therefore the L.H.S. simplifies to give Y momentum equation in Steady State  Conditions as;

 Therefore the L.H.S. simplifies to give Energy Equation in steady State Conditions as;

The above equations are written for steady, compressible, viscous, two dimensional flows in Cartesian coordinates. Where u and v are velocities in x and y directions respectively; represents internal energy per unit mass and  represents the volumetric heating that might occur. All other notations carry their usual meaning. We can simplify the above set of equations via appropriate assumptions, and obtain approximate viscous flow results.