Calculate waterflow on inclined plane

[Stormer]

How can i calculate the waterflow to maintain X level flowing down a flat inclined plane?

For example say you have a waterslide that is 1 meter wide with a incline of 30 degrees and want a sheet of water 10 cm deep flowing down the slide. How many m3/h of waterflow do i need to supply on the top of the slide to maintain that level of water flowing down the waterslide?

 

[Baluncore]

How many m3/h of waterflow do i need to supply on the top of the slide to maintain that level of water flowing down the waterslide?

Your question assumes a stable, steady-state solution exists. Unfortunately, that is not the case.

The water depth on the slide will become unstable, because a slightly deeper flow, will travel faster, forming and supporting, discrete waves of water, that tumble down the wet surface.

 

[jrmichler]

Start by searching open channel flow, which discusses that type of flow. Unfortunately, the research behind open channel flow is based on studying rivers and culverts, few of which are similar to your case of smooth bottom and very steep angle. The MIT hit looks like a good place to start: https://ocw.mit.edu/courses/12-090-...2006/355d3c6b2ddfb45627c9b1fa7cd4463d_ch5.pdf. Then search Manning equation. Just keep in mind that the Manning equation is for flows with lesser slopes and rougher bottoms than your case. But it might give you a rough idea of the flow.

Are you sure that you want a water depth of 10 cm with a 30 degree incline? That is a LOT of flow. I would think that a waterslide would work very well with only a few millimeters depth.

 

[Baluncore]

Key terms are: Sheet flow, Kapitza_instability, and roll waves.
https://en.wikipedia.org/wiki/Kapitza_instability

https://mirjamglessmer.com/2019/01/...ated-friendlywaves-ive-gotten-over-the-years/

https://ponce.sdsu.edu/the_control_of_roll_waves.html





There are approximations for sheet flow on steep inclined plates. Those approximations will NOT hold for 100 mm thick flows on 30° plates.
"Consider a liquid (of density ρ) in laminar flow down an inclined flat plate of length L and width W. The fluid flows as a falling film with negligible rippling under the influence of gravity. End effects may be neglected because L and W are large compared to the film thickness δ."
https://www.syvum.com/cgi/online/serve.cgi/eng/fluid/fluid804.html