I think rather similarly, Noel.
Let’s examine what each fault might do:
A leaking piston-ring would be fairly obvious by water squirting out of the end of the pump.
A badly-leaking bypass valve should show in the tank.
A feed clack stuck closed would cause a hydraulic lock if all the other valves work properly. If the water can find somewhere to squeeze through it may show as jerky running by the locomotive.
What if the pump’s inlet valve is not closing? It ought under boiler pressure, reflected by the water pressure within the pump, but the pump is working enough for it to return water via the bypass, so the inlet can’t be sticking fully open.
On the other hand…
A sticking inlet valve with the bypass closed would cause the water simply to oscillate in the pump and pipe. If the tank oulet is visible that should show if water is simply going backwards and forwards, although this would be hard to observe on a locomotive under way.
Yet the bypass returns a healthy flow? Well, the water will take the line of least resistance, and if the inlet valve is not fully closing more water will escape via the open bypass than will go back through the inlet.
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Clive suggests:
Back-flow through the hand-pump. Only if they share plumbing – and again this needs non-return valves returning.
An air-lock. Unlikely. The air will simply compress to equal the water-pressure but if all else is working it will not impede the flow. It is more likely just to be pushed into the boiler, though a small bubble might occupy the top of the clack-valve chamber. In fact reciprocating pumps and hydraulic rams (the sort that pump stream water) were often fitted with large air-vessels on their outlets, to remove shock and smooth the flow.
…
Any other possibilities?
Is the pump working but simply not passing enough water to make up for that evaporated, due to some obstruction upstream?
E.g.
Tank strainer clogged or too small area?
Dirt, solder or flux in the pipe from tank to pump?
A kinky bend or other damage partially closing the pipe?
Inherently restricted inlet plumbing: sharp elbows, perhaps the pipe a bit undersize, inlet ball not lifting enough?
Or lifting too high so it loses some water on its way back down?
Inlet valve ball partially obstructing the valve outlet?
Fast running could affect it, if the pump is only just matched to the maximum steam demand, by the barrel not being able to fill fully at each inlet stroke. This is particularly so if the inlet pipework is too restrictive. Reciprocating pumps are not too good at fast operation.