A simple technique to simultaneously induce fluid flow through an individual nanopipe and measure the flow rate and the pressure difference across the pipe is described. Two liquid drops of different sizes are positioned at the two ends of the nanopipe. Due to the higher capillary pressure of the smaller drop, flow is driven from the smaller drop to the bigger drop. The instantaneous pressures of the two drops are estimated from the drops' shapes and sizes. The flow rate is estimated by monitoring the sizes of the drops as functions of time with a microscope and a video camera. A theory that correlates the drops' sizes and the flow rate is derived. Measurements are carried out with an ionic salt and glycerin to estimate the effective tube radius of the nanopipes with diameters ranging from 200 to 300 nm. The tubes' diameters are independently measured with a scanning electron microscope. The method is also verified by tracking the motion of fluorescent particles through the nanopipe. The paper provides a simple technique for studying extremely low flow rates in nanofluidic systems. When working with low-evaporation fluids such as ionic salts, the measurements can be carried out with an electron microscope.