Manning's Equation Explained
Manning's Equation provides more variation in analyzing a channel as compared to the Chezy Equation. Therefore this section of the site will discuss Manning's Equation for open channel flow. Note that Manning also came up with an equation for flow through circular pipes which has been described in detail here.
Judgment is required to determine the proper roughness coefficient due to the fact that tabulated values differ greatly.
Manning's Equation for Velocity Based on Channel Conditions: V = \frac{1.49}{n}R^{2/3}\sqrt{S} \text{ [US]}
V = \frac{1.00}{n}R^{2/3}\sqrt{S} \text{ [SI]}

where
 R = hydraulic radius (ft)
 n = Manning's roughness coefficient
 S = slope of channel bed
Note: Manning's roughness coefficient is affected by many factors, including surface roughness, vegetation, channel irregularity, channel alignment, scouring, and silting. See Table of Manning's Roughness Coefficients for a listing of coefficients.
Manning Constant w.r.t. Depth
Manning's Roughness coefficient (n) will vary with depth, although normally this coefficient is taken to be constant, it is at times important to be able to get an accurate coefficient (this decision is left up to the engineer).
Table 1: Varying 'n' for a Circular Channel  
\frac{d}{D}  \frac{Q}{Q_{full}}  \frac{V}{V_{full}} 
0.1  0.02  0.31 
0.2  0.07  0.48 
0.3  0.14  0.61 
0.4  0.26  0.71 
0.5  0.41  0.80 
0.6  0.56  0.88 
0.7  0.72  0.95 
0.8  0.87  1.01 
0.9  0.99  1.04 
1.00  1.00  1.00 
Using the above table you can determine the actual velocity, flow and depth of water in a pipe.
Step 1:
Step 2:
Given the properties of the existing pipe determine either \frac{d}{D} , \frac{Q}{Q_{full}} , or \frac{V}{V_{full}} . Normally Q over Q_{full} will be the easiest to determine.
Step 3:
Use one ratio to go to Table 1 above and determine the others.