Abstract An unsteady fluid flow in a pipe with an orifice or an obstruction is studied. The velocity in the pipe and the force on the obstruction are calculated numerically. Several different forcing functions are considered for this unsteady flow system: a sinusoidal forcing function, a step forcing function, and a ramp forcing function. The response to the sinusoidal forcing function as a function of frequency for the fluid flow system is the main focus of this paper. The results for this non-linear system are found to be significantly different from those of a linear system. The results and the method of this study may be applied to the calculations of unsteady forces acting on objects such as check valves or probes in a pipe with unsteady turbulent flow.