GEOL 340 Sedimentology and Stratigraphy
Lecture 6
1. Flow and the Boundary Layer
2. Entrainment
Flow and the Boundary Layer
Laminar Flow = slow moving parallel unidirectional layered
flow (Fig. 2.3, p. 29)
function of viscosity and velocity
shear stress =
Turbulent Flow = fast moving traverse multidirectional flow
movements
function of viscosity and velocity
changes settling rates, erosion and entrainment
shear stress =
h = eddy viscosity
Reynold's Number (Re) = ratio of inertial and viscous
forces in the fluid
inertail forces cause turbulence, viscous forces suppress turbulence
Re = (ULr)/m = (UL)/u = dimensionless value
U = mean flow velocity
L = length characterizing length of flow (water depth)
u = kinematic viscosity
low Re = low velocity, viscous forces dominate, laminar
(transition at Re = 500 to 2000)
high Re = higher velocity, inertial forces dominate,
turbulent
Boundary Layer No-Slip Condition = fluid sticks to surfaces, velocity
= 0 at contact
also called viscous or laminar sublayer
cross-sectional diagram of flow through a pipe
velocity gradients entirely within fluids
examples:
a. dust on fan blades
b. scale precipitated on pipes, not eroded
c. sand needed for water to erode
Thickness of the Boundary Layer:
= thickness of BL
X = distance from leading edge
R = density of fluid
Umax = free stream maximum velocity
Entrainment and Bedforms by Unidirectional Flow
Entrainment = initial lifting of grain from the bed
more energy needed to put into motion than to keep in motion
Transport Steps:
a. erosion and entrainment
b. sustained downcurrent movement (suspension in medium)
c. deposition
Critical Threshold for Entrainment
a. water parameters [velocity, shear stress (t), kinematic viscosity
(u)]
d. grain parameters [size, shape, density (r)]
Opposing Forces (entrainment figure Fig. 2.4, p. 33)
a. drag force (FD) = to / N = shear force per grain exposed overcomes
gravity,
frictional, and electrochemical adhesion (fine clay-sized particles)
b. lift force (Bernoulli effect) = flow through a smaller cross-sectional
area
(convergence of streamlines) causes higher velocity and resulting
lower
pressure (diagram in handout)
c. total lift force = lift force - drag force
3. Bernoulli Effect
Bernoulli Effect in Pipes
a. divergent streamlines = INCREASE in pressure
INCREASE cross-sectional area = DECREASE fluid velocity = INCREASE
pressure
b. convergent streamlines = DECREASE in pressure
DECREASE cross-sectional area = INCREASE fluid velocity = DECREASE
pressure
Show Bernoulli effect on hydrofoil as well
Empirical Plots
a. Hjulstrom diagram = water transport only
b. Shields diagram = substitute dimensionless numbers, so water
or air transport
Downcurrent Suspension
function of drag of current and settling velocity
Stokes Law = settling velocity a function of particle size
a. only good for particles < 0.1 to 0.2 mm diameter
b. > 0.2 mm have inertial (turbulence) effects, so not good
for sands