Editing Rankine cycle (section)

== Equations ==
<math>\eta_\text{therm}</math> defines the [[thermodynamic efficiency]] of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, it can be simplified:
: <math> \eta_\text{therm} = \frac{\dot{W}_\text{turb} - \dot{W}_\text{pump}}{\dot{Q}_\text{in}} \approx \frac{\dot{W}_\text{turb}}{\dot{Q}_\text{in}}</math>
Each of the next four equations{{ref label | Van_rankine |1| a}} is derived from the [[energy]] and [[mass balance]] for a control volume.

: <math>\frac{\dot{Q}_\text{in}}{\dot{m}} = h_3 - h_2,</math>

: <math>\frac{\dot{Q}_\text{out}}{\dot{m}} = h_4 - h_1,</math>

: <math>\frac{\dot{W}_\text{pump}}{\dot{m}} = h_2 - h_1,</math>

: <math>\frac{\dot{W}_\text{turbine}}{\dot{m}} = h_3 - h_4,</math>

When dealing with the efficiencies of the turbines and pumps, an adjustment to the work terms must be made:

:<math> \frac{\dot{W}_\text{pump}}{\dot{m}} = h_2 - h_1 \approx \frac{v_1 \Delta p}{\eta_\text{pump}} = \frac{v_1 (p_2 - p_1)}{\eta_\text{pump}},</math>

:<math> \frac{\dot{W}_\text{turbine}}{\dot{m}} = h_3-h_4 \approx (h_3 - h_4) \eta_\text{turbine}.</math>