In the past, numerous slip-line models have been developed and presented for continuous chip formation. However the authors of this paper recently proposed a new slip-line model for serrated chip formation in machining with rounded cutting edge. In that model, Oxley's predictive machining theory was integrated for machining of stainless steel material and the model was validated under dry cutting. The current study extends the previously developed slip-line model for orthogonal turning of AISI 304 austenitic stainless steel for various cooling/lubricating conditions. The orthogonal machining experiments were performed under dry, flood cooling, MQL (Minimum Quantity Lubrication) and cryogenic cooling conditions. Good correlations are observed between experimental work and predictions under various cooling/lubricating conditions for cutting force components and maximum and minimum chip thickness values. After achieving the good correlation, several important outputs such as the shear stress, flow stress, ploughing force, stagnation point angle, chip up-curl radius, which are difficult or impossible to measure experimentally were determined by solving the extension of the previously developed model. The lowest tool-chip frictional shear stress was achieved under MQL method whereas the highest was obtained in dry cutting. In addition, the minimum ploughing force was obtained in cryogenic cooling while the maximum value occurred in dry cutting. The stagnation point angle decreased when applying lubricant or coolant and increased with increasing cutting speed. The tool-chip contact length slightly decreased, the chip up-curl radius increased and the thickness of the primary shear zone reduced with increasing cutting speed. Additionally, lower tool-chip contact length, larger chip up-curl radius and larger primary shear zone thickness occurred while using lubricant or coolant. Higher cutting speed caused lower shear strain and flow stress and higher shear strain-rate. The highest and lowest flow stresses were obtained under cryogenic cooling and dry cutting, respectively.