A theoretical model of axisymmetric turbulent fountains in both homogeneous
and stratified fluids is developed. The model quantifies the entrainment o
f ambient fluid into the initial fountain upflow, and the entrainment of fl
uid from both the upflow and environment into the subsequently formed downf
low. Four different variations of the model are considered, comprising the
two most reasonable formulations of the body forces acting on the 'double'
structure and two formulations of the rate of entrainment between the flows
. The four model variations are tested by comparing the predictions from ea
ch of them with experimental measurements of fountains in homogeneous and s
tratified fluids.