Or, instead of a leaky syphon, it could just be a very thin syphon.
Going back to first principles, what I want is to divert the rain water from the roof into the garden, and slow it down as much as possible so that it arrives days, or even weeks after falling from the sky. If I can get a syphon working between each water tank, and make it thin enough, it may be able to do this.
The speed of the fluid in a syphon depends only on the difference in height between the top of the water and the bottom of the outlet pipe. According to wikipedia, it's the square root of the height times 2g. So water in a syphon coming out of a 50cm tank will be moving at around 3 metres per second.
Converting that to volume, if you had a pipe of 1cm diameter, it would drain at 14 litres per minute. A hundred-litre tank would be empty in seven minutes. If the pipe was a millimetre in diameter, it would drain at 8 litres per hour and be empty in 12 hours. Five of these tanks in series and the water is going to get from top to bottom in 2 and a half days.
Of course the rainwater is going to have to be really clean with a pipe this thin as it would be really easy to block it. Also this would have to be in addition to a regular overflow since a pipe this thin is not going to be much help in the event of heavy rainfall.
This syphon is essential going to be the same as having a pipe coming out of the bottom of the tank, leading to the tank below. The differences are that a pipe coming out of the bottom of the tank needs a hole in the bottom of the tank, and the syphon will only start working after the tank has overflowed, and will may not start sending water down the system until it has.
Wikipedia also mentions self-priming syphons with a cotton-filled hose that will suck water up by capillary action, then send it down the other side. These are slower than an open hose, which is even better. The system would then start slowly syphon water down as soon as the bottom of the tank is wet.
Of course it may be a good idea to have a hole in the bottom of every tank since it will make them much easier to drain, unless the tanks are going to be fairly small. The drain could lead to a tap into a lower level of tank, and it would be possible to control the trickle down the system.
