• Newton’s law of viscosity,• Pressure and temperature dependence of
MPD/FFO/Lect_3
• Pressure and temperature dependence of viscosity
Viscosity• Viscosity is a property that represents the
internal resistance of a fluid to motion.
• Ethanol
MPD/FFO/Lect_3
• Water• Honey• Sludge• Slurry• Pastes
Newton’s Law of Viscosity�Shear stress acts tangentially to the
surface (F=tangential force).
F∆X
ForceArea
MPD/FFO/Lect_3
F A
area tangential
force shear=τ
ForceArea
Newton’s Law of Viscosity
• Newton’s law of viscosity states that“Shear stress is directly proportional to velocity gradient”
duτ α duτ µ=
MPD/FFO/Lect_3
µ = Viscosity of the fluidUnit of µKg/m.sPoisePa.s
1 Poise = 1g/cm. s
du
dyτ α du
dyτ µ=
Role of Viscosity
• Statics– Fluids at rest have no relative motion between
layers of fluid and thus du/dy = 0– Therefore the shear stress is _____ and is zerozero
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– Therefore the shear stress is _____ and is independent of the fluid viscosity
• Flows– Fluid viscosity is very important when the fluid
is moving
zerozero
Kinematic viscosity ν
• The ratio µ / ρ appears in many equations. • Kinematic viscosity ν (pronounced: new)
ρµν =
MPD/FFO/Lect_3
ρν =
• Gases: Viscosity increases with increasing temperature, why?
• Liquids: Viscosity decreases with increasing temperature, why?
Temperature and pressure dependence of viscosity
Viscosity of Newtonian fluids depends only on
temperature and pressure
)PP(exp TTE
exp)P,T( oo
0 −β
−∆µ=µ
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)PP(exp T TR
exp)P,T( oo
o0 −β
µ=µ
Whereµo:viscosity at To and Po (reference temperature and pressure)
∆E: activation energy for flowR: gas constantβ:material property [m2/N]
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
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• High pressure can also change the viscosity of a liquid. As pressure increases the relative movement of molecules requires more energy hence viscosity increases
Kinematic Viscosity of Water vs. Temp
Temp (oC) Viscosity (m2/s)
0 1.79 x 10-3
10 1.31 x 10-3
MPD/FFO/Lect_3
10 1.31 x 10
20 1.00 x 10-3
30 7.97x 10--4
40 6.5 x 10-4
50 5.55 x 10-4
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.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)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(a) Dynamic viscosity of oil in cP(b) Kinematic viscosity of oil in Stokes if the
specific gravity of the oil is 0.95Answer: (a) 1363.5 cP (b) 14.35 Stokes
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[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 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 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 = ay2 + by +c)
Answer: 10.2, 5.1 and 0 Pa.s
MPD/FFO/Lect_3
Mixture Different atoms
Element One type of atom
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not bonded together
Compound Different atoms bonded together (molecules)
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