Is a leaking hot water system an emergency? Usually, unless it is the relief valve pipe
A leak from a hot water tank or its pipework is worth treating as urgent, because a storage system stays connected to the mains and keeps refilling as it loses water. A tank in a laundry cupboard, an upstairs room or against a wall can wet plaster, flooring and framing well before the drip looks dramatic.
The common exception is the drain pipe from the temperature and pressure relief valve. Rheem's troubleshooting guide says it is normal and desirable for that valve to let some water escape while the system heats, roughly 1/50 of the hot water you use, because water expands by about that much as it warms.
So the first job is not to judge how much water there is. It is to find where the water starts, and the sections below go through each location in turn. Queensland's Residential Tenancies Authority lists both a serious water service leak and a breakdown of the hot water service as emergency repairs, which is a fair guide to how seriously a real leak should be taken.
