’s law of , • 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 to motion.

• Sludge • Slurry • Pastes

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

Velocity Gradient = ∆U/ ∆Y

MPD/FFO/Lect_3 gradient

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

∆X F Force


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

• Newton’s law of viscosity states that “ 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 Pa.s 1 Poise = 1g/cm. s

MPD/FFO/Lect_3 Role of Viscosity

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 • : Viscosity increases with increasing temperature, why? • : 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 for flow R: 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 . 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 . 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 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 . 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 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