A drilling fluid pumping system including a pump apparatus with a pumping chamber having an inlet valve and an outlet valve and a dampener system in fluid communication with the pumping chamber for damping the flow of fluid, e.g. drilling fluid, This abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure and is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims, 37 C. F. R. 1.72(b).