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Published byMalia Capps Modified about 1 year ago

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Quiz 6 – Quiz 7 –

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Question (15 mins) A small capillary with an inside diameter of 2.22 m and a length m is being used to continuously measure the flow rate of a liquid having a density of 875 kg/m 3 and = 1.13 Pa∙s. The pressure drop reading across the capillary during flow is m water (density 996 kg/m 3 ). What is the flow rate in m 3 /s if the end-effect corrections are neglected? What is the Fanning friction factor for this capillary system? TIME IS UP!!!

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Instead of deriving new correlations for f, an approximation is developed for an equivalent diameter, D eq, which may be used to calculate N Re and f. where R H = hydraulic radius S = cross-sectional area P w = wetted perimeter: sum of the length of the boundaries of the cross-section actually in contact with the fluid Frictional Losses for Non-Circular Conduits

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Determine the equivalent diameter of the following conduit types: 1.Annular space with outside diameter D o and inside diameter D i 2.Rectangular duct with sides a and b 3.Open channels with liquid depth y and liquid width b Equivalent Diameter (D eq )

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Non-Newtonian Fluids

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Newtonian Fluids water ethyl alcohol air

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Non-Newtonian Fluids blood toothpaste ketchup

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Non-Newtonian Fluids grease cake batter polymer melt

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Non-Newtonian Fluids molten metal whipped cream paint

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Foods – Emulsions (mayonnaise, ice cream) – Foams (ice cream, whipped cream) – Suspensions (mustard, chocolate) – Gels (cheese) Biofluids – Suspension (blood) – Gel (mucin) – Solutions (spittle) Personal Care Products – Suspensions (nail polish, face scrubs) – Solutions/Gels (shampoos, conditioners) – Foams (shaving cream) Non-Newtonian Fluids Electronic and Optical Materials – Liquid Crystals (monitor displays) – Melts (soldering paste) Pharmaceuticals – Gels (creams, particle precursors) – Emulsions (creams) – Aerosols (nasal sprays) Polymers

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Why are these fluids non-Newtonian? Non-Newtonian behavior is frequently associated with complex internal structure: The fluid may have large complex molecules (like a polymer), or The fluid may be a heterogeneous solution (like a suspension)... Non-Newtonian Fluids

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Why are these fluids non-Newtonian? Fluid systems may be non-ideal in two ways: 1.The viscosity may depend on shear rate 2.The viscosity may depend on time Some (many) may have both Non-Newtonian Fluids

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Time-Independent Fluids The relation between shearing stress and rate is unique but non-linear The viscosity of the fluid at a given temperature depends on the rate of shearing Classification

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Time-Independent Fluids

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1.Bingham plastics depends on a critical/yield shear stress ( 0 ) and then becomes constant Ex. sludge paint blood ketchup Classification

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Time-Independent Fluids 1.Bingham plastics Classification

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Time-Independent Fluids 2.Power law fluids Classification

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Time-Independent Fluids 2.Power law fluids Pseudoplastic fluids : decreases as the shear rate increases (shear rate thinning) Ex. polymer melts paper pulp in water clay solutions molasses whipped cream Classification

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Time-Independent Fluids 2.Power law fluids Dilatant fluids : decreases as the shear rate increases (shear rate thickening) Ex.Quicksand Starch suspension Wet sand Classification

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Time-Dependent Fluids Shear rate depends on the shearing time or on the previous shear rate history Classification

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Time-Dependent Fluids 1.Thixotropic fluids : shear stress decreases with time at constant shear rate; alternatively, the apparent viscosity decreases with time : the change is reversible; the fluid “rebuilds” itself once shearing is removed Ex. gelatin shortening cream Classification

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Time-Dependent Fluids 2.Rheopectic fluids : shear stress increases with time at constant shear rate; the apparent viscosity increases with time : the change is reversible Ex. highly concentrated starch solutions gravy beating and thickening of egg whites inks Classification

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Viscoelastic Fluids The shear stress is determined by the shear strain and the rate of shear strain when applied stress is removed, the material does not instantly vanish since the internal structure of the material can sustain the stress for some time (relaxation time) due to the internal stress, the fluid will deform on its own, even when external stresses are removed Classification

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Non-Newtonian Fluids For Newtonian fluids: For Non-Newtonian fluids: where is the apparent viscosity and is not constant for non-Newtonian fluids. Shear Stress Behavior

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Modeling Power Law Fluids where: K = flow consistency index n = flow behavior index Shear Stress Behavior

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Modelling Bingham Plastics Shear Stress Behavior (rigid)

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