Solutions of one dimensional steady flow of dusty gas in an anholonomic co-ordinate system

We study the geometry of one-dimensional (i.e. unidirectional) incompressible steady dusty gas flow in Frenet frame field system (anholonomic co-ordinate system) by assuming the paths of velocities of dust and fluid phases to be in the same direction. The intrinsic decompositions of the basic equation are carried out and solutions for velocity of fluid phaseu, velocity of dust phasev and pressure of the fluid are obtained in terms of spin coefficients, i.e. geometrical parameters like curvatures and torsions of the streamline when the flow isparallel straight line i.e.ks = 0parallel andks ≠ 0, under the assumption that, the sum of the deformations at a point of the fluid surface along the stream line, its principal normal and binormal is constant