The velocity field
The fluid as a continuum
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We will study average properties evaluated over a small volume containing a large number
of molecules
These properties will be assumed to vary continuously throughout the fluid.
The limit definition of continuum
fluid density: (a) an elemental
volume in a fluid region of
variable continuum density; (b)
calculated density versus size of
the elemental volume.
The velocity field
• Eulerian method: one may attach a
temperature-measuring device to the top of
the chimney (point 0) and record the
temperature at that point as a function of
time.
• At different times there are different fluid
particles passing by the stationary device.
• In the Lagrangian method, one would attach
the temperature-measuring device to a
particular fluid particle (particle A) and
record that particle’s temperature as it
moves about.
• Fluid dynamic measurements are also suited to the eulerian system.
• For example, when a pressure probe is introduced into a laboratory
flow, it is fixed at a specific position (x, y, z). Its output thus contributes
to the description of the eulerian pressure field p(x, y, z, t).
• To simulate a lagrangian measurement, the probe would have to move
downstream at the fluid particle speeds.
• Foremost among the properties of a flow is the velocity field V(x, y, z, t).
• Velocity is a vector function of space and time.
• The acceleration field