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A. Introduction

• stream flow is ultimate end product of runoff generation

• variations in flow affect amount & type of geomorphic work a river can do

• agenda:

  • examine driving and resisting forces to stream flow

  • explore the mechanics of flow

B. Driving Forces: propel Water Forward

Gravity

• acceleration objects experience due to force of gravity

• essentially constant: 9.81 m/s/s (m/s²); 32.2 ft/s/s (ft/s²)

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

C. Resisting Forces: Slow Forward Momentum

Friction

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

• 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

     

• Reynolds Number: distinguish laminar from turbulent flow

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

Re = v x r x r / m

v = average flow velocity

r = hydraulic radius

r = density

m = viscosity

D. Flow Velocity Patterns

Ratio of driving to resisting forces

• streams in steep mountain environments

• streams along flat coastal plains

Fastest fow

• straight channels: in center just below water surface

• meandering channels: outside of meander bends

Measurement

• equal intervals across channel

  • channel roughness

  • degree of turbulence

• 0.6D or 0.2D and 0.8D if water > 1 m (3 ft) deep

• floats

Manning equation

v = average flow velocity

n = Manning roughness coefficient

r = hydraulic radius

s = channel slope

restricted to uniform flow: constant depth and velocity along some length of channel of constant cross-section and slope

E. Discharge, Q

Q = w x d x v = a x v

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

F. Summary

• Stream flow ultimate end product of runoff generation

• Flow characteristics affected by channel geometry

• Velocity = balance between driving forces (gravity, gradient) and resisting forces (viscosity, friction)

• Flow velocity and depth are inversely related

• Velocity varies in 4 dimensions:

  • with distance from bed

  • withdistance from banks

  • downstream

  • over time

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