#### Linear Momentum: Screencasts

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

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

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

##### Important Equations:

$\sum F_x = \frac{\partial}{\partial t} \int_{CV} u \,\rho\, d\forall \, + \, \int_{CS} u \,\rho \,\vec{V} \cdot \, \vec{n}\,dA$

In this equation, $$\sum F_x$$ means the sum of all external forces acting on the control volume in the $$x$$-direction (units of Newtons); $$u$$ is the x-component of velocity (units of m/s); $$\rho$$ is the density of the fluid (units of kg/m3); and $$\vec{V}\,\cdot \,\vec{n}$$ represents the dot product of the velocity vector and the outward-facing unit normal (units of m/s). The notation “CV” and “CS” stand for “control volume” and “control surface”. $$d\forall$$ and $$dA$$ represent differential volume and area elements within the control volume and the control surface. Similar equations can be written for the $$y$$- and $$z$$-directions:

$\sum F_y = \frac{\partial}{\partial t} \int_{CV} v \,\rho\, d\forall \, + \, \int_{CS} v \,\rho \,\vec{V} \cdot \, \vec{n}\,dA$

$\sum F_z = \frac{\partial}{\partial t} \int_{CV} w \,\rho\, d\forall \, + \, \int_{CS} w \,\rho \,\vec{V} \cdot \, \vec{n}\,dA$

$\dot{m} = \rho \,\vec{V} \cdot \,\vec{n} A$

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