Antenna design for radio energy emission into a fresh-water test tank
why is my resonance antenna length longer than my calculated value?


I calculate wavelength at 76 mm for sea water with a conductivity of 4 S/m using this formula: -

\$\lambda=1000\sqrt{\dfrac{10}{f\cdot \sigma}}\$ = 76 mm

Taken from this document.


  Could it be that the RF field will be disturbed by the air around the
  test tank and if how would this be related to the length?


No, because the attenuation at 434 MHz will be about 721 dB per metre. I used the same document as reference with the formula being: -

Attenuation/metre = \$0.0173\sqrt{f\cdot\sigma}\$ = 721 dB/m

This means, that given the size of your tank, the air outside the tank would be quite invisible due to the massive attenuation factor.


  If I would like to emit as much RF energy as possible into the water,
  what do I have to respect in my antenna design?


100 mW should be OK but this is very specialist and I've never been one for respecting antennas too much. Just make sure you know the conductivity of the water and don't use it to try and ward-off sharks because the range at 433 MHz is tiny.