There is not a fixed conversion factor between BHP and HHP. These magnitudes are used in calculations related to hydraulic pumps or turbines. BHP stands for 'Brake Horsepower' while HHP stands for 'Hydraulic Horsepower'.
In the case of a pump, BHP indicates the power transferred from the motor to the pump, while HHP refers to the hydraulic power actually transferred to the fluid. Thus, they are related according to the expression:
BHP = HHP * eff
where 'eff' refers to the pump overall efficiency.
On the other hand, in the case of a turbine the relation would be written:
HHP = BHP / eff
In conclusion, the conversion factor between BHP and HHP is the macine efficiency, so it depends always on the type of machine and its operating conditions.