The RD-170 consumes 5,300 lbs of fuel per second, including oxidizer. The turbopump produces 230,000 hp. If one assumes that roughly 1 lb of fuel is required to generate 1 lb of thrust (obviously this varies considerably), not including oxidizer. Assuming an oxidizer to fuel ratio of 3, then 3% of total fuel is used to power the turbopump. I realize there are more variables involved, but to get a rough guess, what would be the best path forward to estimate this number?
Your question is a bit confusing because of your use of "fuel" to sometimes mean "fuel" and sometimes mean "propellants". Based on my interpretation of the question here is an answer.
The RD-170 consumes ~2400 kg/s of propellant. ~1800 kg/s of this propellant flows through the preburner of which ~33 kg/s is fuel (RP-1) and ~1767 kg/s is oxidizer (O2). The RP-1 is combusted in an excess of O2.
"If one assumes that roughly 1 lb of fuel is required to generate 1 lb of thrust" that would be a terrible engine. The RD-170 produces ~7900 kN vacuum thrust while consuming ~1729 kg/s of O2 and ~665 kg/s of RP-1.
- The preburner fuel (RP-1) flow of ~33 kg/s is ~5% of the inlet fuel (RP-1) flow.
- The total preburner propellant flow of ~1800 kg/s is ~75% of the total inlet propellant flow.
Source: Cycles for Earth-to-Orbit Propulsion by Manski and Levack