Title
Marine Botany

# Waves are a Drag

An Intuitive Introduction to Flow Fields

Velocity

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.

Pressure

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.

Last updated: Feb. 05, 2009