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The pump receiving less voltage than it needs, from any cause along its supply — a tired relay, a corroded joint, an undersized repair, or a failing pump driver module. The distinction from a worn pump is the whole diagnosis, because the symptoms are identical: low pressure, low flow, and a shortfall that appears under load.

A motor's speed follows its supply voltage, so a pump a volt or two down delivers noticeably less at the top of its range while idling perfectly well. The complaint is a power loss at high load with normal behaviour around town, and a pressure reading that sags as demand rises.

Measure at the pump, not at the relay or the fuse box. The whole point is to include every joint between the battery and the motor in the measurement, and testing upstream excludes the ones most likely to be at fault. Compare the reading against battery voltage with the pump running under load — and check the earth side as carefully as the supply, since a corroded earth drops exactly as many volts and is checked half as often.