  We have used the integral form of the conservation equations, to find a cubic
formula for the drop size in liquid sprays in cross flows. Similar to our work
on axial liquid sprays, the energy balance dictates that the initial kinetic
energy of the gas and injected liquid be distributed into the final surface
tension energy, kinetic energy of the gas and droplets, and viscous dissipation
incurred. Kinetic energy of the cross flow is added to the energy balance.
Then, only the viscous dissipation term needs to be phenomenologically
modelled. The mass and energy balance for the spray flows renders to an
expression that relates the drop size to all of the relevant parameters,
including the gas- and liquid-phase velocities. The results agree well with
experimental data and correlations for the drop size. The solution also
provides for drop size-velocity cross-correlation, leading to drop size
distributions based on the gas-phase velocity distribution. These aspects can
be used in estimating the drop size for practical applications, and also in
computational simulations of liquid injection in cross flows.
