Pneumonia is a disease which causes high mortality in children under five years old, particularly in developing countries. This paper proposes a novel application of ultrasound video analysis for the detection of pneumonia. This application is based on the processing of small video chunks, in which an image processing algorithm analyzes each frame to get some overall video statistics. Then, based on these quantities, the likeness of presence of pneumonia in the video is determined. The algorithm exploits different geometrical properties of typical anatomical and pathological features that commonly appear in lung sonography and which are already clinically typified in the literature. Our technique has been tested on different transverse thoracic scanning protocols and probe's maneuvers, thus, under a variety of clinical and usage protocols. Then, it can be targeted towards screening applications. We present encouraging results (AUC measure between 0.7851 and 0.9177) based on the analysis of 346 videos with an average duration of eight seconds. The analyzed videos were taken from children who were between three and five years old. Finally, our algorithm can be used directly as a classifier, but we detail how its performance may be enhanced if used as a first stage of a larger pipeline of other complementary pneumonia detection processes.