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HomeworkSolutions_C2

HomeworkSolutions_C2 - Problem#1 Based on the Cross model...

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Problem #1: Based on the Cross model, prove that 0 () m K η γ = ± 0 for and ηη ²³ 0 m K =+ ± 0 for: ³ Answer: 0 00 0 0 0 1( ) 11 ( ) ( ) For ( For ( m m m m m m m K K K K K K K ηη ηη ηγ ∞∞ −+− −− = ⇒= = = + ± ± ± ± ²² ± ± ² ± Problem #2: Show the distinct differences in the rheological properties of: - Newtonian fluids - Power law fluids - Bingham plastic fluids Answer: Newtonian Fluid Power Law Fluids Bingham plastic fluids Shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. The viscosity is independent on shear rate Apparent viscosity is dependent on shear rate. It can be an increasing function (shear thickening), or a decreasing function (shear thinning) of shear rate. Linear relationship between shear stress and rate of strain once threshold shear stress exceeded
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Problem #3: The total stress tensor is expressed in a matrix form as x xx yx z yx yy yz zx zy zz τ ττ ⎛⎞ ⎜⎟ = ⎝⎠ τ
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HomeworkSolutions_C2 - Problem#1 Based on the Cross model...

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