Boundary layer theory 4
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This document discusses boundary layer theory and provides formulas to calculate boundary layer thickness, shear stress, and coefficient of drag based on Reynolds number for laminar boundary layer flows. It presents the velocity profile equation and uses it along with Newton's law of viscosity and the momentum integral equation to derive expressions for boundary layer thickness in terms of Reynolds number, shear stress in terms of Reynolds number, and coefficient of drag in terms of Reynolds number.
Boundary layer theory 4
- 1. FLUID MECHANICS BOUNDARY LAYER THEORY LECTURE-04 CONTENTS:- Numerical Based on Momentum Integral Equation PROF. SANJEEV GUPTA
- 2. QUESTION For the velocity profile the laminar boundary layer flows given as 𝒖 𝑼 = 𝟐 𝒚 𝜹 − 𝒚 𝜹 2 Find an expression for boundary layer thickness (δ), shear stress (τo ) and coefficient of drag (CD ) in terms of Reynolds number
- 3. Formula Used Find- (1) Expression for boundary layer thickness (δ) (2) Shear stress (τo ) (3) Co-efficient of drag (CD ) in terms of Reynolds number (5) (2) (3) (4) (1) (6)
- 4. Substituting the value of (u/U) in equation (1)
- 5. According to Newtons Law of Viscosity From given velocity distribution equation
- 6. As the boundary layer thickness (δ) is a function of x only. Hence partial derivative can be changed to total derivative.
- 7. (ii) Shear stress (τo ) in terms of Reynolds Number