Laminar to turbulent flow transition?

In summary, the laminar-turbulent transition occurs at Re = 6E5, and the length of the region of laminar flow is 0.60606 meters.
  • #1
BlueCB
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0

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
 
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  • #2
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.
 
  • #3
Ah, that's completely baffled me now.

Would you happen to know the formula applicable to aerofoils?
 
  • #4
BlueCB said:
Ah, that's completely baffled me now.

Would you happen to know the formula applicable to aerofoils?
They already gave it to you. ReX=5E5
 
  • #5
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?
 
  • #6
BlueCB said:
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.
 
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1. What is the difference between laminar and turbulent flow?

Laminar flow is characterized by smooth and orderly movement of fluid particles in the same direction, while turbulent flow is characterized by chaotic and irregular movement of fluid particles in various directions.

2. How does flow velocity affect the transition from laminar to turbulent flow?

As the flow velocity increases, the likelihood of transition from laminar to turbulent flow also increases. This is because higher velocities result in greater shear forces, causing the fluid to become more turbulent.

3. What factors influence the transition from laminar to turbulent flow?

The main factors that influence the transition from laminar to turbulent flow include flow velocity, fluid viscosity, surface roughness, and the presence of disturbances such as obstacles or changes in geometry.

4. What is the Reynolds number and how does it relate to the transition from laminar to turbulent flow?

The Reynolds number is a dimensionless parameter that represents the ratio of inertial forces to viscous forces in a fluid. When the Reynolds number exceeds a critical value, the flow is more likely to transition from laminar to turbulent.

5. How is the transition from laminar to turbulent flow important in practical applications?

The transition from laminar to turbulent flow has implications in various engineering and scientific fields such as aerodynamics, fluid mechanics, and heat transfer. Understanding and predicting this transition is crucial for designing efficient and safe systems, as turbulent flows can cause increased drag, energy losses, and structural damage.

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