Under which conditions will the rate of flow of a liquid through a metering orifice be greatest, all other factors being equal?

The rate of flow through a metering orifice is primarily influenced by the pressure differential between the unmetered and metered sections. The greater the difference in pressure, the more force drives the liquid through the orifice, thus increasing the flow rate.

In the scenario presented, option B provides an unmetered pressure of 17 psi and a metered pressure of 5 psi. This results in a pressure differential of 12 psi (17 psi - 5 psi), which significantly encourages the flow of liquid through the orifice.

This pressure differential is critical because it establishes the energy that moves the liquid; higher differentials generally lead to higher flow rates. An important consideration here is that the absolute values of the pressures themselves are not just significant; the difference between them (the differential pressure) is what dictates the flow rate.

Other options present lower pressure differentials compared to option B. Therefore, even if they have higher unmetered pressures, the actual flow will be less since the effective driving force (the pressure difference) is smaller. Thus, option B, with a pressure differential of 12 psi, yields the greatest flow rate through the orifice among the choices provided.