The onset of drainage of liquids from fluid-handling components with two or more orifices was evaluated. The components were filled with water, ethylene glycol, or ethyl alcohol and oriented vertically with their orifices facing downward. The lower end of the components was slowly raised toward the horizon. No flow occurred until a critical angle of inclination was reached. The resistance to drainage was greatest for small, closely spaced orifices and declined precipitously as the size and spacing of the orifices increased. The onset of drainage was successfully modeled as a balance between the hydrostatic pressure in the bulk liquid and the Laplace pressure of the air-liquid interfaces present within the orifices.