Overall efficiency ( \eta_total = 1 - \exp\left( -\frac6 Q_l \eta_d xQ_g d_d \right) ), where ( x ) = throat length, ( Q_l ) = liquid flow rate, ( Q_g ) = gas flow rate.
More refined, defines penetration ( P_t = 1 - \eta ): [ P_t = \exp\left( -\frac2 \rho_l Q_l \eta_d L_td_d \rho_g Q_g \right) ] Where ( L_t ) = throat length, ( \rho_l ) = liquid density. This model explicitly includes droplet size prediction via Nukiyama–Tanasawa or Boll’s droplet diameter correlation: [ d_d = \frac0.5 \sigma\rho_g v_t^2 + 0.15 \left( \fracQ_lQ_g \right)^1.5 ] (σ = surface tension).
Accounts for droplet acceleration: [ \Delta P = \frac12 \rho_g v_t^2 \left(1 - \fracA_t^2A_e^2\right) + \fracLG \rho_g v_t^2 \left(1 - \fracv_dv_t\right)^2 ] Where ( v_d ) = droplet velocity at throat exit, requiring iterative solution.