IRP=33 Three-phase Parker's function

IRP = 33 Three-phase functions of Parker et al. (1987).

m = 1 - 1/n

${\bar S_g} = {S_g}/(1 - {S_m})$

${\bar S_l} = ({S_l} - {S_m})/(1 - {S_m})$

${\bar S_n} = ({S_l} + {S_n} - {S_m})/(1 - {S_m})$

${k_{rg}}\quad = \sqrt {{{\bar S}_g}} \;{[1 - {({\bar S_n})^{{1 \mathord{\left/ {\vphantom {1 m}} \right. } m}}}]^{2m}}$

${k_{rl}}\quad = \quad \sqrt {{{\bar S}_l}} \;{\left\{ {1 - {{\left[ {1 - {{({{\bar S}_l})}^{{1 \mathord{\left/ {\vphantom {1 m}} \right. } m}}}} \right]}^m}} \right\}^2}$

$k_{rn} = \sqrt{{\bar S}_n - {\bar S}_l}\left\{ \left[1 - \left(\bar{S}_l\right)^{1/m}\right]^m - \left[1 - \left(\bar{S}_n\right)^{1/m}\right]^m \right\}^2$

where $k_{rg}$, $k_{rl}$, and $k_{rn}$ are limited to values between 0 and 1, with $S_m$ = RP(1), and n = RP(2).