Calculating shear in Channels?

[proletariat]

The typical formula used to calculate shear in a channel bottom is:

62.4 * Depth * slope in ft/ft = Shear in PSF

This is listed in Hec 15, Design of Channels with Flexible Liners.

Is this just an empirical formula? I don't see what slope has to do with shear in a channel, mathematically speaking.

I could see figuring the downward component of the gravity acting on the water to determine shear, but not raw slope.

 

[ccor]

Chow's Open-Channel Hydraulics (1959) shows the derivation which I will not repeat here for brevity. Your equation is correct except that it makes the assumption that in wide channels the hydraulic radius equals the flow depth. So:

t = wRS

Where: t = tractive force, or shear force
w = weight of water (62.4)
R = hydraulic radius
S = channel slope

Chow also explains that, except in wide channels, the tractive force is not uniformly distributed along the wetted perimeter.

 

[cvg]

note that velocity of the flowing water which creates the shearing force is proportional to the square root of the slope. And as you indicated, gravity supplies the driving force and on a steeper slope, there is less of a vertical reaction force, therefor the velocity increases with steeper slopes.

 

[proletariat]

Common sense would have you believe that velocity has something to do with shear. But, I don't think it does.

I wish I had a copy of Chow, but the $300 price of admission is a deterrant.

 

[ccor]

proletariat,

Try

http://www.gettextbooks.com

I found a soft cover international edition for about $50 a couple of years ago. Listed at about $65 now, but its one of the best references I own.