Introduction
Most solids in free fall experience little, if any, change to their physical constitution. Licquids, on the other hand, tend to break up into droplets shortly after being released from a container and allowed to drip. The question then arises: after what distance do water droplets begin to form? It is logical to assume that there is some relation to the pressure being exerted on the water leaking out. David Macaulay says in The Way Things Work that "forcing a liquid through a nozzle requires pressure because the narrow hole restricts the water flow. The liquid emerges in a high-pressure jet which may break up into a spray of droplets as it meets the air." Indeed, if there were no force being applied to the water, it would not drip at all. Since the water is in free fall, it experiences the effects of zer0-gravity, and does not, therefore, retain the shape in which it was released as. Giancoli points out in Physics, it is mentioned that velociyty equals the square root of the quantity 2 times the acceleration of gravity multiplies by times the height of the object. This equation is derived by setting the potential energy equal to the kinetic energy and then solbing for velocity (mgh = .5mv^, v^2 = 2mgh, v = square root (2gh)). There are other factors, however, which may also affect the distance water travlels until droplet formation begins. Giancoli makes a point that between the water and the container, or tube, there exists an internal frictional force called viscosity, which is due to the cohesive forces between molecules. He goes on to say that "if fluid hadno viscosity, it could flow through a level tube or pipe without force being applied. Because of viscosity, a pressure difference between the ends of a tube is necessary for the steady flow of any real fluid… The rate of flow in a round tube depends on the viscosity of the fluid, which in water is equal to .0003 Pascal seconds or (or newton seconds per square meter), the pressure difference, and the dimensions of the tube. The flow rate of water, according to a formula created by a scientist by the name of J.L. Poiseuille, equals pi times the radius quadrupled multiplied by the difference in pressure at the ends of the tube, which is all divided by the quantity 8 times the coefficient of viscosity multiplied by the length of the tuve. This may seem like a mouthful, but it is not so difficult to understand when it is substituted by variables and put into equation form. Also stated in Physics is Bernouli’s principle, which says that where the velocity is high, the pressure is low, and where the velocity is low, the pressure is high. This can be observed by placing water in an upright tube with a small hole in the bottom end. The water in the tape is close to motionless and therefore has a high pressure. The water leaking out of the hole exchanges much of this pressure for an increased velocity. It makes sense then to assume that the greater pressure in the tube would give the outgoing water a greater velocity and thus increase the distance in which the water breaks into droplets. For, as velocity increases, we can see by the equation delta x = vt that the distance increases as well. I will be reasearching the following question: how does droplet formation caused by water leaking out from a vertical tube relate to the height of the water in the tube? I hypothesize that the relation will be close to linear. As the height of the water in the tube becomes greater, I expect that the distance it takes for droplet formation to occur to increase in a linear fashion.

Setup
The setup for my experiment consists of a 5 foot long plastic tube with a diameter of 5/8 of an inch on the inside of the rim. Every 6 inches I drilled a hole in the tube which I then covered up with tape. This is so I could fill up the tube with water, and then tear off a piece of tape, allowing the water to drain down to the desired level. On the top of the tube I attached a funnel for pouring water into, and on the bottom end I glued a plastic cap. In the cap I made a hole using a small nail with a diameter of 1mm. I used the nail to close of the hole; that way I could fill the tube up with water without it leaking, and then remove the nail when I was ready to begin recording droplet formation. Next, I attached the tube in an upright position to a large stepladder. Underneath the bottom of the tube I had a tape measure set up so that I could record the distance that the water would travel before breaking into droplets. One problem in the design that I ran into was leakage. Originally, I had used tape to fasten the cap to the bottom of the tube, but too much water was leaking through, so I used hot glue instead. This stopped most of the leaking, but there was still a little leakage that I could not stop. Measuring the distance for water for water droplet formatin presented a number of obstacles. First of all, it took longer than I expected for water droplets to form, so I had to raise the height of the tube a few feet. Trying to identify the point at which water droplets began forming was very challenging. It was extremely hard to tell just by looking, so I placed a spoon with its concave side facing down underneath the water flow. Although this system of measuring seemed to work much better, there is still a larger than ideal amount of inaccuracy which I could not avoid. I used a long pipe with holes spaced far apart so that I could cut down on this inaccuracy, but this didn’t work as well as I had hoped. Nevertheless, the results I collected were not useless, and they seem to support my hypothesis.  As mentioned earlier, I ran my experiment 3 times. In actuality, I ran it much more than that just trying to make adjustments to my setup. Each experiment provided data which varied moderately. The distance the water took to break into droplets differed anywhere from 0 to 3 inches in each test try. Therefore, my largest uncertainty for the distance it took for droplet formation to occur at each water level would be + or – 1.5 inches.

Data

Height of Water in tube           Distance for droplet formation:
                                 1st try        2nd try        3rd try        average

            6 in.               36 in.        35 in.            37in.            36 in.
            12 in.             39 in.        38 in.            39 in.           39 in.
            18 in.             44 in.        46 in.            43 in.           44 in.
            24 in.             48 in.        49 in.            47 in.           48 in.
            30 in.             52 in.        52 in.            51 in.           52 in.
            36 in.             55 in.        56 in.            54 in.           55 in.
            42 in.             62 in.        61 in.            59 in.           61 in.
            48 in.             65 in.        66 in.            63 in.           65 in.
            54 in.             69 in.        69 in.            67 in.           68 in.
            60 in.             74 in.        72 in.            72 in.           73 in.
Data File
 
 

Conclusion and Extended Research
The data I collected seemed to support my original hypothesis, which was that there would be a linear relationship between the height of the water in the tube and the distance traveled by the water before it would break up into droplets. This can be seen by looking at the height of water vs. distance for droplet formation graph shown earlier. If I were to conduct my experiment again, I would want to make the following adjustments to my reasearch:

1. Use alternative materials to prevent leakage, i.e., corks instead of tape to over outlet holes.
2. Use a slow motion video camera to record water flow so that the exact point where droplets form can be identified.
3. Find a way to feed the tube a constant source of water to prevent pressure changes in the tube while data is being recorded. (Since the tube used in the experiment was fairly thin, by the time I found the point where droplets seemed to form, enough water had already drained out of the tube to change the water level.)
4. In each test try, have a different person fin the distance for droplet formation. (Since it was hard to identify exactly where droplet formation was taking place, I found myself being biased by my first hypothesis and my first test try. That is, I tended to record values in my later tries as close to what I got in my first test try, even though they may have been so close in reality).

Links

Novel-Quality Pressure
Elementary Physics
Pressure Vessel Handbook
SI Pressure Instruments
Pressure Test Pumps

Bibliography

1. Giancoli, Douglas C. Physics. New Jersey 1991.
2. Macaculay, David. The Way Things Work. Houghton Mifflin Company, New York 1988.