Which method is crucial for ensuring each pump can function independently in a common exhaust system?

The correct answer focuses on the importance of using a check valve in a common exhaust system. A check valve allows fluid (in this case, gas or air) to flow in only one direction while preventing backflow. This is particularly crucial in a common exhaust system where multiple pumps are used; each pump must be able to operate independently without interference from the others.

If one pump were to experience an issue or be turned off, a check valve ensures that the exhaust from that pump doesn't flow back into the system and affect the operation of the other pumps. This guarantees the integrity of the exhaust system and the safe and effective operation of each pump.

In contrast, while options such as a manual valve could control flow or isolate specific systems, they do not inherently prevent backflow. Similarly, a bypass line could create an alternate path for flow, but it does not specifically address the need to prevent backflow from affecting other pumps. A grooved joint is primarily used for making connections in a piping system but does not serve the function of ensuring one-way flow. Thus, the check valve stands out as the essential component for ensuring independent operation in a shared exhaust scenario.