In an engine with a gas generator engine cycle, the turbopump has to do more work in pumping, if the thrust chamber operating pressure is raised. This requires an increase in turbine gas flow, which, when exhausted, adds little to the engine specific impulse. If the chamber pressure is raised too much, the decrease in performance due to an excessive portion of the total propellant flow being sent through the turbine and the increased mass of the turbopump will outweigh the gain in specific impulse that can be attained by increased chamber pressure and also by increased thrust chamber nozzle exit area ratio. Outline in detail a method for determining the optimum chamber pressure where the sea$-$level performance will be a maximum for a rocket engine that operates in principle like the one shown in Fig. $1-4.$

FIGURE $1-4.$ Simplified schematic diagram of a liquid propellant rocket engine with one type of turbopump feed system and a separate gas generator, which generates "warm" gas for driving the turbine. Not shown are components necessary for controlling the operation, filling, venting, draining, or flushing out propellants, filters, pilot valves, or sensors$.$ This turbopump assembly consists of two propellant pumps, a gear case, and a high$-$speed turbine. Many turbopumps have no gear case.