pressure and temperature. In general, gases are highly compressible and liquids
have a very low compressibility. Part one : Introduction of Compressible Flow. 1 ...
1. Introduction to Laminar Boundary Layer. Q1. Choose the correct answer. (i). If x
is the distance measured from the leading edge of a flat plate, the laminar.
Oct 6, 2002 ... that the brakes have to deal with about twice the power of what the engine ..... A
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1: User's guide. Minerals Management ...... 19, 609-615. Wang, S. and B.A. ...... Alpert, P., A. Cohen, J. Neuman and E. Doro,, 1982. A model simulation of the ...
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2- Momentum equation for boundary layer. 3- Laminar boundary layer. 4-
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..... best-known is Hermann Schlichting's Boundary-Layer Theory.7. Schlichting
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Boundary Layer Theory ... 6) Exact calculation of the Boundary layer thickness
...... (see also : Schlichting, H. , Gersten, K. (2006): Grenzschicht - Theorie, ...
1. Flat Plate (No Pressure Gradient). Boundary layer properties for laminar and
turbulent flows are summarized in this section, o. U i. Laminar Boundary Layer. 2.
Jan 15, 2009 - where ReL is the Reynolds number of the plate based on the length of the plate in the streamwise direction. Even though the variation of cf with ...
A more precise criterion for the existence of a well-defined laminar boundary
layer is that the Reynolds number should be large, though not so large as to
imply a ...
... differences in the atmospheric pressure When a difference in atmospheric pressure exists air moves from the higher t
... documented facts about global warming Learn about greenhouse gases global temperatures causes and effects politics a
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a) Hydrostatic b) Hydrodynamic c) Aeropowered Lift. 4. Its function/mission a)
Transport. • Tanker. • Bulk Carrier. • Containership. • Passenger ship. • General ...
Fax: +46 18 551124. Email: [email protected]. 2) Dept. of Wind Energy and Atm. Physics, Risø Nat. Lab., P.O. 49, DK-4000 Roskilde, Denmark.
shear-driven, since the wind stress at the surface is the primary .... Wind-driven current in the OML also ..... mous effort has gone into parameterizing ta in terms of.
Chapter 1 : Boundary Layer. Shear stress, τ y u. ∂. ∂. = µ τ. Reynolds number.
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Chapter 1 : Boundary Layer
INTRODUCTION The condition of zero fluid velocity at the solid surface is referred to as ‘no slip’ and the layer of fluid between the surface and the free stream fluid is termed BOUNDARY LAYER.
1
Chapter 1 : Boundary Layer
2
Chapter 1 : Boundary Layer
Shear stress,
τ
∂u τ =µ ∂y Reynolds number The criterion which determines whether flow is laminar or turbulent. Reynolds number along a smooth flat plate:
ρU s x U s x Re x = = µ υ Re < 5 x 105 : Laminar Re ≈ 5 x 105 : Transition (Engineering critical Reynolds number) Re > 5 x 105 : Turbulent 3
Chapter 1 : Boundary Layer
4
Chapter 1 : Boundary Layer
Turbulent layer usually has a greater velocity gradient at the surface, which cause greater shear stress. From a turbulent layer, there is a more ready interchange of particles with the main flow, and this explains the more rapid increase in thickness of a turbulent layer. The thickness of a laminar boundary layer increases as x0.5 (when pressure is uniform), a turbulent layer thickens approximately as x0.8.
5
Chapter 1 : Boundary Layer
BOUNDARY LAYER IN PIPE
Laminar flow; Re < 2000 120 pipe diameters (=120D) Turbulent flow; Re > 2000 60 pipe diameters (=60D)
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Chapter 1 : Boundary Layer
DEFINITION z Boundary layer thickness, δ z Displacement thickness, δ* z Momentum thickness, θ BOUNDARY LAYER THICKNESS, δ
Boundary layer thickness is defined as that distance from the surface where the local velocity equals 99% of the free stream velocity.
δ = y(u =0.99U ) s
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Chapter 1 : Boundary Layer
DISPLACEMENT THICKNESS, δ*
The displacement thickness for the boundary layer is defined as the distance the surface would have to move in the y-direction to reduce the flow passing by a volume equivalent to the real effect of the boundary layer.
δ =∫ *
δ
0
u (1 − )dy Us
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Chapter 1 : Boundary Layer
MOMENTUM THICKNESS θ Momentum thickness is the distance that, when multiplied by the square of the free stream velocity, equals the integral of the momentum defect. Alternatively, the total loss of momentum flux is equivalent to the removal of momentum through a distance θ. It is a theoretical length scale to quantify the effects of fluid viscosity near a physical boundary.
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