The problem of turbulent hydraulic fracturing is considered. Despite it being
a known phenomenon, limited mathematical literature exists in this field.
Prandtl�s mixing length model is utilised to describe the eddy viscosity and
a mathematical model is developed for two distinct cases: turbulence where
the kinematic viscosity is sufficiently small to be neglected and the case
where it is not. These models allow for the examination of the fluid�s behaviour
and its effect on the fracture�s evolution through time. The Lie point
symmetries of both cases are obtained, and a wide range of analytical and
numerical solutions are explored. Solutions of physical significance are calculated
and discussed, and approximate solutions are constructed for ease of
fracture estimation. The non-classical symmetries of these equations are also
investigated. It was found that the incorporation of the kinematic viscosity
within the modelling process was important and necessary.