In the current research, we dealt with the numerical method of Newtonian flow through the conical nozzle under incompressibility constraint by using a Taylor Galerkin Pressure Correction (TGPC) finite element algorithm. The governing equations that describe such problem consist of time-dependent equations for the conservation of momentum and continuity equation. The essential feature of this investigation is concerned with the effect of outlet dimeter of nozzle, length of the cylinder and conical angle on the component of solution. There, we found that the levels of velocity and pressure are increased as these parameters increase, it was found that the maximum velocity increased from 38.39 to 1254.67 when the ratio  increased from 1 to 5 and the maximum pressure also increased from 753.83 to 1254.67. The effect of conical angle was also studied, increasing the β angel from 21.8 to 90 resulted an increasing in the maximum velocity from 13.53 to 30.79 and an increase in the maximum pressure from 214.26 to 615.7. While the maximum velocity decreased from 675.8 to 67.79 when the outlet diameter increased from 0.5 to 1.5 also the maximum pressure decreased from  to 2268.21.