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Lecture 16 Viscous Flow

# Lecture 16 Viscous Flow - Thermal and Fluids Engineering I...

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Lecture 16 – Viscous Flow Viscosity In the Bernoulli equation, viscous forces are assumed negligible. We now turn to cases in which viscous forces caused by internal friction within the fluid are important. Consider two parallel plates containing a fluid. The top plate is moving relative to the bottom plate and the gap, b , is small. Consider a differential volume of fluid There are also pressure forces on the front and back faces (not shown) Lecture 16 Page 1

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Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Forces are due to - pressure - gravity - friction The tangential force, , is due to fluid friction. Shear stress is defined as t F G t F A τ = G G Solid under a shear stress Fluid under a shear stress - finite deformation - deforms continuously By experiment: tw w F A b =∝ G G G V This is true for Newtonian fluids like air, water, oil, etc. Paint and ketchup are non-Newtonian Lecture 16 Page 2
Thermal and Fluids Engineering I Prof. Deborah A. Kaminski Define dynamic viscosity so that w w b τµ = V () w x y y b = x x w d dy τ µτ == In general, x is a function of y , but for this linear velocity profile, the shear stress is the same everywhere. The shear stress in the x -direction for any velocity profile is given by x x d dy = Viscosity is a thermophysical property like thermal conductivity or emissivity. In general, viscosity depends on temperature.

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Lecture 16 Viscous Flow - Thermal and Fluids Engineering I...

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