Here are some of the basic engineering formulas/equations related to
energy conversion systems which are built into the Engineering
Software product line:
Continuity Equation m = vA Momentum Equation F = (vm + pA)_{out - in} Energy Equation Q - W = ((h + v^{2}/2 + gh)m)_{out - in} Ideal Gas State Equation pv = RT/MW Perfect Gas c_{p} = constant k = c_{p} / c_{v} Isentropic Compression T_{2} / T_{1}_{ }= (p_{2}_{ }/ p_{1})^{(k-1)/k} T_{2} / T_{1}_{ }= (V_{1}_{ }/ V_{2})^{(k-1)} p_{2} / p_{1}_{ }= (V_{1}_{ }/ V_{2})^{k} Combustion -- Flame Temperature h_{reactants} = h_{products} Combustion -- HHV T_{1} / T_{2} = (p_{1} / p_{2})^{(k-1)/k} T_{1} / T_{2}_{ }= (V_{2}_{ }/ V_{1})^{(k-1)} p_{1} / p_{2}_{ }= (V_{2}_{ }/ V_{1})^{k} Sonic Velocity vs = (kRT/MW)^{1/2} Mach Number M = v/vs Isentropic Flow T_{t }/ T = (1 + M^{2}(k - 1)/2) p_{t}_{ }/ p = (1 + M^{2}(k - 1)/2)^{k/(k-1)} h_{t }= (h + v^{2}/2) T_{t }= (T + v^{2}/(2c_{p})) Thrust Thrust = vm + (p_{ }- p_{a})A Cycle Efficiency Cycle Efficiency = Net Work/Heat Carnot Cycle Efficiency Carnot Cycle Efficiency = 1 - T_{heat rejection }/ T_{heat addition} Brayton Cycle Efficiency Brayton Cycle Efficiency = 1 - 1/(p_{2} / p_{1})^{(k-1)/k} Otto Cycle Efficiency Compression Ratio = V_{1}_{ }/ V_{2} Otto Cycle Efficiency = 1 - 1/Compression Ratio^{(k-1)} Diesel Cycle Efficiency Compression Ratio (CR) = V_{1}_{ }/ V_{2} Cut-Off Ratio (COR) = V_{3}_{ }/ V_{2} Diesel Cycle Efficiency = 1 - (COR^{k} - 1)/(k*CR^{(k-1) }*(COR - 1))^{ } Fuel Cell Fuel Cell Efficiency = - (G_{out} - G_{in})/HHV Heat Rate Heat Rate = (1/Cycle Efficiency)*3,412
Heat Exchanger (Heat Transfer) m_{hot}(T_{hot inlet} - T_{hot outlet})C_{p-hot} = m_{cold}(T_{cold outlet} - T_{cold inlet})C_{p-cold} Air Conditioner (AC) Operation AC Coefficient of Performance (COP) = 1/(T_{high temperature}/T_{low temperature} -1)
Heat Pump Operation HP Coefficient of Performance (COP) = 1/(1 - T_{low temperature}/T_{high temperature}) Physical Properties For each reaction species, the thermodynamic functions
specific heat, enthalpy and entropy as Cp/R = A1 + A2T + A3T^{2} + A4T^{3} + A5T^{4} H/(R*T) = A1 + A2T/2 + A3T^{2}/3 + A4T^{3}/4 + A5T^{4}/5 + A6/T S/R = A1lnT + A2T + A3T^{2}/2 + A4T^{3}/3 + A5T^{4}/4 + A7 or S/R = A1lnT + A2T + A3T^{2}/2 + A4T^{3}/3 + A5T^{4}/4 + A7 - lnp For each species, two sets of coefficients are included
for two adjacent temperature intervals, 273 to 1,000 [K]
U = H - p*v*MW or U = H - R*T G = H - S*T and u = h - p*v or u = h - R*T/MW g = h - s*T Legend: cp -- Specific Heat [kJ/kg*K] MW -- Molecular Weight [kg/kmol] R -- Universal Gas Constant [kJ/kmol*K] Gas Constant = R/MW [kJ/kg*K] H -- Enthalpy [kJ/kmol] h -- Enthalpy [kJ/kg] T -- Temperature [K] S -- Entropy [kJ/kmol*K] s -- Entropy [kJ/kg*K] p -- Pressure [atm] U -- Internal Energy [kJ/kmol] u -- Internal Energy [kJ/kg] V -- Volume [m^{3}] G -- Gibbs Free Energy [kJ/kmol] g -- Gibbs Free Energy [kJ/kg] |