Manning Equations

[S28]

Hello,

I'm wondering if anyone has a list or a source of simplified Manning Equations. I know the equation itself is simple, but I'm finding sometimes calculating a solution can be a process...

The AI1 has tables, but I've found the tables to often not use slopes that are not uncommon, and it leaves lots of room for interpolation mistakes. Then going through some NCEES Practice examples, the NCEES book whipped out an equation that instantly solves the Manning equation when you need to calculate the diameter. It referenced the Handbook of Hydraulics, 6th edition by Brater and King. I know I could buy the book but I really don't want to buy it just for these Manning Equations.

I'm just trying to figure out how I can easily save some time during the exam, and if I had a bunch of already simplified Manning Equations, I know this could instantly turn solving a 4 minute calculation into a 1 minute calculation.

Any thoughts? Also, I'm not taking the water depth portion, but I know Manning Equation will definitely be on the AM, and I thought posting here would be more appropriate than posting in the general forum.

 

[frazil]

I don't have the CERM with me, but there's a Manning equation nomograph in the appendix. If you don't mind using those things, it can solve for whatever variable you're looking for (S, Rh, V, n) fairly quickly.

 

[K19]

S28, what exactly was the equation that the NCEES referenced to "instantly" solve the problem?

For starters, you should at a minimum know the Manning equations for velocity and flow rate in U.S. units (eq. 19.12 and 19.13, 12th ed. CERM):

v = (1.49/n) * R2/3 * S1/2

Q = (1.49/n) * A * R2/3 * S1/2

FWIW I didn't bother with the Manning nomograph since it was relatively straightforward to crunch the above equations by calculator - I used a TI-30 30XS Multiview (highly recommended).

Make sure that you understand hydraulic radius R (e.g. hydraulic radius does not equal pipe radius!) and how to compute R for relatively simple rectangular/trapezoidal geometries. A very handy variant of the Manning equation is for full-flow diameter in circular pipes (eq. 19.16, 12th ed. CERM) - useful for sizing a pipe (given a design flow) or for calculating the full-flow capacity (given a pipe diameter):

D = 1.335 * (n * Q / S1/2)3/8

For circular pipes flowing partially full, use Appendix 19.C for the relationship of d/D to other flow parameters. HTH and good luck.

 

[S28]

Thanks for the responses. Sorry it took me so long to reply, after reading the first response I kind of forgot to check in again. I understand all of the other concepts, just wish there were more equations that could be just moved around or sismplified to solve for a separate variable rather than using the charts in the back. I know the charts in the back are pretty easy to use, but if there were a way to solve the manning equation for every other scenario and have them all listed on a sheet that would be much faster.

For instance, in the NCEES Problem I was talking about in the original post, NCEES uses D=[2.159 x Q x n / (S) 1/2]3/8 to calculate the diameter of a proposed storm sewer which is to run at steady, uniform flow. So basically it's the same formula you listed, only the 2.159 has already been taken to the 3/8 power in your equation.

I just can't stop thinking about how handy that would be to have all the broken down formulas, in essence it would change any manning equation problem into a "plug and chug" gimme problem that would only take 30 seconds. Oh well.

 

[IlPadrino]

I'm just trying to figure out how I can easily save some time during the exam, and if I had a bunch of already simplified Manning Equations, I know this could instantly turn solving a 4 minute calculation into a 1 minute calculation.

If it takes you four minutes to solve the Manning equation for any of its variables, there's something wrong. What seems to take all that time?

 

[K19]

I know it's a "tough love" answer, but the Manning Equation is-what-it-is, and the equations I referenced are as simplified a it's going to get. You should be fluent enough with your algebra to solve for any of the variables. From my experience having a good calculator (and knowing how to use it) was the best time saver.

For instance, in the NCEES Problem I was talking about in the original post, NCEES uses D=[2.159 x Q x n / (S) 1/2]3/8 to calculate the diameter of a proposed storm sewer which is to run at steady, uniform flow. So basically it's the same formula you listed, only the 2.159 has already been taken to the 3/8 power in your equation.

What's the issue here? That different references express the same equation slightly differently? This equation is also already a quite simplified form of Q = (1.49/n) * A * R2/3 * S1/2 in that both the A and R terms have been substituted with expressions in terms of full-flow diameter (D) and then solved for D.

A = π D2 / 4

R = (π D2 / 4) / (π D) = D / 4

...

Q = (1.49/n) * (π D2 / 4) * (D / 4)2/3 * S1/2

 

[MWC PE]

Are you looking for tables that will solve R and A in terms of d for circular pipes? I know those exist. I think there is one in the CERM, at least there was several editions ago. I don't think having it solved for every slope and every diameter is very practical though.

 

[djgint]

There is a book available now in amazon that has programs for HP 35s or HP 33s calculator for Manning equation for full or partially full circular pipe. There is a program for flow rate Q and a program for velocity V. Just enter the diameter of pipe, depth of water, Manning's n, constant (1.49 for English or 1 for Metric), and slope of energy line to calculate the flow rate. It will only take seconds. If you need to find the slope, just use the SOLVE function.

 

[John QPE]

The concrete pipe handbook, and the Handbook of Hydraulics (6th Ed, not 7th), have pretty much everything you would need.