#### Mechanical Energy Balance: Screencast

The mechanical energy balance is obtained from the steady-state energy balance, and under some conditions, it simplifies to the Bernoulli equation.

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

##### Important Equations:

\[\frac{\Delta P}{\rho} + \frac{\Delta u^2}{2} +g\Delta z + \left(\hat{\Delta U} – \frac{\dot Q}{\dot m} \right) = \frac{\dot W _S}{\dot m}\]

where \(\rho\) = fluid density (g/L),

\(P\) = pressure (bar),

\(\Delta P\) = change in pressure (bar): outlet – inlet,

\(u\) = velocity (m/s),

\(g\) = gravitational constant = 9.81 m/s,

\(z\) = height (m),

\(\Delta z\) = change in height (m): outlet – inlet,

\(\hat{\Delta U}\) = specific change in internal energy (J/g),

\(\dot Q\) = rate of heat added (J/s),

\(\dot m\) = mass flow rate (g/s), and

\(\dot W _S\) = rate of shaft work added (J/s).

\[\frac{\Delta P}{\rho} + \frac{\Delta u^2}{2} +g\Delta z + \hat{\,\,\, F} = \frac{\dot W _S}{\dot m}\]

where \(\hat{\,\,\, F} = \left( \hat{\Delta U} – \frac{\dot Q}{\dot M} \right)\) = friction loss (J/s), and \(\hat{\,\,\, F} > 0\).

Bernoulli equation (obtained when no frictional loss and no shaft work):

\[\frac{\Delta P}{\rho} + \frac{\Delta u^2}{2} +g\Delta z = 0\]