Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.
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Transcript of Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.
![Page 1: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/1.jpg)
Elementary Mechanics of Fluids
CE 319 F
Daene McKinney
Viscosity
![Page 2: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/2.jpg)
Some Simple Flows• Flow between a fixed and a moving plate
Fluid in contact with the plate has the same velocity as the plate
u = x-direction component of velocity
u=VMoving plate
Fixed plate
y
x
V
u=0
B yB
Vyu )( Fluid
![Page 3: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/3.jpg)
Some Simple Flows
• Flow through a long, straight pipeFluid in contact with the pipe wall has the same velocity as the wall
u = x-direction component of velocity
rx
R
21)(
R
rVru
VFluid
![Page 4: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/4.jpg)
Fluid Deformation
• Flow between a fixed and a moving plate
• Force causes plate to move with velocity V and the fluid deforms continuously.
u=VMoving plate
Fixed plate
y
xu=0
Fluid
t0 t1 t2
![Page 5: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/5.jpg)
u=V+VMoving plate
Fixed plate
y
x
u=V
Fluid
Fluid Deformation
t t+t
x
y
L
t Shear stress on the plate is proportional
to deformation rate of the fluid
V
Lt
y
L
y
V
t
y
V
![Page 6: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/6.jpg)
Shear in Different Fluids
• Shear-stress relations for different typesof fluids
• Newtonian fluids: linear relationship
• Slope of line (coefficient of proportionality) is “viscosity”
dy
dV
dy
dV
![Page 7: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/7.jpg)
Viscosity
• Newton’s Law of Viscosity
• Viscosity
• Units
• Water (@ 20oC)– = 1x10-3 N-s/m2
• Air (@ 20oC)– = 1.8x10-5 N-s/m2
• Kinematic viscosity
dydV /
2
2
//
/
m
sN
msm
mN
V
V+dv
dy
dV
![Page 8: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/8.jpg)
Flow between 2 plates
u=VMoving plate
Fixed plate
y
x
V
u=0
B yB
Vyu )( Fluid Force acting
ON the plate
21
21
222111
AA
FAAF
221
1 dy
du
dy
du
Thus, slope of velocity profile is constant and velocity profile is a st. line
Force is same on topand bottom
![Page 9: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/9.jpg)
Flow between 2 plates
u=VMoving plate
Fixed plate
y
x
V
u=0
B yB
Vyu )(
B
V
dy
du Shear stress anywherebetween plates
Shearon fluid
mB
smV
CSAEmsN o
02.0
/3
)38@30(/1.0 2
2
2
/15
)02.0
/3)(/1.0(
mN
m
smmsN
![Page 10: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/10.jpg)
Flow between 2 plates
• 2 different coordinate systems
rx
B
21)(
B
rVru
Vy
x yByCyu )(
![Page 11: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/11.jpg)
Example: Journal Bearing
• Given– Rotation rate, = 1500 rpm
– d = 6 cm
– l = 40 cm
– D = 6.02 cm
– SGoil = 0.88
– oil = 0.003 m2/s
• Find: Torque and Power required to turn the bearing at the indicated speed.
![Page 12: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/12.jpg)
Example: cont.
• Assume: Linear velocity profile in oil film
2/1242/)0002.0(
)2/06.0(1500*60
2
)003.0*998*88.0(
2/)(
)2/( StressShear
mkN
dD
d
dy
dV
mN
dl
dM
2812
06.0)4.0*
2
06.0*000,124*2(
2)
22(Torque
kWsmNMP 1.44/100,441.157*281Power
![Page 13: Elementary Mechanics of Fluids CE 319 F Daene McKinney Viscosity.](https://reader035.fdocuments.us/reader035/viewer/2022081419/56649d885503460f94a6c74a/html5/thumbnails/13.jpg)
Example: Rotating Disk
• Assume linear velocity profile: dV/dy=V/y=r/y
• Find shear stress