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Waves are a Drag
An Intuitive Introduction to Flow Fields
Streamlines provide a handy way to visually analyze flow by describing
the velocity fields around objects in flow. In steady flow, streamlines
lines trace out the paths of particles transported by the fluid. More
generally (i.e., in unsteady flow), streamlines are lines drawn
tangent to the velocity vectors describing the flow field.
When streamlines lie closer together, average
velocity is higher. As streamlines are compressed, the same amount
of mass must pass through a smaller cross-section. The only way to get
the same amount of stuff through a smaller opening is to move it faster.
To help visualize what streamlines represent, imagine yourself
floating along your favorite river. The slowest portions of the river, the
doldrums, are always the widest parts of the river. Here the streamlines
are wide apart and average velocity is low. Rapids (yahoo!),
on the other hand, are the narrower parts of the river.
Here streamlines are pushed close together as the same amount of fluid
must flow through a smaller passage. In a pipe or river, the total flow
rate is the average velocity of the flow multiplied by the cross-sectional
area of its route. Conservation of mass requires that the flow rate remain
constant. As cross-sectional area decreases, average velocity must increase.
This intuitive way of viewing a velocity field also
allows us to picture the change in pressure as fluid travels over an
object. Pressure varies inversely with the square of velocity.
D pressure = proportionality constant * fluid density *
( D velocity)2
In other words, when velocity increases (streamlines become
closer together), pressure decreases. The principle of conservation of energy
underlies this tradeoff. An increase in kinetic energy (proportional to
the square of velocity) necessitates a decrease in pressure energy.
copyright Elizabeth Nelson, Judith Connor
1999, 2000 Non-profit
educational uses permitted.