The correct answer is C) develop the same flow rate across both pump elements with the discharge pressure of the second pump element being substantially higher than that of the first stage. In a two-stage hydraulic pump unit, the first stage pump element generates the initial flow, while the second stage pump element further increases the pressure of the hydraulic fluid. This allows the system to achieve a higher discharge pressure compared to a single-stage pump, without significantly changing the overall flow rate. The higher pressure from the second stage is necessary for certain hydraulic applications that require more force or power. The other options are incorrect because they do not accurately describe the primary function of a two-stage hydraulic pump. Option A would require a variable-displacement pump, option B would describe a backup system rather than the normal operation, and option D would be more characteristic of a multi-circuit hydraulic system rather than a two-stage pump.