Christoffel symbols

In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid. Force density is represented by the symbol f, and given by the following equation, where P is the pressure:

$\mathbf {f} =-\nabla P$.

The net force on a differental volume element dV of the fluid is:

$d\mathbf {F} =\mathbf {f} dV$

Thus, the force density at a point in a fluid, divided by the density, is the acceleration of the fluid at that point.

References

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