Conservation of energy First law of thermodynamics 4 2nd law of thermodynamics

# Conservation of energy first law of thermodynamics 4

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Conservation of energy (First law of thermodynamics) 4. 2nd law of thermodynamics 5. Equation of state ρ = ρ (p,T) Unknowns ρ ,u,v,w,p,T,s Æ total number of equations ? VISCOSITY Density : measure of the “heaviness” of a fluid. Viscosity ( μ ) : measure of the “fluidity” of a fluid. F orce, δ F x Velocity, δ u No slip B C A A’ D D’ δ l δ y No slip y x e.g. water & oil approx. have same density but behave differently when flowing Fluid element at time, t : ABCD Fluid element at time, t + δ t : A’BCD’ δα •ability of a fluid to flow freely N N direction plane that stress acts acts on y x τ 0 lim x x yx Ay y y F dF A dA δ δ τ δ = = y A δ : area of fluid element in contact with the plate 0 Deformation rate = lim For small , tan t d t dt l u t l l y u t y u d du t y dt dy δ δα α δ δ δ δ δ δα δα δα δ δαδ δ δ δ δα δ α δ δ = = = = = = = Subject to shear stress, yx τ fluid experiences a time rate of deformation (shear rate) as du/dy 