#### 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):

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