Fluid Velocity from a Pipe onto an Inclined Plane

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I'm not really sure where to post this. I saw that this Homework section exists even for technically non-homework (I'm designing a machine at work, but the problem is homework-esque and my fluid dynamics knowledge is rusty at best). I'm not sure if this introductory or advanced, and the template didn't really make sense to use either (sorry).


I have water flowing down a pipe and onto a (barely) inclined flat smooth plane with flat smooth walls along the sides. The end is open.

I know the volumetric flow rate and the velocity in the pipe. However, I'm unsure about the velocity on the inclined plane. What I basically want to be able to calculate is what width of the inclined plane I need in order to acheive a specific water depth on the plane with a given volumetric flow rate. And for this I THINK I need the velocity (A=Q/v).

I assume that it will be a (hopefully short) transient where the velocity changes from the one in the pipe to the one on the plane, but I'm after the steady state velocity.

Are there any equations which I can use to solve this?


Any help appreciated! :)
 
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Answers and Replies

  • #2
JBA
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The main problem with your plan is that water as it flows down the plate will be accelerated by gravity and therefore progressively reduce in depth as it proceeds down the plate. As a result, unless the plate channel is tapered to progressively reduce its width toward the bottom end to compensate for this effect, it will not be possible to attain a consistent water depth throughout the length of the plate.

Your best solution may be, if possible, to level the plate and place a weir (dam) plate across the far end of the plate. Then the velocity of the water over the plate can easily be controlled by adjusting the discharge rate from the pipe to the plate; and/or, raising or lowering the end plate to allow the best combination of water depth and flow rate for your application.
 
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  • #3
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Thank you for some very nice pointers and advice, JBA! :)

In reality the plate is really short (<1 meter) with probably several liters flowing per second, so I'm thinking that the water won't accelerate much down the plate, but rather just decelerate since the plate widt is much wider than the pipe diameter. However, the important problem that you pointed out persists. The incline will be there just to make sure that the water is flowing one way.

It would be interesting to se how much the water decelerates or accelerates when it hits the plate with a certain initial velocity from the pipe. Would you need to simulate this problem, or is it a simpler way to calculate the velocity?
 

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