• Newton’s law of viscosity, • Pressure and temperature dependence of viscosity

MPD/FFO/Lect_3 viscosity,

MPD/FFO/Lect_3 Viscosity • Viscosity is a property that represents the internal resistance of a fluid to motion.

• Ethanol • Water • Honey • Sludge • Slurry • Pastes

MPD/FFO/Lect_3 MPD/FFO/Lect_3 Newton’s Law of Viscosity

Velocity Gradient = ∆U/ ∆Y

MPD/FFO/Lect_3 Velocity gradient

MPD/FFO/Lect_3 Newton’s Law of Viscosity ‹Shear stress acts tangentially to the surface (F=tangential force).

∆X F Area Force

A F

τ = shear force tangential area MPD/FFO/Lect_3 Newton’s Law of Viscosity

• Newton’s law of viscosity states that “Shear stress is directly proportional to velocity gradient”

τ α du τ µ= du dy dy Unit of µ µ = Viscosity of the fluid Kg/m.s Poise Pa.s 1 Poise = 1g/cm. s

MPD/FFO/Lect_3 Role of Viscosity

• Statics – Fluids at rest have no relative motion between layers of fluid and thus d u/d y = 0 – Therefore the shear stress is _____zero and is independent of the fluid viscosity • Flows – Fluid viscosity is very important when the fluid is moving

MPD/FFO/Lect_3 Kinematic viscosity ν

• The ratio µ / ρ appears in many equations. • Kinematic viscosity ν (pronounced: new) µ ν = ρ • Gases: Viscosity increases with increasing temperature, why? • Liquids: Viscosity decreases with increasing temperature, why?

MPD/FFO/Lect_3 Kinematic viscosity

• Units • m2/s • Stokes =cm2/s

MPD/FFO/Lect_3 Temperature and pressure dependence of viscosity Viscosity of Newtonian fluids depends only on temperature and pressure

∆ − µ = µ E To T β − (T, P) 0 exp exp (P Po ) R To T Where µo:viscosity at To and Po (reference temperature and pressure) ∆E: activation energy for flow R: gas constant β:material property [m2/N]

MPD/FFO/Lect_3 Temperature and pressure dependency of viscosity • Viscosity will also change with pressure - but under normal conditions this change is negligible in gasses • High pressure can also change the viscosity of a liquid. As pressure increases the relative movement of molecules requires more energy hence viscosity increases

MPD/FFO/Lect_3 Kinematic Viscosity of Water vs. Temp

Temp ( oC) Viscosity (m2/s) 0 1.79 x 10-3 10 1.31 x 10-3 20 1.00 x 10-3 30 7.97x 10--4 40 6.5 x 10-4 50 5.55 x 10-4

MPD/FFO/Lect_3 Element Atoms of the same type

LiquidMPD/FFO/Lect_3 Gas Liquid Atoms can move around but are attracted together

Cold liquid MPD/FFO/Lect_3 Hot liquid Gases Large spaces between atoms

Cold gas MPD/FFO/Lect_3 Hot gas Gases fill the whole space

MPD/FFO/Lect_3 MPD/FFO/Lect_3 Liquids fill containers from the bottom

MPD/FFO/Lect_3 Next Lecture

• Numerical based on viscosity of fluids

• Come with calculator

MPD/FFO/Lect_3 Examples

[1] A plate 0.025 mm apart from a fixed plate moves at 60 cm/s and requires force of 2 N/m2 to maintain the speed. Determine the fluid viscosity between the plates. Answer: 8.33 x10 -5 Pa.s

MPD/FFO/Lect_3 [2] A flat plate of area 1.5 x 106 mm2 is pulled with the speed of 0.4 m/s relative to another plate located at a distance 0.15 mm apart from it. Find the force and power required to maintain the speed, if the fluid separating them having viscosity as 1 Pa.s. (Hint: Power = F.u) Answer: F = 4000 N and Power =1600 Watts

MPD/FFO/Lect_3 [3] The space between two flat parallel plates is filled with an oil. Each side of the plate is 60 cm. The thickness of the oil plate is 12.5 mm. The upper plate which moves at 2.55 m/s requires a force of 98.1 N to maintain the speed. Determine: (a) Dynamic viscosity of oil in cP (b) Kinematic viscosity of oil in Stokes if the specific gravity of the oil is 0.95 Answer: (a) 1363.5 cP (b) 14.35 Stokes

MPD/FFO/Lect_3 [4] The dynamic viscosity of an oil used for lubrication between a shaft and a sleeve is 6 Poise. The shaft is of diameter 0.4 m and rotates at 190 rpm. Calculate the power lost in the bearing for the sleeve length of 90 mm. The thickness of the film is 1.5 mm. (Hint: u =ЛDN/60, T = FD/2, Power = 2ЛNT/60) Answer: 716.48 watts

MPD/FFO/Lect_3 [5] The velocity distribution for a flow over a flat plate is given by:: u= (¾)y-y2 Where, u = velocity (m/s) y = distance above the plate (m) Determine shear stress at y = 0.15 m. Take dynamic viscosity of the fluid as 8.6 Poise. Answer: 0.3875 N/m2

MPD/FFO/Lect_3 [6] If the velocity profile over a flat plate is parabolic with a vortex 20 cm from the plate, where the velocity is 120 cm/s. Calculate the velocity gradient and shear stress at a distance of 0, 10 and 20 cm from the plate. Take viscosity of oil as 8.5 Poise. (Hint: parabolic velocity profile u = ay 2 + by +c) Answer: 10.2, 5.1 and 0 Pa.s

MPD/FFO/Lect_3 MPD/FFO/Lect_3 MPD/FFO/Lect_3 MPD/FFO/Lect_3 MPD/FFO/Lect_3 Atoms

Molecules - Atoms bonded together

MPD/FFO/Lect_3 Element One type of atom

Mixture Different atoms not bonded together

Compound Different atoms bonded together (molecules)

MPD/FFO/Lect_3 Compound Different atoms in fixed proportions

1Y 1G MPD/FFO/Lect_32R 1G 1Y 1R 1B MPD/FFO/Lect_3