## stream flow: ultimate end product of runoff generation

## discharge: Q = width x depth x velocity = cross-sectional area x velocity

## flow characteristics affect amount and type of geomorphic work rivers can do

## learning outcomes - you should be able to:

## explain the driving and resisting forces affecting stream flow;

## calculate stream geometric characteristics and explain the importance of these characteristics to stream flow;

## describe flow velocity patterns in stream channels and explain their occurrence; and,

## calculate the Reynolds and Froude numbers and explain the meaning of your calculated values.

## Gravity

## acceleration of water due to force of gravity

## essentially constant: 9.81 m/s/s (m/s

^{2}); 32.2 ft/s/s (ft/s^{2})## Gradient

## change in elevation/distance; e.g. m/m or m/km or ft/ft or ft/mi

## potential energy: energy available from a particular elevation down to base level

## at base level, no more potential energy to transform to kinetic energy

## kinetic energy: energy of motion; potential energy changes to kinetic energy as water flows downhill

## flow velocity: measure of kinetic energy

## m/s or ft/s

## Friction with channel bed and banks

## channel width (w): distance from banks

## channel depth (d): distance from bed

## cross sectional area: a = w x d

## wetted perimeter (P

_{w}): length of channel perimeter directly contacting water = w + 2d## hydraulic radius (r = a/P

_{w}): distance from center to wetted perimeter## channel roughness

## grain size

## microtopography (e.g. ripples, bars)

## gross channel shape

## Viscosity

## resistance of a fluid to change in shape

## molecular viscosity: friction between individual water molecules as they collide and slide past one another

## affected by temperature and suspended sediment

## eddy viscosity: friction along eddy lines

## laminar flow and turbulent flow

## Ratio of driving to resisting forces

## streams in steep mountain environments

## streams along flat coastal plains

## Fastest flow

## straight channels: in center just below water surface

## meandering channels: outside of meander bends

## Flow equations

## Chezy equation: V = C x [sqrt(rS)]

## Manning equation: V = [1.49 x r^2/3 x S^1/2]/n

## similarities:

## velocity proportional to hydraulic radius (R) and slope (S)

## C and n represent resistance

## Reynolds Number

## distinguishes laminar from turbulent flow

## ratio driving forces (inertial viscosity) to resisting forces (molecular viscosity)

## Re = v x r x r / m

## v = average flow velocity

## r = hydraulic radius

## r = density

## m = viscosity

## Re<500 = laminar flow Re>2000 = turbulent flow

## Froude number

## F = v / sqrt(g x d)

## v = average flow velocity

## g = acceleration due to gravity

## d = average depth

## relates inertia of a mass of streamflow to the rapidity of shallow waves (ripples)

## F<1 subcritical or tranquil flow (deep, slow flow); ripples can travel upstream

## F>1 supercritical or rapid flow (shallow, fast flow); ripples cannot travel upstream

## hydraulic drops and hydraulic jumps

## Questions for thought - according to your textbook:

## What distinguishes uniform flow from non-uniform flow, and steady flow from unsteady flow?

## Why do geomorphologists care about the Reynolds and Froude numbers?

## Stream flow ultimate end product of runoff generation

## Velocity = balance between driving forces (gravity, gradient) and resisting forces (friction from channel perimeter, molecules, and eddies)

## Velocity varies in 4 dimensions:

## with distance from bed

## with distance from banks

## downstream

## over time

## Froude number shows velocity and depth are inversely related

## Flow conditions (velocity, turbulence) impact amount & type of work river does

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©Karen A. Lemke: klemke@uwsp.edu

Last revised September 2, 2014