How to calculate rotor flux of the three phase squirrel cage induction motor?
I don't think the leakage rotor magnetic field it has to be included (since the stator and rotor main magnetic field has to be the same).
However, it can be calculated using T equivalent diagram, the current \$I_{s}\$. At first calculate the equivalent impedance of parallel \$X_m\$ with \$X_{rl}\$ and \$R_r/s\$ and then divide \$V_{sn}\$ by total impedance \$R_{s}+jX_s+jX_m\$||(\$R_{r}/s+jX_{lr}\$).
The result will be the same. \$I_r\$ you can calculate by dividing the \$I_s\$ voltage drop on the equivalent impedance of \$jX_m\$ and \$R_r/s + jX_{lr}\$ by \$Z_r = R_r/s+jX_{lr}\$.
I think the flux units are average values but \$I_s\$ and \$I_r\$ are RMS.
\$I_{av} = 1/π\int_{ωt = 0}^{ωt = π} I_{max}*sin(ωt) \,dt = 2*[I_{max}]\$/π
Given that \$I_{rms}\$ = \$I_{max}/√2\$
\$I_{av}\$ = \$[2*√2*I_{rms}]/π\$