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):

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