Boundary Layer displacement thickness

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SUMMARY

The discussion centers on the calculation of boundary layer displacement thickness, denoted as δ*, for flow over a plate of length 4 meters. The formula provided for δ* is δ* = ∫(1 - u/U) dy, where u is the velocity within the boundary layer and U is the free stream velocity. The user seeks assistance in deriving the equation of the streamline y = y(x) that intersects the boundary layer at x = 4 meters, where y = δ^b. Clarification on the mathematical implications of δ = δ^b is also requested.

PREREQUISITES
  • Understanding of boundary layer theory
  • Familiarity with integral calculus
  • Knowledge of fluid dynamics, specifically flow over flat plates
  • Experience with streamline equations in fluid mechanics
NEXT STEPS
  • Study the derivation of boundary layer equations in fluid dynamics
  • Learn about the implications of displacement thickness in boundary layer flow
  • Research streamline equations and their applications in boundary layer analysis
  • Explore numerical methods for calculating boundary layer characteristics
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Fluid mechanics students, engineers working on aerodynamic designs, and researchers focused on boundary layer analysis will benefit from this discussion.

VooDoo
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Hey guys,


The streamlines just outside a boundary layer are pushed away from the wall by the displacement thickness \delta* and I understand that;

\delta*=\int^{\infty}_{0}(1-\frac{u}{U})dy

Now this is for flow over a plate with length x=4m. At x=0 is the leading edge and at x=4 \delta = \delta^{b}

Now been told to find the equation of the streamline i.e. y=y(x) that touches the boundary layer at x=4 (and y = \delta^{b} I guess).

I know I have to calculate the boundary layer displacement thickness...but I am unsure of how to do that and what I should do after that.
 
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delta = delta ^ b is a mathematical inequality? Therefore if you rewrite the problem literally from your homework a bit more clearly I might be able to help you with this one.
 

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