VELOCITY PROFILE AND SHEAR STRESSES CALCULATION IN HIGH VOLUME RELATIVE BED ROUGHNESS FLOW
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VELOCITY PROFILE AND SHEAR STRESSES CALCULATION IN HIGH
VOLUME RELATIVE BED ROUGHNESS FLOW
Wojciech Bartnik
Andrzej Struzynski
Krakow Agriculture UniversityKrakow Agriculture University
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Flow zones – Introduction
Laboratory measurements
Bed roughness measurements
Log-law velocity distribution
Calculation of velocity and shear stresses
Conclusions
Presentation SchedulePresentation Schedule
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Bed roughness and water surface acts on the flowing water
Flow zonesFlow zones
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Flow zonesFlow zones
I - laminar flow II - log-law velocity distribution III - wake region IV - free surface region
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Flow zonesFlow zones
flat bed
III
III
IV
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Flow zonesFlow zones
rough bed
I
II
III
IV
IV
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Flow zonesFlow zones
[Williams J.J., 1996]
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Bed roughness and water surface acts on the shape of flowing water velocity profile.
Flow zonesFlow zones
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The shape of velocity profile depend on: flow depth, av. velocity of flowing water, bed roughness, relative roughness ...
For hydraulically rough flow conditions I and IV flow zone decreases
Fr = 0.074 Fr = 1.38
4D
Flow zonesFlow zones
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Laboratory measurementsLaboratory measurements
Flume dimensions: l2.0 x 0.5 x 0.6 m(glass walls)Flume rig: micro-propeller flow-meter slope measurements
Bed slope, water surface slope
Discharge: max 0.13 qm s-1 Artificial grains Ø – 4 to 8 cm
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Bed roughness measurementsBed roughness measurements
homogeneous roughnessks = K (1.926 SF2 – 0.488 SF + 4.516)
N
n n Hhn
K1
2
1
1
Profile-meter AG-1
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Log-law velocity distributionLog-law velocity distribution
Maximum velocity moves with relative roughness change flat bed
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Log-law velocity distributionLog-law velocity distribution
Maximum velocity moves with relative roughness change rough bed
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Log-law velocity distributionLog-law velocity distribution
For the same bed roughness curves are parallel flat bed
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Log-law velocity distributionLog-law velocity distribution
For the same bed roughness curves are parallel grains 4M
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Log-law velocity distributionLog-law velocity distribution
For the same bed roughness curves are parallel grains 4D
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Log-law velocity distributionLog-law velocity distribution
For the same bed roughness curves are parallel grains 6D
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Log-law velocity distributionLog-law velocity distribution
For the same bed roughness curves are parallel grains 8D
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Calculation of velocity and shear stressesCalculation of velocity and shear stresses
Log-law velocity distribution for whole profile is used
U/Umax = A log (y/Y) + B
sk
yUU
30log 75,5 * Modified Prandtl equation
B becomes constant - B = 1.12 ± 3%
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Calculation of velocity and shear stressesCalculation of velocity and shear stresses
U/Umax = A log (y/Y) + B
A value changes with relative depth Y/K
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Calculation of velocity and shear stressesCalculation of velocity and shear stresses
U/Umax = A log (y/Y) + B
Comparison of measured to calculated A constant
835.0
38.6
K
YA
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Calculation of velocity and shear stressesCalculation of velocity and shear stresses
Velocity profile reflects shear stresses
|
dy
du
Use of logarithmic equation allow calculating 0 for rough flow conditions
0 = 2.303 K UM y
U
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Calculation of velocity and shear stressesCalculation of velocity and shear stresses
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ConclusionsConclusions
•Near bed the velocity and velocity profile slope calculations (in logarithmic scale) are correct within the second and third flow zone. The use of equation (4) makes the bed level (zero velocity) estimation error negligible (B=1.12).•The use of mentioned method is limited to the rough flow conditions where the maximum velocity lays close to the water surface (the near surface region decreases to 20% of water depth).•The measurements of surface velocity, water depth and bed roughness can be used for calculation of water velocity profile and bed shear stresses for rough flow conditions.