the transition from laminar to turbulent flow is 6 x 10^5, the dynamic viscosity is 2.0 x 10^-5 Ns/m^2, the density of air is 1.100 kg/m^3 and the aircraft velocity is 180 m/s.
What is the length of the region of laminar flow?

Homework Equations

Ellaminar = 0.06 Re

where

Re = Reynolds Number

The Attempt at a Solution

Re = Ro x u x X / μ
X = 0.06 m = 6 cm

 

[Chestermiller]

The formula you gave for laminar-turbulent transition is for flow in a pipe. For flow over an airfoil, the distance parameter in the reynolds number is the distance measured from the leading edge. They already told you in the problem statement that the laminar-turbulent transition occurs at Re = 6E5. So, solve for the distance x.

 

[BlueCB]

Ah, that's completely baffled me now.

Would you happen to know the formula applicable to aerofoils?

 

[Chestermiller]

Ah, that's completely baffled me now.

Would you happen to know the formula applicable to aerofoils?

They already gave it to you. Re_X=5E5

 

[BlueCB]

So what, Reynolds number*length = 6*10^5?

How does that make any sense?
Where does density, dynamic viscosity and velocity come into the equation?

I used an online Reynolds number calculator and used the inputs of the initial question in the formula: p*u*L / µ
For (L) I changed the input until the Reynolds number equaled 600,000
(p = 1.1), (v = 180), (L = 0.060606) and (µ = 2*10^-5).

So for the Reynolds number to be 6*10^5, the length of the region of laminar flow must be 0.60606?

Is that correct?

 

[Chestermiller]

So what, Reynolds number*length = 6*10^5?

I used an online Reynolds number calculator and used the inputs of the initial question in the formula: p*u*L / µ
For (L) I changed the input until the Reynolds number equaled 600,000
(p = 1.1), (v = 180), (L = 0.060606) and (µ = 2*10^-5).

So for the Reynolds number to be 6*10^5, the length of the region of laminar flow must be 0.60606?

Is that correct?

Yes. Now you have the right idea. Of course, you didn't have to do it by trial and error. You could have solved algebraically for L. I haven't checked your units, but, if they are correct, please express L with units.
That is all there really is to this problem. Your teacher wanted to see if you knew how to calculate the transition length L from knowledge of the velocity and the physical properties.