Water heater leak?

Just woke up in the middle of the night because I heard an unusual noise. I followed the sound of running water to the basement utility room where our 12 year old Rheem gas water heater and furnace/air conditioner are located. First I noticed a puddle of water on the floor beneath the water heater. Not a good sign. Fortunately, the concrete floor slopes properly to a nearby drain, so there's no other damage. Seeking the source of the water, I saw a steady drip of water from the vent pipe above the gas water heater, falling onto the top of the water heater, running down its sides, and onto the floor. That vent pipe slopes approximately 45 degrees up and away from the water heater for a few feet to a wye junction where it joins the vent from the gas furnace/air conditioner, then continues vertically through the first floor and attic before exiting through the roof.
The water dripping from the vent made me think the problem was related to condensation, but why did I hear water running continuously to the water heater? Since the water running down the side of the water heater was flowing over the area of the pilot cover, I immediately shut off the main gas valve on the front of the water heater. As an added precaution, I closed a valve in the gas line supplying the wwater heater. Next, I tried to shut a very stiff valve on the cold water supply line to the water heater, but the sound of running water continued. Finally, I shut off the main water valve to the entire house, and the sound of running water ceased.
In a few short hours, my wife will awaken and unhappily discover there's no running water. Although I can turn the water back on temporarily, there'll be no hot showers until I figure out what's going on and fix it. Naturally, it's Sunday, so calling a plumber will involve extra expense, and I'm probably capable of fixing it if I knew what was wrong. Any ideas? Thanks in advance.
Jim Lincoln, Nebraska
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Jim Z wrote:

The "vent" is the flue pipe to the chimney. Inside the heater, the flue is a ~4" diam steel tube which runs coaxially down to the "firebox". So, the tube has hot flue gas on its inside and water pressure on its "outside".
Your heater has failed by having that central flue perforate. Full water pressure is pushing thru a pinhole(s) and sending a fine stream of water up the flue.
You'll have to be able to shut off the valve feeding the heater in oder to have *any* water in the house. Try loosening the packing nut on the valve; often the stem gets so corroded making the handle hard to turn.
Jim
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