Thread: Trajectory of a jet of water

Hi!

As the title suggests, my question concerns the trajectory of a jet of water, for example arising from water flowing out of a vessel with a hole in it. The standard approach to this phenomenon would be to treat the jet of water as undergoing free fall, and approximating its trajectory by a quadratic curve.

However, I have some doubts about the validity of this model, specificially, the assumption that the water of the jet undergoes free fall. There are obviously internal forces in the jet of water, so when concidering a small segment of said jet, there is, in my opinion, not only the force of gravity to consider, and therefore we are not dealing with free fall.

Any attempts at shedding some light on this issue are most welcome.

I think a free fall would be a very good approximation, neglecting air resistance. What internal forces do you think would exist? As the water exits the hole, it is depressurized. If the stream of water is a constant velocity, the water droplets are all leaving at the same speed and undergo the same acceleration. There wouldn't be any tendency for a droplet to catch up to the droplet ahead of it. It's a liquid, so there wouldn't be any shear forces, or hardly any. The droplets would tend to form into bigger drops due to surface tension. I don't think it would signficantly alter the trajectory. As the droplets fall they will pick up speed and the stream will get thinner because the same volumetric flow rate is spread out over a larger distance. This will tend to separate the stream into smaller drops.

I think you are right. At first I mas making the analogy between the jet of water and a sequence of balls connected with springs, making the point that as the speed of the jet was increasing the separation between the water molecules would increase and thus give rise to an internal force. However, as you pointed out, the water jet merely gets thinner and the separation of the water molecules remains constant, so there is no such effect as I first suggested.

Thanks!