How Does Height Affect the Diameter of a Water Drop Impact?

[DizzyDoo]

Homework Statement

Next lesson, I am doing a water drop experiment. The basic idea is that a drop of liquid food colouring will be dropped from an eye dropper at different heights. The diameter of the wet mark that is left is then recorded for all these heights. I imagine I'll then plot a graph of diameter to height.

What I am wondering is what the relationship between the height and the diameter will be?

2. The attempt at a solution

Obviously, the higher the drop is dropped from, the large the diameter of the mark left. But do you think that the diameter will be in a linear relationship with the height? I assumed so at first, but now I think about it, perhaps a squared relationship would be more obvious. Why would this be the case? And how is energy transferred in this dropping scenario?

Thank you for your time.

 

[LowlyPion]

What I am wondering is what the relationship between the height and the diameter will be?

This is why you are doing the experiment.

The problem ultimately is how you measure. The furthest droplet? The largest contiguous stain?

There comes a point where 1 drop cannot be expected to cover too much area.

 

[thomate1]

I find this experiment very interesting and I am glad you are exploring the relationship between the height and diameter of a water drop. The relationship between these two variables is actually quite complex and can be affected by various factors such as air resistance, surface tension, and viscosity of the liquid.

In terms of the relationship between height and diameter, it is not a simple linear or squared relationship. It is actually a power law relationship, where the diameter of the drop is proportional to the height raised to a certain power. This power can vary depending on the factors mentioned above.

Air resistance plays a significant role in this experiment, as it can affect the shape and size of the drop as it falls. This is due to the drag force acting on the drop as it falls through the air. As the drop falls from a greater height, it will experience a greater drag force, resulting in a larger diameter of the mark left on the surface.

Surface tension also plays a role in this experiment, as it determines the shape and stability of the drop. The lower the surface tension, the more spread out the drop will be, resulting in a larger diameter of the mark left.

In terms of energy transfer, when the drop falls, it gains kinetic energy due to its motion. As it hits the surface, this kinetic energy is transferred to the surface, resulting in the formation of the wet mark. This energy transfer is also affected by air resistance and surface tension, as they can affect the speed and shape of the drop as it falls.

Overall, this experiment has many interesting variables and I am excited to see your results and the graph you will create. Keep in mind that the relationship between height and diameter may not be a simple one and can be affected by various factors. Good luck with your experiment!