Here we go... OwillisCan you post the answers?
Thanks
owillis
Here we go... Owillis
a) Normal depth
1.85'
B) Normal velocity
8.82 fps
c) Critical depth; and
2.06'
d) Flow regime
Yc > Yn
SuperCritical
There is an add-in function in Excel called Goal Seek. It does the iterative procedure necessary to solve for normal depth. You would put in the diameter, the n-value, and the slope with a flow value and it will iterate until it finds a depth of water that satisfies both sides of Manning's equation.I'm not a water resources guy, so maybe I am missing something...
...how do you calculate the normal depth of a round pipe?
Just curious, all the problems I have worked usually give you a different channel geometry to try and solve for (rectangular, trapezoidal, etc.) or give you the normal depth for a circular pipe.
The CERM makes it very clear that it isn't easy to calculate the normal depth of a round pipe directly unless the pipe is running gull or half full.
Thanks, I just wanted to know if there was a way other then finding it iteratively. My NCEES approved calculator doesn't seem to have excel on it.There is an add-in function in Excel called Goal Seek. It does the iterative procedure necessary to solve for normal depth. You would put in the diameter, the n-value, and the slope with a flow value and it will iterate until it finds a depth of water that satisfies both sides of Manning's equation.
I'm looking through this problem right now, and I agree, the CERM does say that "normal depth in circular channels can be calculated directly only under limited conditions..."Thanks, I just wanted to know if there was a way other then finding it iteratively. My NCEES approved calculator doesn't seem to have excel on it.
Thanks for looking into it. Any example problem of this type I have come across so far has either been a shape where the normal depth can be computed directly or is a round pipe where you are told to assume the pipe is flowing full or half full. I'm not sure if that is meant to indicate that calculating normal depth in a round pipe isn't expected on the exam (b/c it seems that it can only be achieved iteratively) or if their is truly an alternative (less time consuming) method that the CERM doesn't want you to know .I'm looking through this problem right now, and I agree, the CERM does say that "normal depth in circular channels can be calculated directly only under limited conditions..."
I'm going to work on it this morning/afternoon, and I will attempt to post my solutions today.
JR,I have attached a nomograph that provides a way to determing normal depth for either circular or rectangular/trapezoidal cross-sections. It is pretty straight-forward, no iterations necessary. I am also adding a nomograph for computing critical depth for good measure. Maybe this might help some
JR
JRNomograph A graphical relationship between a set of variables that are related by a mathematical equation or law. The fundamental principle involved in the construction of a nomographic or alignment chart consists of representing an equation containing three variables, f(u,v,w) = 0, by means of three scales in such a manner that a straight line cuts the three scales in values of u, v, and w, satisfying the equation. The cutting line is called the isopleth or index line. Numbers may be quickly and easily read from the scales of such a chart even by one unfamiliar with the construction of the chart and the equation involved. The illustration shows such an example. Assume that it is desired to find the value of E when D = 2 and Q = 50. Lay a straightedge through 50 on the Q scale and through 2 on the D scale and read 11.8 at its intersection with the E scale. As another example, it might be desired to know what value or values of D should be used if E and Q are required to be 10 and 60, respectively. A straightedge through E = 10 and Q = 60 cuts the D scale in two points, D = 2.8 and D = 9.4. This is equivalent to finding two positive roots of the cubic equation D3 − 10D2 + 56.25 = 0. It is assumed that g = 32 ft/s2 in this equation.
I'm going to have to start paying for these lessons!^^^ A nomograph is considered to be a graph consisting of three coplanar curves, each graduated for a different variable so that a straight line cutting all three curves ..
.
This is the nomograph for trapezoid channel.I'm going to have to start paying for these lessons!
Now that's a NOMOGRAPH!This is the nomograph for trapezoid channel.
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