# Laminar flow exits an inclined tube

## Main Question or Discussion Point

I am working on a problem in which viscous flow comes out from an inclined tube, forming some kind of a fountain. In the tube the fluid is Newtonian and the flow can be treated as Poiseuille flow. I want to study the movement of the fluid after it leaves the tube. Can someone point me about the existing study and research on this? Thanks.

Last edited:

Related Other Physics Topics News on Phys.org
It comes out from the top end of the inclined tube?

It comes out from the top end of the inclined tube?
Yes

mfb
Mentor
Is the fountain very high/large compared to the diameter of the pipe? Is there a good reason to expect a large deviation from a ballistic trajectory?

Is the fountain very high/large compared to the diameter of the pipe? Is there a good reason to expect a large deviation from a ballistic trajectory?
I attached a photo of the experiment I am trying to model. The fluid has significant deformation.

#### Attachments

• 23.6 KB Views: 340
mfb
Mentor
Oh, and with a surface nearby, then things get complicated.

Oh, and with a surface nearby, then things get complicated.
Yes. Is it possible to get some asymptotic relation of the depth averaged radial exit velocity (parallel to the surface) distribution? I mean, if the surface is horizontal, surely the exit velocity is a constant and depth are the same. When the surface has an inclination $\alpha$, my guess is that the flux per length behaves like
$$Q=\oint\boldsymbol{n}\cdot\boldsymbol{u}h dl\sim\int_{-\pi}^{\pi}\Gamma(\alpha,\theta)rd\theta,$$
where $r$ is the radius of the tube, and the flux $\Gamma$ satisfies
$$\Gamma(\alpha,-\pi)=\Gamma(\alpha,\pi)=0,\,\Gamma(\alpha,-\theta)=\Gamma(\alpha,\theta),\,\Gamma(0,\theta)=\text{constant}.$$

I do not need to solve the exact trajectory of the fluid, an approximated distribution of $\Gamma$ is enough.

mfb
Mentor
Inside the tube and far away from the exit, flux should still follow a parabolic profile. Close to the exit, things get different. For a horizontal surface, the exiting water will fall back on the stream, and then I don't see how you could avoid numerical simulations. Those are a good idea for inclined planes as well, I think.