Gradually varied flow

From Ken Edwards, Ph.D and P.E. of LMNO Engineering:

Since we will soon have a GVF calculation on our website, I am discussing GVF calculations today. A GVF calculation first requires computation of the normal and critical depths (Yn and Yc). If the discharge, channel slope, channel material, and channel dimensions (except water depth) are known, then Yn can be computed using Manning's equation. Yn is also known as the uniform flow depth. It is the depth that water seeks in a long channel. Yc is computed by setting the Froude number to 1.0 and solving for depth. Please see
<a href="http://www.LMNOeng.com/Channels/trapezoid.htm">http://www.LMNOeng.com/Channels/trapezoid.htm</a> for normal and critical depth equations and computations. If Yn is greater than, equal to, or less than Yc, then the channel has a mild slope, critical slope, or steep slope, respectively.

To perform a GVF calculation, you need to know the water depth at some location in your channel (call this Ys, for start depth). For example, maybe you know the water depth behind a dam at a certain discharge - such as 10 m at 30 cms (cubic meters per second). Or, maybe you know the water depth under a sluice gate at a certain discharge. If the channel slope is mild and Ys is greater than Yc, then the channel has downstream control and the GVF calculation proceeds upstream. If the slope is steep and Ys is less than Yc, then the channel has upstream control and the GVF calculation proceeds downstream. The GVF computation then provides the water depth profile in the channel upstream or downstream of Ys, depending on whether or not there is downstream or upstream control.

Thank you for your interest in the LMNO Engineering newsletter, Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer) LMNO Engineering, Research, and Software, Ltd. <a href="http://www.LMNOeng.com">http://www.LMNOeng.com</a>

LMNO Engineering's previous newsletters can be viewed at <a href="http://www.LMNOeng.com/Newsletters/newsletter4.htm">http://www.LMNOeng.com/Newsletters/newsletter4.htm</a>

(c) 2002 LMNO Engineering, Research, and Software, Ltd. Received on Tue Apr 16 00:26:00 2002