VELOCITY PROFILE AND SHEAR STRESSES CALCULATION IN HIGH VOLUME RELATIVE BED ROUGHNESS FLOW Wojciech Bartnik Andrzej Struzynski Krakow Agriculture University

Flow zones – Introduction Laboratory measurements Bed roughness measurements Log-law velocity distribution Calculation of velocity and shear stresses Conclusions Presentation Schedule

Bed roughness and water surface acts on the flowing water Flow zones

I- laminar flow II- log-law velocity distribution III- wake region IV- free surface region

Flow zones flat bed II I III IV

Flow zones rough bed I II III IV

Flow zones [Williams J.J., 1996]

Bed roughness and water surface acts on the shape of flowing water velocity profile. Flow zones

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 = 0.074Fr = D Flow zones

Laboratory 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

Bed roughness measurements homogeneous roughness k s = K (1.926 SF 2 – SF ) Profile-meter AG-1

Log-law velocity distribution Maximum velocity moves with relative roughness change flat bed

Log-law velocity distribution Maximum velocity moves with relative roughness change rough bed

Log-law velocity distribution For the same bed roughness curves are parallel flat bed

Log-law velocity distribution For the same bed roughness curves are parallel grains 4M

Log-law velocity distribution For the same bed roughness curves are parallel grains 4D

Log-law velocity distribution For the same bed roughness curves are parallel grains 6D

Log-law velocity distribution For the same bed roughness curves are parallel grains 8D

Calculation of velocity and shear stresses Log-law velocity distribution for whole profile is used U/U max = A log (y/Y) + B Modified Prandtl equation B becomes constant -B = 1.12 ± 3%

Calculation of velocity and shear stresses U/U max = A log (y/Y) + B A value changes with relative depth Y/K

Calculation of velocity and shear stresses U/U max = A log (y/Y) + B Comparison of measured to calculated A constant

Calculation of velocity and shear stresses Velocity profile reflects shear stresses Use of logarithmic equation allow calculating  0 for rough flow conditions  0 = K U M

Calculation of velocity and shear stresses

Conclusions 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.