Investigating the Slow-down of Droplets on a Toothpick

[Dead_Bush_Sanpai]

TL;DR Summary

The water height not affect the drop speed, is water drop push stick back and fill the hole?

[Mentor Note -- See post #2 for an attempt to clarify this thread start]

Question​

I'd wondering what force make drop slow down? Does every time a drop push toothpick back into bottle? And of course how to solve it.

Struct​

This is a bottle be pierced by a wooden toothpick, made for continually drop water onto plant. The toothpick not connect to bottle, so no pressure make them "rigid".

Water height doesn't matter as explain below. 69 wooden toothpicks result 7.4g.

Phenomenon​

The water drop interval continually slow down, worth note that even add water into bottle(to increase fluid pressure) won't speed it up(OR speed up obviously, I didn't measure it).

To plot the measure(manually count, mistake count include) `drop`(counts) by `time`(10*milliseconds) in Octave:

drop = 1:1:100
TIME=[99, 192, 301, 417, 544, 696, 859, 1032, 1224, 1415, 1636, 1870, 2114, 2348, 2593, 2837, 3085, 3334, 3584, 3836, 4094, 4367, 4635, 4908, 5280, 5457, 5697, 6014, 6298, 6590, 6880, 7163, 7459, 7755, 8026, 8298, 8570, 8846, 9117, 9390, 9670, 9949, 10229, 10509, 10792, 11070, 11354, 11654, 11965, 12278, 12595, 12912, 13228, 13557, 13873, 14193, 14519, 14846, 15172, 15499, 15828, 16154, 16487, 16810, 17148, 17475, 17805, 18140, 18394, 18814, 19156, 19495, 19833, 20164, 20494, 20826, 21163, 21499, 21838, 22183, 22517, 22865, 23201, 23542, 23897, 24259, 24630, 24986, 25350, 25722, 26093, 26453, 26815, 27179, 27561, 27905, 28268, 28631, 28997, 29370]
plot(TIME(drop), drop)

 

[berkeman]

Welcome to PF.

I'm trying to understand your question -- It looks like you've made a simple drip irrigation water bottle to water your plants using a plastic bottle of some sort and a wooden toothpick? And you are asking why the drip rate is changing?

Could you please upload a picture of your setup to help us understand it? Use the "Attach files" link below the Edit window to upload a JPEG or PDF copy of your picture. Thanks.

And I plotted your data that you included in comma-seperated variable format. It looks like there is some noise in the time between drops, and some trending as well...

 

[berkeman]

Wait, what exactly is your data? Is it time between drops in seconds, or drops per some time interval?

 

[Dead_Bush_Sanpai]

Could you please upload a picture of your setup to help us understand it?

(The bottle cap is not closed)

It looks like there is some noise in the time between drops

manually count, mistake count include

I measure these data use eyes and phone, so can't provide very precise result.

what exactly is your data?

Think this screenshot explain better than my English.

 

[berkeman]

Think this screenshot explain better than my English.

Oh, so it's measured using a stopwatch app, and the CSV data represent time (in 10 milliseconds) between drops:

[Note: changed "milliseconds" to "10 milliseconds in the sentence above]

 

[berkeman]

How long does it take to drain the bottle? If you keep refilling the bottle whenever it gets half empty, does the drip rate stabilize at some number?

 

[DaveC426913]

So, not to totally derail the experimental, applied approach to this analysis, but water drip rates are a favourite example of chaos theory.

"Dripping water from a faucet is a well-known example of chaotic dynamical systems easily seen in daily life. O.E. Rössler introduced the dynamics of a leaky faucet as a model of a nonlinear chaotic system in 1977. He suggested that the formation of water drops at the nipple of a faucet could exhibit chaotic behavior."
http://www.cs.cmu.edu/~sensing-sensors/readings/ChaoticWaterDrop_New.pdf

 

[hmmm27]

Toothpick made of... ?

 

[berkeman]

Toothpick made of... ?

He did mention that it is made of wood in his OP, and in the figure he posted in his OP:

This is a bottle be pierced by a wooden toothpick

So yeah, as it gets wet and saturated with water, its characteristics may change...

 

[Rive]

Yeah. Dry wood expands when got wet and fills up the hole.

 

[Baluncore]

There are many things to consider ...

The pressure drop across the orifice is equal to the hydrostatic head. To get less variation in pressure, use a wider container with a thin tube hanging down to the orifice.

Horticultural drippers are designed with a longer, meandering flow path, to better regulate flow.

The viscosity of the water, and so the flow, changes with the temperature of the water in the orifice.

Evaporation of water from the surface of the drop, before it releases, may lengthen the period between drops.

Changes in surface tension with temperature may alter the volume of a water drop. The presence of surfactants or proteins, maybe from algae in the water, also change surface tension.

The rate of water flow through the orifice, will be more regular than the time between drops, which will be triggered by physical vibration, with a chaotic behaviour. A high vibration environment will result in lower average volume drops, implying a higher drop rate.

The instants of release are separated by periods of time. An early drop will tend to be followed by a later drop, since some water remains attached externally to the orifice exit. You should compute a running average over two or three drops to eliminate most of that noise.

 

[berkeman]

An early drop will tend to be followed by a later drop, since some water remains attached externally to the orifice exit.

Interesting. That could explain events like this in his data:

 

[Baluncore]

Interesting. That could explain events like this in his data:

Most of the minor noise will be removable with a filter.
I would attribute the few obvious symmetrical spikes to observational or one second typographic errors in the recording.

 

[jrmichler]

I had a similar challenge three years ago. My problem was to calibrate some tipping bucket rain gauges. This is done by dripping water into the rain gauge using a setup similar to that of the OP. The desired flow rate is 1 liter in about 1 to 2 hours. The flow rate needs to be roughly constant because tipping bucket rain gauges have calibration constants that are a function of the rainfall rate. Even that flow rate was higher than desired because 75% of the measured rainfall was at rates less than 0.6" per hour.

At very low flow rates, any tiny speck of dust will (and did) partially plug the orifice, so it was necessary to spend that hour or two listening to it drip. In addition, as stated above, the flow rate depends on the hydrostatic head and toothpick swelling. I got better results when I made a larger orifice plugged with a wadded piece of cloth because a few specks of dirt had negligible effect on flow. A 10" long piece of 0.125" OD tube reduced the effect of hydrostatic head.

 

[Baluncore]

Methinks, an alternative way to generate regular drips, might be to hang a new wick for a kerosene/paraffin lamp or candle, over the side of the water container.

A wick would also filter the water.

It would be an interesting experiment to see how the change in head and flow-path length, were countered by the capillary action.

 

[Tom.G]

Methinks, an alternative way to generate regular drips, might be to hang a new wick for a kerosene/paraffin lamp or candle, over the side of the water container.

Ordinary cotton string also works well, and is more readily available.

This was a quick-fix for one place I lived. A small leak developed in the roof and, during a rain event, water was dripping from the wall at the top of a window to the window sill.

First fix was place containers to catch the drips... however this was late in the day and in the bedroom. drip-splash . . . drip-splash . . . no-sleep.

Some cotton kite string, held to the wall with masking tape, was routed down to the containers. You could see the drops silently running down the strings into the containers.

A good nights sleep followed.

Cheers,
Tom

p.s. make sure the string is wet before expecting the drips to follow it.

 

[Dead_Bush_Sanpai]

I take another same measure,(except I need re-plug stick to somewhere undetermined, to let water start drop; Also haven't control water height, this time is just about 1cm away around last time), the result seem slow down in different rate, although it still continually slow down.
(I didn't keep water height because it is hard to add water and measure it at same time)

TIME=[162, 311, 468, 638, 774, 938, 1099, 1268, 1430, 1588, 1747, 1908, 2047, 2232, 2395, 2537, 2702, 2865, 3019, 3181, 3339, 3513, 3673, 3832, 3968, 4125, 4284, 4454, 4616, 4792, 4954, 5115, 5295, 5451, 5614, 5753, 5921, 6000, 6088, 6249, 6580, 6753, 6906, 7050, 7210, 7388, 7561, 7714, 7875, 8038, 8224, 8384, 8536, 8695, 8838, 9016, 9179, 9356, 9517, 9669, 9824, 10015, 10184, 10347, 10506, 10660, 10826, 10994, 11177, 11325, 11490, 11639, 11796, 11969, 12146, 12325, 12504, 12672, 12833, 12990, 13160, 13323, 13490, 13666, 13824, 13986, 14158, 14314, 14504, 14671, 14839, 15013, 15164, 15339, 15512, 15665, 15834, 16003, 16160, 16341, 16513, 16675, 16846, 17015, 17204, 17359, 17509, 17669, 17857, 18018, 18183, 18338, 18509, 18714, 18893, 19040, 19223, 19371, 19562, 19737, 19901, 20052, 20220, 20390, 20558, 20718, 20901, 21097, 21263, 21442, 21620, 21794, 21964, 22138, 22279, 22466, 22615, 22786, 23006, 23173, 23320, 23506, 23681, 23861, 24038, 24215, 24381, 24561, 24733, 24887, 25047, 25229, 25404, 25585, 25780, 25958, 26113, 26302, 26450, 26628, 26789, 26965, 27192, 27369, 27519, 27701, 27872, 28068, 28218, 28394, 28533, 28718, 28900, 29091, 29259, 29406, 29569, 29748, 29900, 30075, 30279, 30435, 30615, 30778, 30941, 31131, 31291, 31455, 31624, 31796, 31974, 32153, 32312, 32463, 32607, 32818, 32958, 33177, 33355, 33530, 33691, 33866, 34026, 34208, 34357, 34537, 34705, 34897, 35073, 35237, 35399, 35578, 35741, 35933, 36105, 36242, 36436, 36622, 36787, 36940, 37147, 37321, 37494, 37680, 37829, 38036, 38203, 38379, 38554, 38735, 38916, 39080, 39261, 39438, 39614, 39774, 39960, 40127, 40300, 40482, 40668, 40841, 41023, 41192, 41362, 41556, 41753, 41926, 42102, 42278, 42464, 42630, 42790, 42965, 43146, 43327, 43510, 43700, 43882, 44043, 44208, 44375, 44607, 44794, 44966, 45145, 45319, 45470, 45656, 45846, 46033, 46173, 46407, 46586, 46740, 46940, 47123, 47312, 47483, 47641, 47856, 48014, 48215, 48403, 48589, 48775, 48955, 49117, 49292, 49497, 49676, 49877, 50037, 50231, 50435, 50617, 50792, 50977, 51149, 51342, 51522, 51730, 51917, 52091, 52258, 52444, 52630, 52816, 52991, 53190, 53370, 53556, 53744, 53933, 54126, 54302, 54476, 54670, 54863, 55024, 55229, 55429, 55614, 55789, 55977, 56170, 56328, 56524, 56711, 56915, 57113, 57275, 57494, 57679, 57849, 58020, 58225, 58426, 58617, 58779, 58953, 59159, 59571, 59734, 59910, 60116, 60310, 60484, 60658, 60880, 61081, 61269, 61429, 61653, 61816, 62011, 62214, 62413, 62582, 62758, 62954, 63155, 63350, 63539, 63722, 63918, 64114, 64310, 64518, 64668, 64862, 65084, 65271, 65457, 65627, 65820, 66017, 66208, 66390, 66572, 66756, 66942, 67112, 67323, 67532, 67724, 67879, 68082, 68277, 68483, 68665, 68857, 69029, 69209, 69402, 69586, 69810, 69981, 69989, 70190, 70376, 70566, 70764, 70975, 71186, 71352, 71551, 71746, 71941, 72143, 72334, 72543, 72727, 72924, 73138, 73336, 73532, 73726, 73928, 74111]
drop=1:1:420
plot(TIME(drop), drop)

So yeah, as it gets wet and saturated with water, its characteristics may change...

Yeah. Dry wood expands when got wet and fills up the hole.

This seem explainable, but when they slow down too much(about 1drop/3s, but not stop), I re-plug it and still observe they get slow down. Thank you for reminding me that the wood itself will expand.

Interesting. That could explain events like this in his data:

View attachment 323576

These noise cause by I assume water drop and my eyes need a blink so I didn't count it correctly. Next time I'll take a video and measure it smartly, sorry for the incorrect data.

The toothpick is more sharp and might not same with faucet.

At very low flow rates, any tiny speck of dust will (and did) partially plug the orifice

I have noticed this(so I put cap onto bottle), but using distilled water onto plant would be waste, anyway thank you for sharing these experiences to confirm that these small dust affects the results.

Methinks, an alternative way to generate regular drips

Oh I remember some flowerpot does have these string(although for different purpose), will try it after I get bored from this toothpick. :)

 

[Borek]

Funny thing, over a decade ago I had a leaking burette and decided to make a plot - amount of water lost (50 mL burette) vs time (in seconds). Leak was nicely getting slower with the lower height of the water.

I don't remember why there is hole in the data, probably had to do something else for a moment.