Quiz 6 – 2014.01.10 Quiz 7 – 2014.01.10
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Transcript of Quiz 6 – 2014.01.10 Quiz 7 – 2014.01.10
Quiz 6 – 2014.01.10Quiz 7 – 2014.01.10
Question (15 mins)A small capillary with an inside diameter of 2.22 10-3 m and a length 0.317 m is being used to continuously measure the flow rate of a liquid having a density of 875 kg/m3 and = 1.13 10-3 Pa s. The pressure drop reading across the capillary during flow ∙is 0.0655 m water (density 996 kg/m3). What is the flow rate in m3/s if the end-effect corrections are neglected? What is the Fanning friction factor for this capillary system?
TIME IS UP!!!
Instead of deriving new correlations for f, an approximation is developed for an equivalent diameter, Deq, which may be used to calculate NRe and f.
where RH = hydraulic radiusS = cross-sectional areaPw = wetted perimeter: sum of the length of the boundaries of the cross-section actually in contact with the fluid
4 4eq Hw
SD RP
Frictional Losses for Non-Circular Conduits
Determine the equivalent diameter of the following conduit types:
1.Annular space with outside diameter Do and inside diameter Di
2.Rectangular duct with sides a and b3.Open channels with liquid depth y and liquid
width b
4 4eq Hw
SD RP
Equivalent Diameter (Deq)
Non-Newtonian Fluids
Newtonian Fluids
water
ethyl alcohol
air
Non-Newtonian Fluids
blood
toothpasteketchup
Non-Newtonian Fluids
grease
cake batterpolymer melt
Non-Newtonian Fluids
molten metal
whipped cream
paint
• 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
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
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
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
Classification
Time-Independent Fluids
Time-Independent Fluids 1. Bingham plastics
h depends on a critical/yield shear stress (t0) and then becomes constant
Ex. sludge paint bloodketchup
Classification
Time-Independent Fluids 1. Bingham plastics
Classification
Time-Independent Fluids 2. Power law fluids
Classification
Time-Independent Fluids 2. Power law fluids
Pseudoplastic fluids : h decreases as the shear rate increases (shear rate thinning)
Ex. polymer melts paper pulp in water clay solutionsmolasseswhipped cream
Classification
Time-Independent Fluids 2. Power law fluids
Dilatant fluids : h decreases as the shear rate increases (shear rate thickening)
Ex. QuicksandStarch suspensionWet sand
Classification
Time-Dependent Fluids Shear rate depends on the shearing time or on the previous shear rate history
Classification
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 removedEx. gelatin
shorteningcream
Classification
Time-Dependent Fluids 2. Rheopectic fluids
: shear stress increases with time at constant shear rate; the apparent viscosity increases with time : the change is reversibleEx. highly concentrated starch solutions
gravybeating and thickening of egg whitesinks
Classification
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
Non-Newtonian Fluids
• For Newtonian fluids:
• For Non-Newtonian fluids:
where h is the apparent viscosity and is not constant for non-Newtonian fluids.
zrz
ddrt
Shear Stress Behavior
zrz
ddrt h
Modeling Power Law Fluids
where:K = flow consistency indexn = flow behavior index
Shear Stress Behavior
1n nz z z
rzdu du duK Kdr dr dr
t
eff
Shear Stress Behavior
Modelling Bingham Plastics
Shear Stress Behavior
0tt rz 0zdudr
(rigid)
0tt rz
0z
rzdudr
t t