In this study, the flow characteristics of a FPN (Fountain Pen Nano-Lithography) using active membrane pumping are investigated. The FPN has integrated chamber, micro channel, and high capacity reservoir for continuous ink feed. The most important aspect in this probe provided control of fluid injection using active membrane pumping in chamber. The flow rates in channel by capillary force are theoretically analyzed, including the control of the mass flow rates by the deflection of the membrane. The above results are compared with the numerical simulations that calculated by commercial code, FLUENT. The velocity of the fluid in micro channel shows linear behaviors. And the mass flows are proportional to the second order function of the pumping pressure that is imposed to the membrane.