Mathematical model of a fountain with a water picture in the shape of an hourglass

Abstract

The work presents a mathematical model of a fountain providing an hourglass-shaped water image based on four of its basic parameters: height H, coefficient of contraction χ, diameter of n nozzles arrangement Dna, and coefficient of contraction location σ. The developed model makes possible to determine the angle α specifying the slope of the nozzles to the horizontal plane and determining the remaining parameters of the fountain, especially its outer diameter Df as well as the diameter of the position of the stream tops Dmax. The developed model has been implemented in an Excel spreadsheet, which enables quick conversion of desired water images. The developed model works for n≤24 nozzles, however, derived dependencies allow for a quick extension of the model for n>24.