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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Pump work (Rankine cycle)
In the Rankine cycle, the condensed water must be pressurized by the feed pump before it enters the boiler. The specific work spent doing so is w_pump = v × (P₂ − P₁): the specific volume of the liquid v (m³/kg, about 0.001 for water) multiplied by the pressure rise (P₂ − P₁) in kPa, giving kJ/kg. The formula holds because liquid is practically incompressible — its volume barely changes under compression, so the reversible work is simply volume times pressure change. The real cleverness of the Rankine cycle lies exactly here: since pumping liquid costs almost no energy (the specific volume is tiny), the pump work is negligible next to what the turbine delivers. Compressing vapor instead, with a specific volume hundreds of times larger, would demand enormous work — which is why the Rankine cycle condenses the steam completely before pressurizing it, rather than following a two-fluid Carnot cycle. Enter the specific volume and the pump outlet and inlet pressures.
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.
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.
PWM Output Voltage
Calculate the average output voltage of a PWM signal, V_out = (duty ÷ 100) × V_sup, from the duty cycle (in %) and the supply voltage V_sup. The result, in volts, is the effective average voltage delivered to a load (motor, LED, heater) by rapidly switching the supply on and off. Varying the duty cycle from 0 to 100% varies the average voltage from 0 to V_sup, allowing power control without dissipating energy in resistors — the basis of motor speed and LED brightness control in microcontrollers. Enter the duty cycle and the supply voltage.
Injection Shot Volume
Compute the shot volume of a plastic part by dividing the injected mass by the molten material density. The shot is the total volume of plastic injected per cycle (parts + runners), a parameter that must fit the injection barrel capacity. Together with the machine capacity, it defines how many cavities can be filled per cycle. Enter the injected mass (g) and the material density (g/cm³).
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