So, I gave it a go, and of course it went wrong at first... :)
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At any rate, I now know how to replicate a kitchen!
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Then I found an old thread on an American forum:
http://www.apug.org/forums/forum43/44875-kodak-tray-siphon-2.html
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And that’s how it worked: turn the tap on full so that a lot of water flows out. Use your fingers to cover the suction holes on the sides until the water gurgles out of the spout, then let go. Then it sucks up as much water as flows in, which means the bowl doesn’t drain properly if you hang the thing too low. Carefully turn the tap back down so that there’s still a flow, but the vacuum doesn’t break. And then it just carries on. It just keeps slurping away.
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A deeper tray would therefore be useful, or you can just water 1 or 2 sheets. With PE it doesn’t really matter, as it’s only for a few minutes anyway.
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With baryta, I’d perhaps use a circulation pump; otherwise, you do end up using quite a lot of water.
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I still need to tinker with the hose connection – it wasn’t properly sealed, which is why the kitchen got wet.