The formulation of artificial dissipation terms for a semi-implicit, pressure based flow solver, similar to SIMPLE type formulations, is presented and is applied to both the Euler and the Navier-Stokes equations. The formulation uses generalized coordinates and a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations. The relationship between SIMPLE and time marching formulations is discussed briefly. The artificial dissipation inherent in some commonly used semi-implicit formulations, e.g. upwind differencing, powerlaw, QUICK and pressure weighting, is investigated. The scheme used here includes these dissipation terms directly, but retains the ability to mimic previous schemes. The potential for errors introduced by the simultaneous use of artificial dissipation in the continuity equation and central differencing of convective terms, is revealed. The effect of the amount of dissipation on the accuracy of the solution and the convergence rate is quantitatively demonstrated for two-dimensional inviscid flow in a mildly curved duct, three-dimensional laminar flow in a square cross section elbow with strong secondary flows, and two-dimensional turbulent flow through a turbine nozzle. The spurious effects of artificial dissipation, particularly second order dissipation, inherent in some commonly used algorithms, is clearly shown. The effect of artificial dissipation on the convergence rate is also demonstrated. The main conclusion drawn from the results is that the minimum amount of artificial dissipation that gives the required accuracy, but also an adequate convergence rate for a particular case, has to be used. This amount of dissipation is case dependent. The direct inclusion of artificial dissipation terms provides control over the amount of dissipation used.