Clastic transport and fluid flow

Transport: Weathered rock is transported from source areas to depositional sites by three kinds of processes:

Fluid-driven Transport:

Hydraulics - the properties of fluid flow

Fluid plays an important role in most models of sediment transport. Thus knowledge of hydraulics, the science of fluid flow, is essential to sedimentation and stratigraphy. Fluids resist forces that tend to change their volume, but readily alter their shape in response to external forces. The ability of a fluid to entrain particles is dependent on:

The first two are straightforward.

Density: Mass per unit volume. Typically measured in Kg/m3 or the equivalent g/cm3. Examples:

Velocity: Distance traveled per unit time.


Simulation of viscous (below)
and non-viscous (above)
fluid from Wikipedia
Viscosity: the constant of proportionality between shear stress and shear rate. Stated simply, a more viscous fluid resists deformation more strongly than a less viscous. All fluids will deform when stressed. The more they are stressed, the more they are deformed. For most fluids, this relationship is directly proportional and can be written as follows:

τ = μ*du/dy

Where τ is shear stress, du/dy is shear rate, and μ is viscosity. Fluids of this type are called Newtonian fluids. Viscosity can be described as internal friction. Units of this force are in Poise (P) (=1 g * cm-1 * s-1). The names Poiseuille and the shortened Poise are from the French physician, Jean Louis Poiseuille (1799 - 1869).

Examples of the viscosities of common substances at 20 deg. C:

Water 1.002 x 10-2 Poise
Air ~1.7 x 10-5 P
Natural gas 1.0 x 10-5 P
Glacial ice 1.0 x 1011 P
Mantle rock 1.0 x 1020 P

Viscosity is temperature dependent (compare honey that has been heated on a stove with honey coming from a refrigerator.) This table demonstrates the change of water viscosity with temperature:

Temperature (deg. C) Viscosity cP
0 1.792
20 1.002
40 0.656
60 0.469
80 0.357
100 0.284

Scaling issue - boundary layers:

When a fluid flows around an object (or an object moves through a fluid) the region directly adjacent to the object - the boundary layer - is dominated by viscous and electrostatic forces that make it tend to adhere to the object. The thickness of this layer varies with: The presence of this boundary layer has important consequences for sediment transport.


Laminar and turbulent flow from
Physics and Chemistry for IG and A level
Flow conditions: Although fluid flow is describable by the continuous variables given above, it typically falls into one of two discrete states:

The image of cigarette smoke (right) shows the abrupt transition between these states.

Numeric descriptors of flow:

Relationships of velocity, density, viscosity and flow state are numerically described using two dimensionless numbers:

Particle Transport

Particle motion in flowing fluid: We care about hydraulics because of flowing fluids' ability to transport sediment. Why, however, does this actually happen?

Whereas ions in solution are simply part of the fluid, clasts must be moved by mechanical forces. This involves three distinct processes:

  • Entrainment: Clasts are initially mobilized by two forces:

    Drag exerts a horizontal force, which causes particles to roll in the direction of current flow, whereas lift raises the particles vertically into the current (obliquely to current). Lift force is an example of Bernoulli's principle, which states that the sum of the velocity and pressure on an object in a flow must be constant. Whenever a flow speeds up, it exerts less pressure than a slower moving part of the flow. We are familiar with this from the airfoil shape of aircraft wings, deliberately engineered to create lift (right above). Fluid moving over a clast also generates lift (right below).

    In flowing streams, FD and FL combine to yield a composite fluid force, FF.

    The sediment, itself, is transported as three distinct loads:

    There is a relationship between a stream's velocity (energy) and the size clast that it can transport. Intuitively we sense that larger clasts need more energy to be moved than smaller ones, but reality is more subtle. This is shown in the Hjulstrom diagram, that gives a zone of sediment transport in black. The upper limit is the velocity at which a clast of a given size is entrained, the lower limit is the velocity at which an entrained clast is deposited.

    Above all, larger clasts are entrained at higher velocities. Why?

    Stokes' Law:

    Developed by Sir George Gabriel Stokes, An object falling through a fluid experiences three forces:

    Terminal fall velocity: The speed with which it falls is the balance of these forces. Gravity tends to accelerate it downward, however, the laws of fluid dynamics tell us that the faster the object falls, the more drag it experiences, slowing it down. Eventually it reaches a settling rate, a point at which drag and bouyancy balance gravitational acceleration, the terminal fall velocity (Fd).

    Essentially, this is expressed as Fd = Fg - Fup

    Stokes calculated the fall velocity for small particles, < 0.1 mm diameter. First, consider the frictional resistance that the fluid offers to movement of a settling sphere:

  • Fd = Cdπ(d2/4)(ρf V2/2)

    where:

    Then consider the force of gravity pulling the sphere downward:

  • Fg = 4/3 π(d/2)3ρsg

    where ρs = density of the sphere and g = acceleration due to gravity.

    The bouyant force of the liquid is given by:

  • Fup = 4/3π(d/2)3ρfg

    where ρf = density of the fluid

    Substituting these details into the original equation gives us:

  • Cdπ(d2/4)(ρf V2/2) = 4/3 π(d/2)3ρsg - 4/3π(d/2)3ρfg

    This can be simplified into:

  • V2 = 4gd(ρs - ρf)/3Cdρf

    If the temperature and fluid density are constant and the sphere and fluid densities known then this equation can be simplified significantly using the Reynolds number relationship to:

  • V = Cd2

    where C is a constant given by (ρs - ρf)g/18μ. At 20 deg C, in water, with a sphere density of 2.65 g/cc, C = 3.59 x 104

    The punchline: In words, with density and viscosity constant, velocity increases as the square of grain diameter.

    If we rotate the arrangement 90 degrees: With density and viscosity constant, the velocity required to move a clast through drag increases as the square of grain diameter.