A leaking duct carries a flow that is a characteristic of several applications. Devices for cross-flow microfiltration are composed of a duct, the walls of which are semi-permeable membranes. In subsurface irrigation, the walls of watering pipes can be of porous clay, whereas the watering hoses are riddled with holes or made of porous material, in surface drip irrigation. In these applications, the first approach consists of assuming that the flow concerns a pure fluid (as in a microfiltration system operating at a very low species concentration), and that the wall's leakage depends only on the local pressure difference between both inner and outer sides of the wall.