Bernoulli ekvation

The energy equation for steady, incompressible flow is expressed as:

$$\begin{gathered} \frac{P_1}{\rho g}+{\alpha }_1\frac{{V_1}^2}{2g}+z_1+h_{pump,u}=\frac{P_2}{\rho g}+{\alpha }_2\frac{{V_2}^2}{2g}+z_2+h_{turbine,u}+h_L \\ where \\ {h}_{pump,u}=\frac{w_{pump,u}}{g}=\frac{{\dot{W}}_{pump,u}}{\dot{m}g}=\frac{{\eta }_{pump}{\dot{W}}_{pump}}{\dot{m}g} \\ {h}_{turbine,e}=\frac{w_{turbine,e}}{g}=\frac{{\dot{W}}_{turbine,e}}{\dot{m}g}=\frac{{\dot{W}}_{turbine,e}}{{\eta }_{turbine}\dot{m}g} \\ {h}_L=\frac{e_{mech loss, piping}}{g}=\frac{{\dot{E}}_{mech loss, piping}}{\dot{m}g} \\ {e}_{mech,loss}=u_2-u_1-q_{net,in} \end{gathered}$$