Calculating velocity/depth change in narrowing open channel 1

[miketingscott]

For a currant project I am designing a model waterwheel to work in a flume. Basically I am narrowing the flume in order to increase the fluid velocity.

I know that the equation u1.a1=u2.a2 cannot be used as this is for a closed pipe but have heard there is an equation to calculate for open channels.

Is anyone able to point me in the right direction?

Thanks,

Mike

 

[cvg]

try Mannings equation for normal depth gravity flow in open channels

http://www.engineeringtoolbox.com/mannings-formula-gravity-flow-d_800.html

 

[miketingscott]

Thanks, are the SI units for kn m/s? I would like to use m/s int he calulation.

Mike

 

[miketingscott]

The problem with this equation is that I do not know what the new hydraulic radius will be as I do not know how much the water level will rise by. I know the width of the new channel but the water is unconstrained in terms of the height it can rise to.

Mike

 

[cvg]

discharge remains the same
iterate hydraulic depth until your calculated discharge converges

 

[miketingscott]

I'll just outline the problem with better details if that's ok just to double check that it can be done with the data I have.

Water is travelling down a flume, with dimensions of flow 0.6x0.05m at 1.67m/s. I want to narrow the flow in a 0.1m wide channel.

And I would then like to calculate the new velocity and depth.

Is this data sufficient to carry out the iteration you mention?

Thanks, I really appreciate this.

 

[BigInch]

You might just be backing up the flow, unless you radically steepen the down-slope in the narrowed section, as that's a pretty significant "narrowing".

From "BigInch's Extremely simple theory of everything."

 

[cvg]

the method is fine for calculating "Normal Depth". Where other downstream features do not control the flow upstream. It does not take into account backwater, momentum losses or other hydraulic controls such as weirs, orifices etc.

does slope change?

In addition to the large increase in water depth due to the very narrow flume, there will also be some energy loss in the contraction. how long is the transition?

 

[vpl]

BigInch -- If it's an open flume, wouldn't it just spill over?

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[miketingscott]

The flume has sides that are 0.3m high and I will be constructing walls this high to constrict the flow. The transition is over about 0.3m, using an arc shape.

I understand there will be lots of losses, so by the sounds of it, there isn't really an equation that will be able to calculate anything with any accuracy?

Mike

 

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[cvg]

no, you can calculate it perfectly accurately, just not with one equation. However, suggest you need to read up on this subject. Suggest Open Channel Hydraulics by Ven Te Chow might be a good place to start. You could do this analysis using HEC-RAS in about 10 minutes.

 

[miketingscott]

Thanks for the help everyone, I thought about HEC-RAS. Haven't used it in quite a while but will give that a go.

Mike

 

[BigInch]

vpl, depends on the height of the flume's edges
If it backed up, rather than spilled over, perhaps enough head would be available to increase velocity in the narrows a little, even if the slope wasn't steepened. If it spilled over, velocity wouldn't have a chance to increase under any circumstances.

From "BigInch's Extremely simple theory of everything."