Hello all,

My friends at work and I debated on a simple flow phenomena, and since non of us have backgrounds in Fluids, I decided to post it at this site.

Here is a simple question for all you fluid dynamics gurus:

I observed the shape of free falling fluids. If the fluid has not reached very high velocities, it is forming a conical shape. (just imagine the shape of the water jet coming out of a faucet, or imagine honey being poured from a spoon).

My explaination of this shape is follows: Because the flow is faster at the bottom, area of flow must be decreasing because flow must be constant. In other words, volume per time must be constant.

On the other hand, their argument is that, the shape has to be conical because of the surface tension. They say that the wide opening of the faucet overcomes surface tension first, and then gradually area decreases.

I appreciate any answers on this simple question,

Thanks everyone,

Your explanation is of course correct, at least as long as the free-falling water-jet doesn't break up. Mass-conservation demands that the area decreases as the jet accelerates due to gravity. Surface tension might play a role for very thin jets, but for real-life examples like the faucet it is surely negligible.

To convince your colleges you could turn their reasoning around - they must agree that mass conservation demands a smaller jet-area as the jet accelerates, then what they are saying is that it is the surface tension which accelerates the jet and not the gravity - That sounds a bit strange and might convince them about the primary cause of this effect.

It's really a very interesting subject. I think, under certain conditions, the properties of the fluid such as the viscosity and surface tension, and the flow rate ( velocity) probably will affect the shape of the fluid column. When the viscosity and the surface tension are very high, and the velocity very low, The effect due to the gravitational force maybe less important. And when the surface instability sets in, the shape may become sausage like. Indeed a very interesting jet and spray problem.

For the applications in question here (low-velocity flow from a faucet and honey-flow from a spoon) I think that you can safely neglect surface tension effects. Don't you agree?

Yes, I agree with you that in these two cases the free falling motion of the liquid in the gravitational field will accelerate the speed of the liquid. So, in order to satisfy the continuity equation, the flow area has to decrease so that ( rho * U(y) * area(y) ) remains constant. I was simply trying to point out another door related to the surface tension of liquid. I would think, it's an important subject in space station environment.

Gentleman,

As Jonas stated, my question was for laminar flow, with low velocity and/or high viscosity.

Thank you for your responses!

I agree with Jonas Larsson and John C. Chien that the gravatational force was the main reason. There are several papers related to this problem. However, there are lots of things playing inside this system. In a paper written by SP Lin on Physics of fluid in 97 or 98, several pictures of jet flow been taken under different parameters. The pictures show that under micro gravity that the diameter of the jet remains the same.