#### Conservation of Mass: Screencast

Demonstrates how to use the Continuity equation in integral form.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

\[0 = \frac{\partial}{\partial t} \int_{CV} \rho\,d\forall \,+\,\int_{CS} \rho\,\vec{V} \cdotp \vec{n} \, dA\]

where \(CV\) represents the control volume. The variable \(d\forall\) is used to represent a differential volume (units of m^{3}). The “V” looks different so you don’t confuse it with velocity.

\(CS\) represents the control surface. The variable \(dA\) represents a differential area (units of m^{2}).

The operator \(\partial/\partial t\) represents the time rate of change (units of 1/s).

\(\rho\) is the density of the fluid (units of kg/m^{3}).

\(\vec{V} \cdotp \vec{n}\) is the velocity vector and the outward facing until normal (units of m/s). This quantity is positive in regions where fluid is flowing out of the control volume. It is negative in regions where fluid is flowing in to the control volume. It is zero in regions where the fluid is flowing parallel to the surface of the control volume.

\[\dot{m} = \rho Q = \rho \bar{V} A\]

where \(\dot{m}\) is the mass flow rate of the fluid (units of kg/s).

\(\rho\) is the density of the fluid (units of kg/m^{3}).

\(Q\) is the volumetric flow rate of the fluid (units of m^{3}/s).

\(\bar{V}\) is the average speed of the fluid (units of m/s).

\(A\) is the cross-sectional area through which the fluid is flowing (units of m^{2}).