Back Work Ratio (BWR)
Calculate the back work ratio (BWR) of a power cycle, BWR = w_compressor ÷ w_turbine, dividing the work consumed by the compressor (or pump) by the gross work produced by the turbine. The dimensionless result shows what fraction of turbine work is reinvested to compress the fluid. In gas turbines (Brayton cycle) the BWR is high (0.4–0.6), since compressing gas is costly; in steam Rankine cycles it is tiny (~0.01), since pumping liquid is cheap. A high BWR makes the cycle sensitive to component efficiencies. Enter the compressor work and the turbine work.
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Back work ratio
Every turbine puts out work, but part of it has to be handed back to drive the compressor (or the pump) that pressurizes the working fluid. The back work ratio (BWR) measures that share: BWR = w_compressor ÷ w_turbine. It is the fraction of the gross turbine work that never survives as useful output, having been reinvested in compression. The value reveals the character of the cycle. In a gas turbine (Brayton cycle), compressing air is expensive and the BWR lands between 0.4 and 0.6 — more than half of the turbine work goes straight back to the compressor! That makes the gas turbine highly sensitive to the efficiency of its components: a small drop in compressor or turbine efficiency can wipe out the net work altogether. In a steam Rankine cycle, by contrast, the pump compresses a liquid (minimal work), so the BWR is tiny, on the order of 0.01. Steam cycles therefore tolerate less efficient components and still deliver power. Enter the compressor work and the turbine work.
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Calculate the effectiveness of a regenerator (heat recuperator), ε = (T_out − T_in) ÷ (T_hot − T_in), comparing the actual heating of the cold fluid with the maximum possible (if it reached the hot exhaust gas temperature). The result (between 0 and 1, or ×100%) measures heat-exchange effectiveness: a regenerator uses a gas turbine's exhaust heat to preheat the air before the combustor, cutting fuel use and raising the regenerative Brayton cycle efficiency. Typical effectiveness is 0.7–0.9. Enter the inlet, outlet and hot-gas temperatures.
Rankine Cycle Efficiency
Calculate the thermal efficiency of a Rankine cycle, η = (w_turbine − w_pump) ÷ q_boiler × 100%, dividing the net work (turbine work minus pump work) by the heat added in the boiler, all in kJ/kg. The Rankine cycle is the basis of steam power plants: water is pumped, heated and vaporized in the boiler, expands through the turbine producing work, then condenses. The result, in %, measures how much boiler heat becomes useful work; real cycles run 30–45%. Enter the turbine work, the pump work and the boiler heat.
Compressor Work (Isentropic)
Compute the specific compression work in an ideal refrigeration cycle, W = h₂ − h₁, the enthalpy difference between the compressor outlet and inlet (isentropic compression, at constant entropy). It is the energy the compressor adds to the refrigerant per kilogram — the cycle's 'electricity bill'. Together with the refrigerating effect, it defines the COP (COP = refrigerating effect/work). Enter the outlet and inlet enthalpies.
Combined Cycle Efficiency
Calculate the efficiency of a gas-steam combined cycle, η_cc = η_gas + η_steam − (η_gas × η_steam ÷ 100), combining the gas turbine efficiency (Brayton, topping) with the steam cycle (Rankine, bottoming) that recovers heat from the exhaust gases. The result, in %, exceeds either cycle alone because the heat rejected by the gas turbine, instead of being wasted, raises steam for a second turbine. This is why modern combined-cycle plants top 60% efficiency, the highest in thermal generation. Enter the gas-cycle and steam-cycle efficiencies (in %).
Stripping Ratio (SR)
Compute the stripping ratio (SR) of an open-pit mine by dividing the amount of waste (worthless rock that must be removed) by the ore extracted. It is the central economic indicator of open-pit mining: the higher the SR, the more useless material is moved per tonne of ore, and the higher the cost. It defines the pit limit and the viability of the operation. Enter the waste and ore quantities.
Square-Wave RMS Current
Calculate the RMS value of a pulsing square-wave current, I_rms = I_p × √D, from the peak current I_p and the duty cycle D (fraction of the period the current flows). The result, in amperes, is the RMS current that determines the actual heating (I²R losses) of a component that conducts in pulses — such as a transistor or winding in a switching converter. Unlike the average value, the RMS is what matters for sizing conductors, resistances and dissipation. The smaller the duty cycle, the lower the RMS for the same peak current. Enter the peak current and the duty cycle.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.