What is the thrust equation using the velocity in and out of a turbine?
$$T=\dot m (v_{ex} - v_{\infty} )$$
What is the thermal efficiency for a Brayton cycle? (Using the more accurate method)
$$\eta_{th, B}=\frac{W_{net}}{q_{in}}$$
What is the backwork ratio equation?
$$\frac{W_{in}}{W_{out}}$$
What is the isentropic relation between temperature and pressure?
$$\frac{T_2}{T_1}=(\frac{P_2}{P_1})^{\frac{\kappa-1}{\kappa}}$$
What are some notable associated principles of the Carnot Cycle?
It is an ideal heat engine, it is reversible, it provides the highest thermal efficiency, it is the best model for an actual heat engine, and it cannot be built!
In Layman's terms, what is the Brayton Cycle?
An ideal cycle for gas turbine engines.
For a compressor, why is it that the actual enthalpy of the outputted air is greater than the ideal enthalpy?
Because the enthalpy with increase due to the nature of the compressor, but the output enthalpy will also increase due to heat transfer with the compressor. This heat transfer is not reversible, hence, not ideal.
For isentropic, polytropic, and isothermal processes, what is the cooling amount for each and how does the temperature change?
For isentropic, there is no cooling, so T increases. For polytropic, there is some cooling, so T mildly increases. For isothermal, there is the most cooling, so T remains constant.
What is the gas constant, R, in terms of specific heat at a constant pressure and specific heat at a constant volume?
$$R=C_p - C_v$$
What is the heat capacity ratio in terms of specific heat at a constant pressure and specific heat at a constant volume?
$$\gamma=\frac{C_p}{C_v}$$
What is the isentropic efficiency of a compressor?
$$\eta_{c}=\frac{h_{2s}-h_1}{h_2-h_1}$$
What is the isentropic efficiency of a turbine?
$$\eta_{t}=\frac{h_3-h_4}{h_3-h_{4s}}$$
When is entropy generation equal to zero for a process?
When the process is reversible.
What general assumption can we make about entropy generation if a process is irreversible?
$$S_{gen}>0$$
What is the 1st Gibbs' Eq?
$$ds=\frac{du}{T}+\frac{Pd\nu}{T}$$
What is the 2nd Gibbs' Eq?
$$ds=\frac{dh}{T}-\frac{\nu dP}{T}$$
What is the equation for delta S in terms of temperature and volume?
$$\Delta S=C_v \ln{\frac{T_2}{T_1}}+R \ln{\frac{V_2}{V_1}}$$
What is the equation for delta S in terms of temperature and pressure?
$$\Delta S=C_p \ln{\frac{T_2}{T_1}}-R \ln{\frac{P_2}{P_1}}$$
What is the Clausius inequality?
$$\oint \frac{dQ}{T} \le 0$$