Plunger pumps are needed for heavy duty sludge pumping at wastewater treatment facilities. America's leading pump manufacturer Wastecorp Inc. brought their plunger pump problem to us in late 2009. It was found that when the ow rate reaches a critical value, the plunger pump starts to generate a clicking noise. A one-dimensional model was built for studying the ow of a typical plunger pump operation. The velocities and pressures are calculated at certain interesting locations. Pressure jumps have been found while opening or closing the valves. The valve motion is then modeled with considerations to its geometry. The results show that as the plunger speed reaches a critical value, the valve moves more rapidly and more likely to hit the wall and generates a noise. We also provide a methodology to study the ow across the valve in higher resolution. A nite-di erence approach to the Navier-Stokes equations are presented with the immersed boundary method. / UOIT