Start of a Water Rocket -
Course of events

-0.067 s
 

0.0 s  Trigger
ring down

0.067 s
 

0.13 s
 

0.2 s
 

 0.27 s

0.33 s

 0.4 s

 1.07 s

 another start

-0.067sec

Rocket, 1 liter, with 200ml water, at 8 bar pressure, waiting for the pull on the trigger line.

0.00 sec

Trigger ring (black) is pulled down, the rocket does just barely move.

0.067 sec

The rocket has left the picture already!
Just above the launch tube: a horizontally oriented cloud has formed. It is produced by the air inside the launcher which escapes right after the rocket leaves the launch tube.
Middle: the water column. The top of it is dispersed by the air that came out of the rocket after the water. This produced the cloud in the middle of the picture.
The air escaping right after the water has a temperature of about -50°C. This low temperature results from the adiabatic expansion of the pressurized air during the phase of water ejection.
Top: After the ejection of the water, all remaining compressed air is ejected as well. This is another fast adiabatic axpansion, which lowers the temperature to about surprisingly low -130°C. This air is very humid, forming tiny frozen ice crystals, which give the rocket exhaust temporarily the appearance of smoke.

acceleration

From the original pictures (the ones above are cut down to save file size) I took the following measures:
known launcher length:   0.65 m
distance from launcher to upper pic margin:   s=3.25 m (the rocket is somewhere above that). For the minimum average rocket acceleration, we get from s=1/2*a*t²   :
     a >= 2*s/t² = 1448 m/s² or 148 G
Too bad we can't really see where the rocket is at 0.067 sec: if it was at say 4,25 m above the launcher instead, the average acceleration results in 193 G.

0.13 sec

The high pressured clouds from before have expanded to ambient pressure. There is only little change in the size of these clouds until 1.07 sec.

The movements of the water are very interesting. Clifford Heath wrote this convincing explanation: "Remember that a good water rocket will eject the last of the water while the water still has an upwards velocity! Optimum rocket efficiency comes when the ejected mass is stationary - it carries no kinetic energy. Obviously you cannot lift off under that condition though!  So the initial ejecta travels downwards, and the final ejecta upwards, and somewhere in the middle the optimum is passed."

This can be seen very clearly on these pics.

0.2 sec

The big water drops have been thrown up, the smaller ones follow.

0.33 sec

The first of the thrown up water drops falls down again.

1.07 sec

The last drops which are visible on the video fall down. Smaller drops keep falling for a while in the surrounding of the launcher.

another start

The last picture shows the same rocket from another start sequence, with a wider viewing angle, at a similar position as in the 0.067s position above. No accurate time mark can be given. Pressure has been less, therefore the launcher cloud has not developed as clearly. The -100°C water "smoke" has developed similarly as above. The rocket can be seen just above the tree line.

While you have read the above, probably this animated picture has been downloaded. It is from the same video as the pics above, presented in 3x slow motion: