I have an Arduino Nano that needs to be powered by a battery that can fit inside a 29mm tube. I have a barometer connected with the Arduino and the entire system only needs to operate for around 30 seconds. Any suggestions for such a battery?
An Arduino Pro Mini or clone (3.3V, 8 MHz) would be a much better choice, as you can remove the regulator, the power LED and have the equivalent of a "bare bones" processor.
Using sleep modes, it and a barometer module could run for years on a coin cell. Excellent low power tutorial here.