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In a hot water system, static head refers to the vertical distance that water must be pumped against gravity. This static pressure has a significant effect on the output of the recirculating pump. As the static head increases, the pump must work harder to overcome this pressure. Therefore, the higher the static head, the greater the resistance the pump faces, which can directly reduce the flow rate, measured in gallons per minute.

When the pump operates under these conditions, it may not maintain its designed flow rate due to the additional pressure required to move the water to the desired elevation. Consequently, the correlation between static head and pump output is critical for understanding system dynamics.

Regarding the other options, the temperature of the water affects the viscosity and density, but it doesn't directly relate to how static head influences the output of the pump in a straightforward manner. Therefore, the notion that the static head will reduce the flow rate is accurate and reflects the fundamental principles of pump operation in fluid mechanics.