Total Energy of a system on a unit mass basis

    \[e=\frac{E}{m}(\frac{kJ}{kg})\]

Kinetic Energy

    \[KE=m(kg)\frac{v^2(m/s)^2}{2}(kJ/kg)\]

Kinetic Energy on a unit mass basis

    \[KE=\frac{v^2(\frac{m}{s})^2}{2}(kJ/kg)\]

Potential Energy

    \[PE=mgz(kJ)\]

Potential energy on a unit mass basis

    \[PE = mz (kJ/kg)\]

Internal Energies

    \[E=U+KE+PE=U+\frac{v^2}{2}+gz(kJ/kg)\]

Mechanical Energy

    \[e_{mech}=\frac{P}{\rho}+\frac{v^2}{2}+gz\]

Mass flow rate

    \[\dot{m}=\rho \dot{V} = \rho A_c V_{avg} (kg/s) where A_c =\pi D^2/4\]

Energy flow rate

    \[\dot{E}=\dot{m}e (kJ/s) or (kW)\]

The work done per unit mass

    \[w = W/m (kJ/kg)\]

Work

    \[W = F\Delta s (kJ) or W = Fs(kJ)\]

where s is shaft work

    \[s =(2\pi nT)\]

Electric Work

    \[\dot{W_e} = VI(W)\]

Torque T

    \[T=Fr\]

Work Shaft

    \[\dot{W_{sh}}=2\pi \dot{n}T (kW)\]

Conduction Heat Transfer

    \[Q_{cond}=-Ak_t\frac{\Delta T}{\Delta x} (W)\]

Convection Heat Transfer

    \[Q_{conv}=hA(T_s-T_f)(W)\]

Radiative Heat Transfer

    \[Q_{rad}=\mathcal{E} \sigma A(T_s^4-T_f^4) (W)\]