How to Approach the Prandtl Boundary Layer Equation for Steady Laminar Flow?

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SUMMARY

The discussion focuses on the Prandtl Boundary Layer Equation in the context of steady laminar flow. It emphasizes that the Bernoulli equation is applicable only in inviscid flow conditions, where boundary layers do not exist. The key takeaway is that while Bernoulli's principle can be used in the free stream away from the boundary, it cannot be applied within the boundary layer itself. Understanding this distinction is crucial for correctly analyzing fluid flow in boundary layer theory.

PREREQUISITES
  • Understanding of the Prandtl Boundary Layer Equation
  • Familiarity with steady laminar flow concepts
  • Knowledge of Bernoulli's equation and its limitations
  • Basic principles of fluid dynamics
NEXT STEPS
  • Study the derivation and applications of the Prandtl Boundary Layer Equation
  • Learn about the characteristics of steady laminar flow in fluid dynamics
  • Explore the limitations and proper applications of Bernoulli's equation
  • Investigate boundary layer theory and its implications in engineering
USEFUL FOR

Students and professionals in fluid dynamics, mechanical engineers, and anyone involved in analyzing laminar flow and boundary layer phenomena.

sakif
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Homework Statement
Prove the following statement
Relevant Equations
Prandtl boundary layer equation for a two dimensional steady laminar flow of incompressible fluid over a semi infinite plate
I have tried to approach in the following way
IMG_20230120_052745.jpg

IMG_20230120_052751.jpg


I am stuck. How should I approach this next.please help
 

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I see you try to use the Bernoulli equation. But that is never going to work since that equation is only valid for inviscid flow. And in an inviscid flow no boundary layer can exist.
 
Arjan82 said:
I see you try to use the Bernoulli equation. But that is never going to work since that equation is only valid for inviscid flow. And in an inviscid flow no boundary layer can exist.
Far from the boundary, in the free stream, it is valid to use the Bernoulli equation. That's what boundary layer theory is all about.
 

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