# Why does water flowing from a tap become thinner as it flows down

When I opened the tap, water flowing out from the openening became thinner as it flowed down. The same thing also happened when weather came out of a bottle. What is the reason for this?

Is it because the velocity of water increases as it flows down which results in a decrease in cross sectional area?

Is it because the velocity of water increases as it flows down which results in a decrease in cross sectional area?

I believe you're right. We can also add that in the usual case of flow conservation, that water flow is constrained to "stick in one piece" by the tube inside of which it is flowing. In the case of the tap, the water flow binds together because of surface tension forces. But when the flow becomes to thin, an instability occurs as you can see it loses its circular shape.

• It's not only surface tension. It's also viscous stresses. physics.stackexchange.com/questions/231267/… – Chet Miller Feb 2 '16 at 13:44
• "The water flow is constrained to stick together" @dimitri that's a very relevant point. In those taps with a net on them, the flow appears to stay the same size as it falls. That is because the many little pieces shrink, but maintain their position. – Andrea Feb 2 '16 at 20:36
• I have a question. When we make the mass conservation argument for the thinning of the jet, we don't explicitly use surface tension anywhere. It seems that the argument should also hold for a flow with arbitrarily low surface tension. I am aware that it may not be physically meaningful to speak of zero surface tension (physics.stackexchange.com/questions/2615/…) But mass conservation seems to predict that for any value of the surface tension, we get the same steady state shape. This seems counter-intuitive to me. Where does it go wrong? – Cyclone Jan 20 '17 at 14:33
• The surface tension (and other binding forces) argument is hidden in the condition $\rho =$ constant. If you do not have this argument, the water flow would keep a cylindrical shape of $r = cst$ and become less dense as you go down the flow. – Dimitri Jan 20 '17 at 14:38
• Mh, I would rather think that there is some middle ground between a perfectly incompressible fluid and a weakly compressible one. The fluid jet could either thin OR increase its density. How would it decide? I would expect whichever is energetically more favourable in some sense. Also you're making the connection between incompressibility and surface tension. I would have thought in the first place that these are two independent properties of a fluid. Aren't they? If not, how can one understand this? Is it because they are both related to inner binding forces? – Cyclone Jan 20 '17 at 14:41

Yes, you are right. The conservation of mass (for incompressible fluids, as water is) states that

$$A_1 V_1 = A_2 V_2$$

where $A$ is the area of the stream and $V$ the velocity of the fluid. Hence, as water accelerates due to gravity, $V_2>V_1$, so

$$A_2 = \frac{V_1}{V_2}A_1 \rightarrow A_2<A_1$$ and the stream becomes thinner as the water flows down. There are two reasons for this, as follows.

First, surface tension tends to pull the jet of water together as it falls down, reducing its cross-section.

Second, the center of the jet is initially moving faster than the outer skin of the jet, and the flow is laminar. This also tends to urge the jet together rather than allowing it to spread out.

Note that this is true only for the case of a small jet that is moving relatively slowly, so that any aerodynamic effects are negligible.

Note also that once the jet has narrowed significantly, it becomes susceptible to a condition known as rayleigh instability, in which a tiny perturbation will cause the jet to separate into individual sphere-shaped droplets with a characteristic spacing or "frequency".

it is because the velocity of water inreases as it flows down which results in a decrease in cross sectional area

• While this answers the question directly, we generally prefer answers to extend a bit more (i.e., go into details as to why it is correct, physically). – Kyle Kanos May 16 '17 at 13:16