The image is taken from this video.
We notice that the hose in this video is always curved and never straightened. It gives us the feeling that there is always a force perpendicular to the outlet section and opposite to the flow direction applied to the fluid at the outlet section.
How did this force come from?
As shown in the figure, the fluid flows in the hose and the hose generates pressure. Affected by the pressure, the downstream diameter of the hose is small and the upstream diameter is large. Therefore, "vena Contracta" is generated at the outlet of the hose. In this way, the pressure at the outlet section of the hose will be higher than atmospheric pressure. This pressure results in a force perpendicular to the outlet section and opposite to the flow direction. This force, together with the force generated by the bending of the hose, causes the hose to swing back and forth.
Is my explanation right?
Reference:
https://en.wikipedia.org/wiki/Vena_contracta
Best Answer
In the video, by the looks of it, the tube is overall hanging down. Even when wriggling the general orientation is still down.
I don't think the vena contracta aspect makes any difference here.
How I would approach this:
I imagine the water flow initially very slow, and the rate of flow is gradually increased, to explore the entire range of rates of flow.
The lower the flow rate the lower the exit velocity of the water.
When water exits a nozzle (more generally, when any fluid/gas exits a nozzle) there is a recoil force. If the nozzle would be secured to some cart then the recoil force would propel the cart.
At low flow rate the force of gravity is larger than the recoil force at the nozzle. The larger the flow rate, the larger the recoil force. At some flow rate the recoil force will be enough to lift the nozzle against gravity.
The tube is flexible, so the tube bends. That makes the nozzle point sideways. With the nozzle pointing sideways the tube is moved sideways, and gravity has opportunity once again to pull the nozzle down.
The result is that the nozzle is violently swinging from side to side, flexing the tube all the time.
In addition there is the inertia of the water flow in the tube itself. When the water is forced to move along a bend in the tube the inertia of the water will tend to straighten the bend, contributing to the overall chaos of the motion.