Please help me with the attached problems. I also attached slides that could help.

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Chapter 6 Rheology of Fluids 1. Viscosity 2. Types of fluids 3. Factors affecting viscosity 4. Measurement of viscosity

Fluidity and Viscosity • Concentration • Temperature • Solute and solvent • Structure and size of solute molecules

Liquid flows in a pipe Velocity v v v

1. Viscosity Definition: resistance to flow. F F ?L Fluid Fluid Layers ?l X ? x Velocity gradient F = shear force (N), v = velocity (m/s), x = fluid thickness (m), L = distance (m).

Viscosity F ?dv and F ? 1 dx ? FA ? dv dx or by introducing a coefficient?, FA =? · dv dx t = FA =? · A· dv dx A =? · dv dx let ?? = dv dx , t =??? and ? = t?? F = shear force (N), v = velocity (m/s), x = fluid thickness (m), A = area of the plate (m2), t = shear stress (Pa), ? ? = shear rate (s-1), and ? = viscosity (Pa·s)

Viscosity (represented by the symbol ? “eta”) is the ratio of the shearing stress (F/A) to the velocity gradient (?v/?x or dv/dx) in a fluid. The more usual form of this relationship, called Newton’s equation, states that the resultPlease help me with the attached problems. I also attached slides that could help.

Document Preview:

Chapter 6 Rheology of Fluids 1. Viscosity 2. Types of fluids 3. Factors affecting viscosity 4. Measurement of viscosity

Fluidity and Viscosity • Concentration • Temperature • Solute and solvent • Structure and size of solute molecules

Liquid flows in a pipe Velocity v v v

1. Viscosity Definition: resistance to flow. F F ?L Fluid Fluid Layers ?l X ? x Velocity gradient F = shear force (N), v = velocity (m/s), x = fluid thickness (m), L = distance (m).

Viscosity F ?dv and F ? 1 dx ? FA ? dv dx or by introducing a coefficient?, FA =? · dv dx t = FA =? · A· dv dx A =? · dv dx let ?? = dv dx , t =??? and ? = t?? F = shear force (N), v = velocity (m/s), x = fluid thickness (m), A = area of the plate (m2), t = shear stress (Pa), ? ? = shear rate (s-1), and ? = viscosity (Pa·s)

Viscosity (represented by the symbol ? “eta”) is the ratio of the shearing stress (F/A) to the velocity gradient (?v/?x or dv/dx) in a fluid. The more usual form of this relationship, called Newton’s equation, states that the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton’s second law of motion (F = ma) should be apparent. ? = FA ?v ?x or ? = FA dv dx = t?? dt vs F m dv dx dv AF =? . =

Viscosity ? ? t a dl dx ?? ??? ?1 dt t a ?? or t =? ?? ? = t?? slope= viscosity, ? (Pa.s) Shear stress (Pa) Shear rate (s-1) Newtonian (ideal) fluid

Ø? Absolute (dynamic) viscosity SI unit: Pa·s, mPa·s CGS unit: Poise (dyne·s/cm2, or g/cm·s) (P), centipoise (cP) 1 mPa·s = 1 cP = 0.01 P Ø? Kinematic viscosity ? ? ? = ? = t?? Unit: m2/s, cm2/s (Stokes), mm2/s (centistokes) Unit of Viscosity

simple liquids T (ºC) ? (mPa·s) alcohol, ethyl (grain) 20 1.1 alcohol, isopropyl 20 2.4 alcohol, methyl (wood) 20 0.59 blood 37 3 -4 ethylene glycol 25 16.1 ethylene glycol 100 1.98 freon 11 (propellant) -25 0.74 freon 11 (propellant) 0 0.54 freon 11 (propellant) +25 0.42 freon 12 (refrigerant) +15 0.20 glycerin 20 1420…

Attachments:ing shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. The similarity to Newton’s second law of motion (F = ma) should be apparent. ? = FA ?v ?x or ? = FA dv dx = t?? dt vs F m dv dx dv AF =? . =

Viscosity ? ? t a dl dx ?? ??? ?1 dt t a ?? or t =? ?? ? = t?? slope= viscosity, ? (Pa.s) Shear stress (Pa) Shear rate (s-1) Newtonian (ideal) fluid

Ø? Absolute (dynamic) viscosity SI unit: Pa·s, mPa·s CGS unit: Poise (dyne·s/cm2, or g/cm·s) (P), centipoise (cP) 1 mPa·s = 1 cP = 0.01 P Ø? Kinematic viscosity ? ? ? = ? = t?? Unit: m2/s, cm2/s (Stokes), mm2/s (centistokes) Unit of Viscosity

simple liquids T (ºC) ? (mPa·s) alcohol, ethyl (grain) 20 1.1 alcohol, isopropyl 20 2.4 alcohol, methyl (wood) 20 0.59 blood 37 3 -4 ethylene glycol 25 16.1 ethylene glycol 100 1.98 freon 11 (propellant) -25 0.74 freon 11 (propellant) 0 0.54 freon 11 (propellant) +25 0.42 freon 12 (refrigerant) +15 0.20 glycerin 20 1420…

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