Reynolds Transport Theorem
In a Nutshell: You can study
fluid motion either by following fluid particles (system, the Lagrangian point
of view) or by observing fluid flow past a control volume (finite volume, Eulerian point of view).
Let B
denote extensive property related to fluid flow such as mass, linear
momentum, angular momentum,
or energy. Let b
denote comparable intensive
property such as mass per unit mass, linear
momentum per unit mass, angular momentum per unit mass, or energy
per unit mass. Then Reynolds
transport theorem is:
cv
= control volume, cs = control surface where B = the extensive property (contained in the system,
fixed quantity) b =
the intensive property = property per unit mass ρ =
the mass density of the fluid ∂/∂t =
the time rate of change dV =
the element of volume within
the control volume V =
the fluid velocity crossing the control surface n = the unit outward normal to the control
surface V
. n = the normal component of velocity crossing
the control surface (dot product) dS = the element of area on the control surface Physical
Interpretation of Reynolds Transport Theorem DB/dt represents the
time rate of change of the arbitrary extensive property, B ∂/∂t ∫ ρb dV represents the
time rate of change of B within the
control volume cv ∫ ρb V . n dS represents the flux of B
across the control surface cs |
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