Chp5_331

# Chp5_331 - 5 Fluid Kinematics As the fluid flows a fluid...

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5. Fluid Kinematics As the fluid flows, a fluid particle can be deformed, strained or rotated. 5.1. Dilatation - A u ( x ) ; B u ( x )+ u x x A v ( y ) ; C v ( y )+ v y y L x =( u B u A ) t = u x x t L x t = u x x L y =( v C v A ) t = v y y t L y t = v y y 46

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υ = x y .1 ; ∆υ =( x + L x )( y + L y )– x y 1 υ ∆υ t = 1 x y ( x + u x x t )( y + v y y t )– x y t lim t 0 1 υ ∆υ t = u x + v y = . V = div V For incompressible flow, the rate of volume dilatation is zero, . V = 0 . 5.2. Strain - angular deformation. A v ( x ) , B v ( x )+ v x x ; ∆η = v x x t t x v x η α α Δ Δ Δ ) tan(Δ Δ 47
A u ( y ) , C u ( y )+ u y y ; ∆ξ = u y y t t y u y Δ Δ Δ ) tan(Δ Δ ∆γ = ∆α + ∆β → ∆γ t = v x + u y ∂γ t = v x + u y y u x v t τ xy d d The shear stress is related to the rate of angular deformation through the fluid viscosity. 5.3. Rotation

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Chp5_331 - 5 Fluid Kinematics As the fluid flows a fluid...

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