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LECTURE UNIT NO. 2 8. Absolute Viscosity or Coefficient of Viscosity or Dynamic Viscosity or simply “Viscosity” - Measures of the sluggishness with which a fluid flows. When the viscosity is low, indicative of a “thin” fluid like water, the fluid flows easily. Conversely, the “thickest” fluids, such as certain types of oil, are the most viscous and do not flow easily.Mathematical Definition of Viscosity ν F ν ν Moving Plate P dν H dy Velocity Profile Stationary Plate Slope = _dν_ = _ν_ = velocity gradient dy HBy experiment, force F is proportional to the plate area A and to the slope of the velocity profile. F α A ν_ HThe constant of proportionality is called the absolute viscosity, μ F = μν A HF/A is the shear stress developed in the fluid and acting on the bottom surface of the moving plate. μ = _ τ__ For two closely parallel plates, velocity gradient ν/H is constant μ = _ τ __ For non constant velocity gradient dν/dyUnits of Absolute viscosity Eng’g Units: lbf_-sec ft2 SI Units: N – s or Pa-s or Poise, P m2 Note: 1 poise = 100 cP 1 poise = 1 dyne-s/cm2 = 0.1 Pa - s where: 105 dynes = 1 NKinematic Viscosity - Ratio of absolute viscosity to mass density of fluid ν = _μ_ ρ Eng’g Units: ft2/sec SI Units: m2/s Note: 1 stroke (S) = 1 cm2/s = 1 x 10-4 m2/s
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Effects of Viscosity: Too high viscosity - High resistance to flow, which causes sluggish operation. - Increased power consumption due to increased frictional losses. Too low viscosity - Increased leakage losses past seals. - Excessive wear due to the breakdown of the oil film between mating components.Measurement of Viscosity - The devices designed to measure viscosity are called viscometers or viscosimeters.Four commonly used viscometers 1. Rotating drum viscometer 2. Falling-ball viscometer 3. Capillary tube viscometer 4. Saybolt viscometerSurface Tension - Property that results from the attractive forces between moleculesCapillary - due to adhesion and cohesion d θ F F h h θ d F F Has greater adhesion Has greater cohesion θ < 90° θ > 90° Where: σ = surface tension, N/m γ = specific weight of liquid, N/m3 See table A.1 Physical Properties of water and table A.4 Physical Properties of Common Liquids at Standard atmospheric Pressure (Fluid Mechanics with Engineering Applications by Daugherty, Franzini and Finnemore) θ = wetting angle, degrees d = diameter of tube, m h = capillary rise, m
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----------------------------------------------------------------------------------------------------------------PROBLEMS: 1. Convert a pressure of -5 psi into absolute pressure. Convert a pressure of 150 kPa (abs) into a gage pressure 2. A viscometer is constructed with two 30-cm long concentric cylinders, one 20.0 cm in diameter and the other 22 cm in diameter. A torque of 0.13 N m is required to rotate the inner cylinder at 400 rpm (revolutions per minute). Calculate the viscosity. 3. A liquid has an absolute viscosity of 23.0 cP. It weighs 8.4 kN/m 3. What is its kinematic viscosity? 4. Determine the height that 20 ºC water would climb in a vertical 0.2 cm diameter tube if it attaches to the wall with an angle of 20 º to the vertical. 5. A 2 mm diameter clean glass tube is inserted in water at 15 ºC. Determine the height that the water will climb up the tube. The water makes a contact angle of 0 º with the clean glass. 6. (a) Find the depression h of the mercury in the glass capillary tube having a diameter of 2 mm if the surface tension is 0.514 N/m for θ = 40° (b) Compute the force caused by surface tension (c) Determine the density of mercury 7. (a) Determine the surface tension in a tube with 0.2 m radius and wetting angle 0° and capillary rise of 5mm. (b) Determine the surface tension in lb/ft (c) If wetting angle θ = 80°, determine the surface tension----------------------------------------------------------------------------------------------------------------------
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