What happens is that the pump will cavitate if run too fast , can`t **** the oil up fast enough . Cavitation destroys pumps . Now , you say the rpm is a " little higher " . How much higher ? A few rpm ( +/- 50 will only effect flow output ) . You didn`t say what kind of a pump .... gear , gerotor ??? All pumps have a max rpm and definite suction line requirements that must be followed . Some industrial gear pumps can run up to 3000 + rpm , while Ag pumps generally are much lower and the duty cycle isn`t continuous as the industrial stuff is . Why don`t you get the pump model number , manufacturer etc and go to their site and see what they say their specs are .
BTW , I used to work for Parker with the Hydraulics Group and have torn down many pumps over the years . Most pumps are destroyed by only several things ..... cavitation , heat and dirt in the systems . We rarely saw pumps that were overspeeded ( if such a word exists ) .
As far as hp requirements , there are several formulas .... HP = (gpm x psi) divided by (1714 x pump efficiency) . Assume 85% eff and you`ll be safe as most pumps run about 90% overall . Notice I said overall , as pump efficiency consists of volumetric and mechanical efficiency .
A general formula for flow is ( rpm x displacement in cubic inches) divided by 231 ( I assumed 100% volumetric efficiency ) .
Have I confused you now ???