Model Mathematics

PL = Pm - (R omega \frac{VT}{2.0} \sin (time omega) + E (2.5 - (\frac{VT}{2.0} \cos (time omega)))) omega = \frac{2.0 3.141}{5.0} QA = q + Dc (pc - pac) + Do (po - pao) \frac{d}{d time} (PA) = \frac{Pm E}{PA} QA + delta_PL \frac{d}{d time} (PL) = delta_PL \frac{d}{d time} (fo) = \frac{1.0}{VA} (Do (po - pao) + qi (foi - fo) - (fo (Dc (pc - pac) + Do (po - pao)))) \frac{d}{d time} (fc) = \frac{1.0}{VA} (Dc (pc - pac) + qi (fci - fc) - (fc (Do (po - pao) + Dc (pc - pac)))) foi = \{\begin{matrix} fo if VT < VD \\ \frac{fo VD + fom (VT - VD)}{VT} otherwise \end{matrix} fci = \{\begin{matrix} fc if VT < VD \\ \frac{fc VD + fcm (VT - VD)}{VT} otherwise \end{matrix} \frac{d}{d time} (po) = \frac{Do}{sigma Vc {(2.0 + \frac{4.0 Th}{sigma} df_dpo)}^{1.0} (- (fo (PA - pw) po))} \frac{d}{d time} (pc) = \frac{Dc}{sigma_c Vc} (pac - pc) + \frac{delta l2}{sigma_c} h z - (delta r2 pc) \frac{d}{d time} (z) = delta r2 sigma_c pc - (delta l2 h z) \frac{d}{d po} (f) = df_dpo