Under which conditions will the rate of flow of a liquid through a metering orifice be the greatest?

The rate of flow of a liquid through a metering orifice is influenced by the pressure differential between the upstream (where the liquid is) and the downstream (where the liquid is flowing to). The greater the pressure difference, the higher the flow rate through the orifice.

In the correct option, unmetered pressure at 17 psi and metered pressure at 5 psi create a significant pressure differential. The liquid experiences a higher pressure from the unmetered side, enabling it to flow through the orifice more vigorously compared to scenarios where the pressure differential is lower. This substantial difference of 12 psi (17 psi - 5 psi) provides a strong driving force for flow.

In contrast, other options present lower pressure differentials. For instance, metered pressure matched with atmospheric pressure does not create any driving force, while unmetered pressure at 5 psi combined with metered pressure of 5 psi results in no effective flow. The pressure conditions must favor the flow from higher pressures to lower pressures for optimal flow rate through the metering orifice. Thus, the scenario with 17 psi unmetered pressure and 5 psi metered pressure results in the greatest flow rate.