Fluid Mechanics: With Problems and Solutions, and an by Prof. Dr. Egon Krause (auth.)

By Prof. Dr. Egon Krause (auth.)

Despite dramatic advances in numerical and experimental equipment of fluid mechanics, the basics are nonetheless the place to begin for fixing stream difficulties. This textbook introduces the main branches of fluid mechanics of incompressible and compressible media, the fundamental legislation governing their stream, and gasdynamics. "Fluid Mechanics" demonstrates how flows could be categorized and the way particular engineering difficulties could be pointed out, formulated and solved, utilizing the tools of utilized arithmetic. the cloth is elaborated in detailed purposes sections through greater than 2 hundred routines and individually indexed options. the ultimate part contains the Aerodynamics Laboratory, an creation to experimental equipment treating 11 movement experiments. This class-tested textbook bargains a special mixture of advent to the most important basics, many routines, and a close description of experiments.

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Additional info for Fluid Mechanics: With Problems and Solutions, and an Aerodynamic Laboratory

Example text

89) The circulation is equal to twice the value of the flux of vorticity through the surface spanned over a closed curve (Stokes’ theorem). In an incompressible, inviscid flow the circulation does not change, if the volume forces possess a potential U . 91) are introduced with the volume forces assumed to possess a potential g = ∇ U . There results dΓ = dt d C U− p v2 + ρ 2 For an inviscid flow (ν = 0) it follows that for all times (Thomson’s theorem). dΓ dt +ν C ∇2 v · ds . 92) = 0. 2 Vorticity Transport Equation For incompressible flow the components of the vorticity vector ω can easily be introduced in the conservation equations for mass and momentum.

For two-dimensional flows, instead of the potential a scalar function Ψ , the stream function, can be introduced. It satisfies the continuity equation identically. It has to be determined with the condition of irrotationality. 104) ∂x ∂y is satisfied. 105) ∂x ∂y leads to the Laplace equation for the stream function. 106) The differential equation for the streamline follows from the total differential ∂Ψ ∂Ψ dx + dy = −v dx + u dy dΨ = ∂x ∂y with Ψ = const. v dy . 108) Hence streamlines are given by lines Ψ (x,y) = const.

The turbulent shear stress vanishes at the wall, as the velocity fluctuations have to vanish there because of Stokes’ no-slip condition. The mixing length l therefore has also to vanish in the vicinity of the wall. 153) . In the above equation k is a constant. 152). 152), the universal law of the wall for turbulent pipe flow is obtained y u∗ u¯ 1 +C = ln u∗ k ν . 4 is named after von K´arm´an; k and C were determined from experiments. 5. 28 1. Fluid Mechanics I The logarithmic form of the universal law of the wall shows, that it looses its validity in the immediate vicinity of the wall.

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