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This paper present a mathematical study on drag reduction by polymer additive such as poly isobutylene (PIB) with kerosene in turbulent pipe flow by using computational fluid dynamic commercial package program (COMSOL 4.4) solution. Theoretically the computational study was used to calculate the pressure drop in two dimensions geometric model with 6m length and 80 mm width as a diameter of the pipe, Geometric shape has been drawing by tools of the program windows, and to simulated the flow region mathematically the flow region is divide into very small parts (mesh generation). The model that used in the mathematical modelling method was (k-ɛ ( mathematical turbulent model to study the internal pipe flow properties. The continuity and momentum equations and two k-ɛ model equations have been solved by the program to obtain the theoretical results. There variables that used in the theoretical study were effective density, effective viscosity, inlet velocity, and outlet pressure. The boundary condition was inlet and outlet velocity, temperature, and pressure of flow, and the velocity (u=0) at the pipe wall. The theoretical calculations show that the velocity and drag reduction percentage increases with polymer concentration and volume flow rate increasing where maximum DR% is 15.8% at volume flow rate 500 l⁄min with polymer concentration 100 ppm, pressure drop decreases with polymer concentration increasing. Friction factor decreases with polymer concentration increased, also shear stress decrease with polymer concentration increasing.

MATHEMATICAL MODEL TO INVESTIGATE THE DRAG REDUCTION OF KEROSENE WITH POLYMER UNDER TURBULENT FLOW