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Give the physical interpretation of the substantial derivative?
Wiki User
∙ 11y ago
The first ∂/∂t term is called V the local derivative. The second ~· ∇ term is called the convective derivative. In steady flows, ∂/∂t =0, and only the convective derivative
The substantial derivative has a physical meaning: the rate of change of a quantity (mass,
energy, momentum) as experienced by an observer that is moving along with the flow. The
observations made by a moving observer are affected by the stationary time-rate-of-change
of the property (∂f/∂t), but what is observed also depends on where the observer goes as
it floats along with the flow (v · ∇f). If the flow takes the observer into a region where, for
example, the local energy is higher, then the observed amount of energy will be higher due
to this change in location. The rate of change from the point of view of an observer floating
along with a flow appears naturally in the equations of change.
Wiki User
∙ 11y ago
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