Flow in channels

Jim Hurley jhurley at infostations.com
Fri Jul 2 09:16:21 CDT 2004

>Message: 16
>Date: Thu, 1 Jul 2004 19:55:33 -0700 (PDT)
>From: Alejandro Tejada <capellan2000 at yahoo.com>
>Subject: Re: Flow in channels
>To: use-revolution at lists.runrev.com
>Message-ID: <20040702025533.18873.qmail at web40508.mail.yahoo.com>
>Content-Type: text/plain; charset=us-ascii
>on Thu, 1 Jul 2004
>Jim Hurley wrote:
>>  I have just posted an application which allows one
>>  to determine the
>>  flow rate in water channels.
>I could easily imagine an ultra-complex java applet
>to accomplish this! ;-)
>>  I realize this is of almost no interest to Run
>>  Revers,
>There is an interesting stack showing
>the interaction between the eyes and diverse
>I do not remember if Michael J. Lew posted a
>link in this list:
>Good ideas in teaching pharmacology


I wasn't able to run the the OS 9 application (get a message: can't 
find application), but I can guess how bezier curves might work in 
this example.

>>  but it is a
>>  good illustration of the use of Bezier curves in Run
>>  Rev, allowing
>>  one to predict the velocity and flow rates in
>>  channels of arbitrary
>>  shape.
>I agree that this stack is an interesting and
>use of bezier curves. Nice work, Jim!
>I noticed that in channels with flat floors
>the water velocity is slower than in channels with
>cilindrical shaped floors. Is this expected?

Very perceptive of you. It is an interesting physics problem.

Flow in channels, canals, creeks, rivers, etc. are all examples of 
free fall under gravity. The water continues to accelerate away from 
the source until the gravitational force is just balanced by the 
frictional force. At this point the water has reached its terminal 

The terminal velocity of a rock is greater than the terminal velocity 
of a feather because the frictional force on the rock is a smaller 
fraction of the  gravitation force than it is for a feather.

The same thing applies to falling water, whether rain drops or stream 
flow. With great volumes of water the terminal velocity is large and 
for small volumes it is small.

And in the case you mention of the flat-bottom channel verses the 
round bottom you can see that the wetted perimeter is greater 
fraction of the cross-sectional area. (The velocity is proportional 
to the two thirds power of  the hydraulic radius which is the ratio 
of area to the the perimeter.)

>How is this stack used by hydraulic Engieners?

Say they wanted to build a channel to carry 40 cfs of water. How deep 
and wide should the channel be given the available slope of the land? 
Manning's formula allows them to make this determination. I'm not 
sure whether they have the tools to make this determination for 
complicated shapes. It is very difficult calculation to perform 
analytically. Even for a circular shape it is messy. It is relatively 
simple in my stack where the integrals for the area and perimeter are 
calculated numerically from the points that define the shape of the 
water's cross-section. I didn't do this for the engineers. I did it 
so that we (our group is "Save Our Historic Canals") could challenge 
the Irrigation District's EIR (Environmental Impact Report). They 
want to abandon the canal and put the water in a pipe. Good 
engineering but not good for the hundreds of people who walk the 
canal trail.

I find, more and more, how useful Run Rev is to me personally, simply 
as a tool to find answers to problems that interest me.


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