Energy Balance Calculator

Steady-Flow Energy Equation (SFEE)

Q − W_s = ΔH + ΔKE + ΔPE, where ΔH = ṁ_out · h_out − ṁ_in · h_in; the tool solves either Q = W_s + ΔH + ΔKE + ΔPE or W_s = Q − ΔH − ΔKE − ΔPE

Variables: Q = net rate of heat transfer, positive INTO the control volume (kW); W_s = shaft power, positive for work done BY the fluid on its surroundings, so a turbine is positive and a pump or compressor is negative (kW) — the input field ("+ = out of system") and the result caption ("Work output (turbine)" for a positive value) use the same convention. ṁ_in, ṁ_out = inlet and outlet mass flow rate (kg/s); these are entered independently, so mass conservation ṁ_in = ṁ_out is not enforced and an unbalanced pair yields a meaningless ΔH. h_in, h_out = specific enthalpy of the inlet and outlet stream (kJ/kg); ΔH = rate of enthalpy change across the control volume (kW); ΔKE = rate of kinetic energy change (kW); ΔPE = rate of potential energy change (kW). Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 5 (Mass and Energy Analysis of Control Volumes — steady-flow energy balance)

Kinetic and Potential Energy Rate Terms

ΔKE = (½ · ṁ_out · v_out² − ½ · ṁ_in · v_in²) / 1000 | ΔPE = (ṁ_out · g · z_out − ṁ_in · g · z_in) / 1000

Variables: ΔKE = rate of kinetic energy change (kW); ΔPE = rate of potential energy change (kW); ṁ_in, ṁ_out = inlet and outlet mass flow rate (kg/s); v_in, v_out = stream velocity (m/s); z_in, z_out = stream elevation above a common arbitrary datum (m); g = gravitational acceleration, fixed internally at 9.81 m/s² and not user-editable. Each numerator evaluates in watts, since (kg/s) · (m/s)² = kg·m²/s³ = W and (kg/s) · (m/s²) · (m) = W, so the factor 1/1000 converts both to kW to match ΔH. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 5 (energy transport by mass — kinetic and potential energy of a flowing fluid)

Stream Enthalpy for Water and Steam (IAPWS-IF97)

Liquid or superheated: h = h(T, P) from the IAPWS-IF97 equation of the region the state lies in. | Saturated mixture: h = h_f(P) + x · (h_g(P) − h_f(P)). | Saturated vapour: h = h_g(P).

Variables: h = specific enthalpy of the stream (kJ/kg) on the IAPWS reference state (internal energy and entropy of saturated liquid are zero at the triple point, so h_f(0.01 °C) = 0.000612 kJ/kg); T = stream temperature (°C); P = absolute stream pressure (kPa); x = vapour quality (dimensionless, 0 to 1); h_f, h_g = saturated-liquid and saturated-vapour enthalpy at P (kJ/kg). The phase menu is checked against the state: a "Liquid" stream whose T and P make it vapour, or a "Superheated" stream whose T and P make it liquid, is rejected with an explanation instead of being evaluated with the wrong phase. For the saturated phases the temperature field is not used; T is the saturation temperature at P. Range: 0–800 °C up to 100 MPa and 800–2000 °C up to 50 MPa, pressures from 0.611213 kPa. Source: IAPWS R7-97(2012), Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

Constant-Specific-Heat Stream Enthalpy (fluids other than water and steam)

h = c_p · T

Variables: h = specific enthalpy (kJ/kg), referenced to h = 0 at T = 0 °C; T = stream temperature (°C); c_p = constant specific heat taken from the built-in table (kJ/(kg·K)) — air 1.006, nitrogen 1.04, oxygen 0.919, methane 2.22, ethanol (liquid) 2.44, benzene (liquid) 1.72, toluene (liquid) 1.69, CO₂ 0.844. This branch applies only to the fluids listed above: selecting "Water / steam (IAPWS-IF97)" uses the IAPWS equations instead of this constant-c_p table. Only the eight named non-water fluids have constant-c_p entries. Source: Cengel & Boles, Thermodynamics: An Engineering Approach, 8th ed., Ch. 4 (specific heats: Δh = c_p·ΔT for ideal gases, Δh ≈ c·ΔT for incompressible liquids); values comparable to Table A-2 for the gases and Table A-3 for the liquids