Question

SHAPE OF WATER STREAM
Here is something really reasonable - 9-th grade more or less.
Water flows from the circular kitchen faucet, and the stream falls down naturally. Open and see - the stream becomes narrower down.
What is the shape of the stream ?

Answer 1

@experimentX @radar give you 9 minutes to solve !

Answer 2

@mukushla hi - do me a favor , if noone solves it - solve it for others

Answer 3

Not now - just as a last resort

Answer 4

you have already mentioned in your question stream gets narrower lol is it why at the place of what :)

Answer 5

I mentioned - but am asking YOU - WHY ? and HOW - in eggzahktlee voht shaipe ?

Answer 6

why does the stream become thinner is the Q ?

Answer 7

This is the rough part, the fine part - exactly in what manner (mathematical descr.P)

Answer 8

i'm not getting the problem ...

Answer 9

Open the water tap - yes, yes really

Answer 10

yes then ... water flows down.

Answer 11

The stream narrows down - your eyes can see that

Answer 12

Why - and precisely how

Answer 13

isn't it natural ... the amount of water is constant while the rate per unit area per unit time is greater.

Answer 14

@estudier - care to join us ?

Answer 15

Ok warmer - what shape exactly

Answer 16

at what point do you want the shape ...

Answer 17

It's a RACE for the medal !!!!

Answer 18

no ... not really interested in medal ... instead interested in learning something new.

Answer 19

\[0 \rightarrow \infty \]

Answer 20

at inifnity you will get droplets

Answer 21

Our patron saint @TuringTest TT- for short is closing in on the leader

Answer 22

New competitors join the race @ghazi

Answer 23

They enter the final lap, the ladies are holding their breath ... ! ...

Answer 24

@mikael sorry i am not interested here ..but would love to give a small explanation though not sound mathematically ...
It narrows because of the continuity equation. As the water falls, its velocity increases and therefore the diameter of the flow needed to carry the same volume of water decreases. If there is a wide river that narrows, the water moves faster in the narrow section.

Answer 25

*invited not interested

Answer 26

sorry for the mistake @mikael ...by the way this is a good one

Answer 27

sorry I got distracted, but I'm having trouble making it clear
I wanna say it has to do with gravity accelerating the water further down the stream

Answer 28

Well the newcomer makes a dangerous jump to the finish line - who will cross the first ??!!!

Answer 29

OK to make the joy last a bit longer - Quest 2 :
At what stage does the stream become droplets ?

Answer 30

also there is an electrostatic attraction between the water molecules driving them together, but that seems hard to quantify

Answer 31

the surface tension minimizes the surface ... it should be same as the tap. as ->0 ... at should be circular ... in between ...

Answer 32

Noo you went TOO LOW (in scale I mean) our patron saint @TuringTest

Answer 33

I figured, just brainstorming :)

Answer 34

Mr. @experimentX AT WHAT WIDTH DOES IT "DROPLETIZE" ?

Answer 35

It is because velocity is inversely proportional to the cross-sectional area. As the water runs down from the faucet it changes velocity because of the pull of gravity, hence the liquid will be narrower as it falls down the ground.
so i guess equation would be \[V=K*\frac{ 1 }{ area }\] so water would be droplet when it is beyond narrowest .....that is at infinity if a pulling force acts continuously

Answer 36

haven't worked out ... let's see

Answer 37

@ghazi was able to put into words what I was thinking earlier about the effect of gravity.

Answer 38

This last question is NOT so easy - the answer is deeper ( @ghazi practically answered the first question - but nowhere close to the second ....)

Answer 39

I would say it begins to "dropletize" when drag force equals forge of gravity on the stream

Answer 40

force*

Answer 41

By the way - award ghazi 1 medal, but I MUST give mine to the solver of the SECOND one

Answer 42

!Not warmer Mr. TT

Answer 43

@mukushla PLEASE SOLVE the dropletization location

Answer 44

i cant :) just watching...and love to know what is the answer :)

Answer 45

I addressed u because of your profession

Answer 46

let's begin with the width w and velocity zero. the flux remains constant/

Answer 47

Yes go on

Answer 48

hmm...i need to go to infinity ...lol let's see...when a stream can be changed in to droplet....see it can become droplet when narrowness of stream tends to zero .....that we see whilst closing tap....so no to go to infinity...by the way @mikael i haven't received medal :(

Answer 49

Open the tap @ghazi - infinity is far far away - but you see the drops, don't you ?!

Answer 50

he is saving it for the answerer of the seecond, so I gave it to you
you articulated my instinct @ghazi

Answer 51

@TuringTest was on his way to the 2-nd , but stopped for no reason....

Answer 52

thanks @TuringTest @mukushla and @mikael i just said that in my comments ..now we just need a bit of mathematics that is it :)

Answer 53

NO , this is more than mathemat

Answer 54

fluid dynamics

Answer 55

A medal to @experimentX !
But droplets are closer to @TuringTest

Answer 56

@ghazi share amedal to Mr @experimentX

Answer 57

I'll do the medal thing...

Answer 58

sorry i gave it to Turing :( why don't you give it....and just thanks to the solver lol

Answer 59

@ghazi share amedal to Mr @experimentX
But droplets - need another PRINCIPLE

Answer 60

surface tension overcomes... something?

Answer 61

\[ r = {\sqrt{\text{original flow rate} \over\sqrt{gd} \pi }}\]

Answer 62

Yeeesss ????

Answer 63

... cmon !

Answer 64

overcomes drag?

Answer 65

http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability

Answer 66

Good Bye and see you near the next amazing mathematics at home kitchen ! By the way you can give me something also

Answer 67

@mikael what was the purpose behind posting this question ? lol

Answer 68

no not drag ... drag is directed opposite to motion.

Answer 69

I solved this question mathematically when in 9-th grade. I thought you will all share the great joy of such beauty from simple water tap !

Answer 70

Aand as my last link
http://en.wikipedia.org/wiki/Plateau%E2%80%93Rayleigh_instability
shows this is DEEP INTO NONLINEAR EQUATIONS AND BIFURCATION

THE PURPOSE IS WIDOM AND BEAUTY !

Answer 71

wait let me do this now i am gonna finish it up

Answer 72

THE PURPOSE IS WISDOM AND BEAUTY !!!

Answer 73

what's up with this draw app ... ican't fix it in one place.