Rate of Loss of Mass of Fluid per Unit Volume

Theorem

Let $B$ be a body of fluid.

The rate of loss of mass of fluid from $B$ per unit volume is given by:

$\rho \operatorname {div} \mathbf v$

where:

$\rho$ denotes the density of $B$

$\mathbf v$ denotes the velocity of $B$

$\operatorname {div}$ denotes the divergence operator.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): divergence: 2. (div)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): divergence: 2. (div)