A mathematical model was developed for the rapid filling of an initially dry pipe. The pipe was assumed to be horizontal and to contain an orifice at the downstream end. The key elements of the model were the momentum equation governing the flow of the water, the thermodynamic equations for the compression and discharge of the entrapped air, and the equations for waterhammer resulting from the impact of the water with the orifice. A computer program of this model was then developed and tested. After initial testing, the model was used to examine the magnitudes of the pressures that could be produced from waterhammer and air compression for various lengths of pipe. The effects that different orifice diameters had on the flow were also analyzed. The results indicated that extremely high pressures can be generated from both waterhammer and air compression during the filling process. These pressures tend to increase as the orifice diameter is reduced. However, below a certain size the orifice constricts the air discharge enough to stop the water prior to its reaching the orifice. This results in an oscillatory behavior of the flow, and the relation between waterhammer and orifice diameter becomes much more difficult to predict. The results also demonstrated that these pressures are significantly reduced for longer pipe lengths, and for pipes with smaller diameters or otherwise offering greater frictional resistance to the flow. / M.S.