# water drops

by koat
Tags: drops, water
 P: 40 Why, in terms of Physics so forces etc... does the diameter of a the splash from a raindrop increase when the height is also increased? Thanks (:
 PF Gold P: 11,013 Because the velocity of the drop increases as the height increases until it reaches terminal velocity. When it impacts a surface the kinetic energy is transferred into the splash.
 P: 52 At a higher height it has more potential gravitational energy as well (m*g*h)... And i agree with drakkith's post as well.
P: 40

## water drops

 Quote by Drakkith Because the velocity of the drop increases as the height increases until it reaches terminal velocity. When it impacts a surface the kinetic energy is transferred into the splash.
Thanks but I don't really understand it.
Can you tell me why v increases when the height increases?
And also can you explain what terminal velocity has to do with this problem?

thanks
PF Gold
P: 11,013
 Quote by koat Thanks but I don't really understand it. Can you tell me why v increases when the height increases? And also can you explain what terminal velocity has to do with this problem? thanks
Gravity on earth causes everything to accelerate at approximately 9.8 m/s^2. So the higher the object is when it starts falling, the longer it falls and the faster it gets. If a drop falls for 2 seconds its current velocity is less than an identical drop that has fallen for 4 seconds.

Terminal velocity causes there to be a maximum velocity something can reach while falling due to drag, or air resistance on the object. A rock has a much higher terminal velocity than a feather because the mass, size, and shape of the rock causes it to experience less drag.

Take a sheet of paper and just drop it from arms length. As it falls you will notice that it falls very slowly when the paper is horizontal. As it falls the paper will generally twist and turn so that it is no longer horizontal. When it starts to become more vertical it will fall much faster than before. Now, take that same sheet of paper and crumple it up into a ball and drop it. It has much less surface area than it did as a sheet and therefore experiences less drag.

It applies to your question because a water drop can only reach a certain speed before the resistance due to drag equals out the acceleration from gravity and the droplet more or less stops accelerating. Because air is less dense at higher altitudes a water drop from a cloud will accelerate, reach terminal velocity, and then start to slow down as the air becomes thicker and drag starts to increase.
P: 40
 Quote by Drakkith Gravity on earth causes everything to accelerate at approximately 9.8 m/s^2. So the higher the object is when it starts falling, the longer it falls and the faster it gets. If a drop falls for 2 seconds its current velocity is less than an identical drop that has fallen for 4 seconds. Terminal velocity causes there to be a maximum velocity something can reach while falling due to drag, or air resistance on the object. A rock has a much higher terminal velocity than a feather because the mass, size, and shape of the rock causes it to experience less drag. Take a sheet of paper and just drop it from arms length. As it falls you will notice that it falls very slowly when the paper is horizontal. As it falls the paper will generally twist and turn so that it is no longer horizontal. When it starts to become more vertical it will fall much faster than before. Now, take that same sheet of paper and crumple it up into a ball and drop it. It has much less surface area than it did as a sheet and therefore experiences less drag. It applies to your question because a water drop can only reach a certain speed before the resistance due to drag equals out the acceleration from gravity and the droplet more or less stops accelerating. Because air is less dense at higher altitudes a water drop from a cloud will accelerate, reach terminal velocity, and then start to slow down as the air becomes thicker and drag starts to increase.
Ok I understand it so far but why does the diameter increse?
PF Gold
P: 11,013
 Quote by koat Ok I understand it so far but why does the diameter increse?
When you increase the velocity of the drop it aquires more kinetic energy. This energy has to go somewhere. When the drop hits, a faster drop has more energy to transfer into the splash than a slower drop does.

Go outside and find a rock or a baseball or something. Take it and drop it into some dirt. Notice that some of the dirt has been thrown away from the impact point, similar to the splash of a water drop. Now take that same object and THROW it into the dirt. Now much more dirt has been thrown out and to a longer distance. The extra energy provided by you had to go somewhere, and that somewhere was into the dirt.
P: 40
 Quote by Drakkith When you increase the velocity of the drop it aquires more kinetic energy. This energy has to go somewhere. When the drop hits, a faster drop has more energy to transfer into the splash than a slower drop does. Go outside and find a rock or a baseball or something. Take it and drop it into some dirt. Notice that some of the dirt has been thrown away from the impact point, similar to the splash of a water drop. Now take that same object and THROW it into the dirt. Now much more dirt has been thrown out and to a longer distance. The extra energy provided by you had to go somewhere, and that somewhere was into the dirt.
But didn't you say that the drop slows down?
Why does the v increse now?
PF Gold
P: 11,013
 Quote by koat But didn't you say that the drop slows down? Why does the v increse now?
The water drop only slows down if it falls from a high enough altitude, like from a rain cloud, to reach terminal velocity at that altitude and then keep falling through denser air. At ground level and at the scale of us people nothing has enough time to reach terminal velocity, so unless you get on a really tall building or tower then everything you drop will continue to accelerate until it hits the ground.
P: 40
 Quote by Drakkith The water drop only slows down if it falls from a high enough altitude, like from a rain cloud, to reach terminal velocity at that altitude and then keep falling through denser air. At ground level and at the scale of us people nothing has enough time to reach terminal velocity, so unless you get on a really tall building or tower then everything you drop will continue to accelerate until it hits the ground.
Do you mean that there is no terminal v at all?
PF Gold
P: 11,013
 Quote by koat Do you mean that there is no terminal v at all?
Terminal velocity changes with the altitude. Or more correctly, it changes with the density of the medium, in this case the air in the atmosphere. Since air is denser at lower altitudes the amount of drag increases as you get lower, causing the terminal velocity of an object to gradually decrease as an it falls.
 PF Gold P: 11,013 Look up terminal velocity on wikipedia and see if that helps!
P: 40
 Quote by Drakkith Terminal velocity changes with the altitude. Or more correctly, it changes with the density of the medium, in this case the air in the atmosphere. Since air is denser at lower altitudes the amount of drag increases as you get lower, causing the terminal velocity of an object to gradually decrease as an it falls.
I know what terminal v is I am just confused because here you say that the terminal v decreases but in the previous post you said it's just normally accelerating downwards.
Sorry but can you maybe explain that again?
PF Gold
P: 11,013
 Quote by koat I know what terminal v is I am just confused because here you say that the terminal v decreases but in the previous post you said it's just normally accelerating downwards. Sorry but can you maybe explain that again?
Alright! The speed of an objects terminal velocity depends on the density of the air (among other things, but lets just look at the air for now). As you increase in altitude the air gets thinner, IE less dense. So an objects terminal velocity at 10,000 feet is higher than it is at 5,000 feet.

Now I am assuming you aren't dropping water drops from 10,000 feet but from ground level. So in the space of 1-15 ft or so that you might test this, the terminal velocity won't change and the drop will hit the ground long before it can reach terminal velocity anyways. Don't confuse the velocity that the drop is actually falling with the possible terminal velocity, they aren't the same thing.

An object, not travelling at terminal velocity already, will accelerate when dropped until it reaches terminal v. So a drop of water, when dropped from say a raincloud will immediately start to accelerate until it reaches terminal velocity OR it hits something like the ground. For a raindrop it generally will reach terminal velocity since the cloud is usually pretty high in altitude. If the drop has enough distance to reach terminal velocity before hitting the ground, its velocity will gradually DECREASE because the terminal velocity is slowing down due to the denser air. Remember that this is only looking at it over a large distance of falling. Over short distances of a few feet this change is so small that you can effectively ignore it.

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