Those normally work in 30min increments minimum, this stays on for 20 seconds, once a week. I already own a "smart outlet" so the cost for me would be less than $10 to build this, I just got into growing herbs and this would be a really awesome setup.
This wouldn't work if you want 1 minute a week (since the cycle repeats every 35 minutes), but for hydroponics sometimes you want a short duration with very frequent repetitions, and the electronic timers (which are preferable in most other ways) don't provide enough on/off cycles per day or week.
Interesting, I did some more searches and found this http://smile.amazon.com/Digital-Programmable-Socket-Energy-S... According to the Q&A you can get it down to second acuracy so you could do the 20 seconds. I'd much rather do this than a wifi switch that I need another system to toggle it.
I wonder if you could chain two timers, picking their periods and durations appropriately to get a much longer combined period with the correct duration.
Well, you could use 2 timers with the same period, if they are accurate.
You would plug in timer 1, so that its output (output 1) is on. You would set timer 2 so that output 2 would turn on as soon as timer 2 receives power. When there are only 30 seconds left in timer 1's on cycle, you would plug timer 2 into a separate outlet.
Since they are synced, but only overlap by 30 seconds, they will only both be on for 30 seconds. You would then need some kind of AND that would only turn on the pump if output 2 and output 1 are both on.
It may be possible, but perhaps not, to just lower the pump output so that it takes 30 minutes to water the plant. That might be too little output to work though, because that is 2 orders of magnitude longer.
"A Word on WiFi Sockets: They suck. They take the simplest operation of closing a circuit and abstract it in a shitty smartphone app that only works half the time."
Short interval timers are a bit harder to come by, as several others have mentioned, but they do exist and aren't very expensive. E.g. this one can go as short as one minute per week:
