Boundary Layer Thickness

Boundary Layer Thickness

We define the thickness of the boundary layer as the distance from the wall to the point where the velocity is 99% of the “free stream” velocity. For laminar boundary layers over a flat plate, the Blasius solution of the flow governing equations gives:

Boundary Layer Thickness - laminar

where Rex is the Reynolds number based on the length of the plate.

For a turbulent flow the boundary layer thickness is given by:

Boundary Layer Thickness -turbulent

This equation was derived with several assumptions. The turbulent boundary layer thickness formula assumes that the flow is turbulent right from the start of the boundary layer.

Boundary layer on flat plate

Example: Boundary Layer Thickness

Consider a water flow (20°C) at v =  0.1 m/s past a flat plate 1 m long. Compute the boundary layer thickness in the middle of the plate. Assume that kinematic viscosity of water at 20°C is equal to 1×10-6 m2/s.

The Reynolds number for the middle of the plate is equal to:

ReL/2 = 0.1 [m/s] x 0.5 [m] / 1×10-6 [m2/s] = 50 000

This satisfies the laminar conditions. The boundary layer thickness is therefore equal to:

δ ≈ 5.0 x 0.5 / (50 000)½ = 0.011 m

 
Example: Transition Layer
A long thin flat plate is placed parallel to a 1 m/s stream of water at 20°C. Assume that kinematic viscosity of water at 20°C is equal to 1×10-6 m2/s.

At what distance x from the leading edge will be the transition from laminar to turbulent boundary layer (i.e. find Rex ~ 500,000).

Solution:

In order to locate the transition from laminar to turbulent boundary layer, we have to find x at which Rex ~ 500,000.

x = 500 000 x 1×10-6 [m2/s] / 1 [m/s] = 0.5 m

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Boundary Layer