**Does Manning’s equation work for pipes, not just “open” channels?
**Yes! As I’ve previously discussed, Manning’s equation can also be used for pipes, as long as there is a free, exposed water surface. The area and wetted perimeter are hard to calculate, but doable if you utilize the graphs that relate circular pipe ratios (D/D

_{full}, Q/Q

_{full}, etc.). Here’s Manning’s equation below:

(English Units)

(English Units)

*Note: If the pipe is pressurized, then Manning’s equation should not be used, but there’s one exception. *You can actually use Manning’s equation for a pipe flowing *just* full, but not technically pressurized. The assumption is that the pipe has just barely become full, and that any additional infinitesimal flow would make the pipe pressurized. The discharge of the pipe in this condition is usually called Q_{full }or Q_{full capacity}. Q_{full }is actually extremely important, because a pipe flowing under the Q_{full }condition has less discharge than a pipe flowing just below the full depth (a circular pipe conveys the most flow at about 94% of its full depth). The reason why Q_{full} is less than Q_{94% }depth is because even though there is more flow area in the full-condition, there is even more friction (wetted perimeter) gained as a result of the pipe closing in on itself. This additional friction cancels out the additional flow area and slows down the water.

Take a look at this example to see how this concept applies to a nine foot pipe:

If you still can’t believe this is true (because I definitely didn’t at first!), check out this graph and look for where Q/Q_{full} is maximum:

Note: This graph assumes “n” does not change with depth.

Q_{full} is actually pretty usefull (pun intended). At work, I use a popular program called Flowmaster to calculate Q_{full}. During the beginning, planning stages of sizing a pipe, I’ll use Q_{full} to get an idea of my pipe’s maximum capacity rather than Q_{94% depth}. Q_{full} is a safer number to use since there’s always a chance the pipe will seal up with water, especially if there’s a clog in the system or backwater effects.

But remember, gravity-drained systems, such as storm drains, should not be designed solely on the basis of Q_{full}. A more detailed hydraulic analysis, utilizing the energy equation and a whole lot of iterative calculations (standard-step method) is usually needed, especially if there are any transitions to different-sized pipes, tight curves, abrupt changes in the slope, and/or the pipe becomes pressurized.

As a shortcut for the PE exam, here’s the formula for calculating Q_{full }in a circular stormwater or sewage pipe. If the pipe is not full, use the circular pipe ratio graphs to calculate A and R for use in Manning’s equation: