Download Reynolds Number (Re)

Flow Energy
PE = mgh
H1
H2
Datum
• PE + KE = constant between any two points
• PE (loss) = KE (gain)
• Rivers are non-conservative; some energy is lost
from the system and can not do mechanical work
Available Energy is Used To:
• Overcome Viscous shear and turbulence (internal
friction within the fluid);
• Overcome friction at the channel boundaries;
• Erode sediment from the channel boundaries;
• Transport the sediment once it has been eroded.
Flow Energy
PE = mgh
H1
H2
Datum
• Rate of potential energy loss along the channel
can be determined by the slope of the water
surface – commonly referred to as the energygrade line.
Flow Types
Laminar vs. Turbulent
• Laminar:
– Water particles move
along paths that do not
disrupt the movement
of neighboring
particles.
– Most resistance is
caused by
intermolecular viscous
forces.
– Resistance is  to
velocity
• Turbulent Flow
– Water particles move in all
directions and velocity
constantly fluctuates
– Most resistance is
generated along channel
perimeter; related to
channel shape, particle
size, and concentration.
– Resistance is  to square
of velocity
Velocity Distribution in Open Channels
Modified from Wolman, 1955;
Figure from Ritter et al., 2002
Flow Types
Steady/Uniform Flow
• Uniform/non-uniform: velocity is
constant/variable with position;
• Steady/unsteady: velocity is
constant/variable with time at any given
location
Manning Equation
Describes Flow and Resistance in
Open Channels
V = 1.49(R2/3)(S1/2)/n
n = Manning’s roughness
Coefficient
Slope = water surface slope
Assumes English units; remove 1.49
from equation for metric
Influence of Manning’s n
on Resistance and Suspended Sediment
Sediment Transport Terminology
• Entrainment: the processes that initiate the motion of a
particle.
• Competence: the size of the largest particle a stream can
entrain under any give set of hydraulic conditions.
• Capacity: the maximum amount of sediment that the stream
can carry given the current hydraulic conditions.
• Load: amount of sediment that is actually carried by the
stream.
• Sediment discharge: time rate of movement through a
cross-section (weight/time; tons/day)
Load Types
Classification Based on Mode of Transport
• Suspended Load: Particles transported mainly or
entirely in suspension through the supporting
action of turbulence.
• Bedload: Sediment which moves by skipping,
sliding, and rolling along the channel bed.
Remains within a few grain diameters of the
channel bed.
Types of Sediment Load
Chernicoff S., Fox, HA.,
and Venkatakrishnan, R.,
1997, Essentials of
Geology, Worth
Publishers, Fig. 13-13,
pg. 261
Load Types
Classification Based on Bottom
Sediment Characteristics
• Wash Load: Particles so fine that they are not
found in appreciable amounts in the channel bed.
• Bed Material Load: Particle sizes that are found in
great quantities in the stream bed.
– Most bed material load is actually transported in
suspension.
Methods Used to Describe
Entrainment
• Critical Bed Velocity
Velocity (V)

Water
– Impact or momentum of
the water mass on the
exposed part of the
particle.
– 6th power law: Size of
particle entrained
increases with the 6th
power of the velocity.
– Very difficult to measure
Methods Used to Describe
Entrainment
• Critical Tractive Force
Depth (D)

Slope (S)
– Dragging force is exerted
on the exposed part of the
particle.
–  = γDS
•
(Duboy’s Equation)
– Fairly Easy to measure
From Knighton, 1998, Fluvial Forms and Processes, Arnold, Figure 4.4a, page 108.
Shield’s Dimensionless Values
• Dimensionless
Shear Stress
=
Dimensionless Reynolds
Numbers

(γf - γs) d
γ - Specific weight of
solid and fluid
R* =
V*d

V * = (gRS)1/2
d = Intermediate grain diameter
R = Hydraulic Radius
Dimensionless Shields Plot
Hjulstrom Plot
Stream Power
•
•
•
•
 = γ QS
 = γ wdvS
/w = ((γ dS)v)/w
/w =  v
East Fork River Bedload Trap
Flow
Bedload Trap