There are two general classes of mathematical problems encountered in science and engineering for which high-speed mechanical computation is required. One of these embraces those problems of such complexity that it is impractical to obtain even a few solutions by conventional analysis. In the other class are problems which may be of only moderate complexity, but in which it is necessary to obtain a large number of solutions before the results become of practical value. It is the intent of this paper to discuss some of the applications that have been made of the California Institute of Technology “electric-analog computer” to heat-transfer and fluid-flow problems of both of the classes mentioned.