Pump Work (Rankine)
Calculate the specific work consumed by the pump of a Rankine cycle, w_pump = v × (P₂ − P₁), multiplying the liquid specific volume (m³/kg, ~0.001 for water) by the pump pressure rise (kPa). The result, in kJ/kg, is the energy spent pressurizing the condensate before the boiler. Because the liquid is nearly incompressible, this work is tiny compared with the turbine's — which is why the Rankine cycle pumps a liquid (not a gas, as a gas Carnot cycle would), sharply reducing the back work. Enter the specific volume and the pump outlet and inlet pressures.
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Trabalho da bomba (ciclo Rankine)
No ciclo Rankine, antes de entrar na caldeira a água condensada precisa ser pressurizada pela bomba de alimentação. O trabalho específico gasto nisso é w_bomba = v × (P₂ − P₁): o volume específico do líquido v (m³/kg, cerca de 0,001 para a água) multiplicado pelo aumento de pressão (P₂ − P₁), em kPa, resultando em kJ/kg. A fórmula vale porque o líquido é praticamente incompressível — seu volume quase não muda ao ser comprimido, então o trabalho reversível é simplesmente volume vezes variação de pressão. A grande sacada do ciclo Rankine está justamente aqui: como bombear líquido consome pouquíssima energia (o volume específico é minúsculo), o trabalho da bomba é desprezível perto do que a turbina produz. Se comprimíssemos vapor (gás), com volume específico centenas de vezes maior, o trabalho seria enorme — é por isso que o ciclo Rankine condensa o vapor totalmente antes de pressurizar, em vez de seguir um ciclo de Carnot a dois fluidos. Informe o volume específico e as pressões de saída e entrada da bomba.
Related Tools
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.
Boost Converter (Step-Up)
Calculate the output voltage of a boost (step-up) DC-DC converter in continuous conduction, V_out = V_in ÷ (1 − D), from the input voltage V_in and the duty cycle D (0 to 1). The result, in volts, is always greater than the input — the boost converter raises voltage by storing energy in an inductor and releasing it in series with the source. As D approaches 1, the output tends to infinity (limited by real losses). It is used in supplies that must step up voltage (LEDs, batteries, power factor correction) and in photovoltaic systems. Enter the input voltage and the duty cycle.
Buck Converter (Step-Down)
Calculate the output voltage of a buck (step-down) DC-DC converter in continuous conduction, V_out = D × V_in, from the duty cycle D (0 to 1) and the input voltage V_in. The result, in volts, is always less than or equal to the input — the buck converter lowers voltage efficiently (without dissipating the excess, unlike a linear regulator), by switching rapidly and filtering with an inductor and capacitor. Varying the duty cycle adjusts the output from 0 to V_in. It is the most common topology in switching power supplies and point-of-load regulators. Enter the duty cycle and the input voltage.
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