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Friday, 16 March 2018

Design of Ogee Spillway | DHS Termwork

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Ogee Spillway, the 2 S curves, and Stilling Basin

Designing a spillway is a part of termwork of the subject, Dams and Hydraulic Structures (DHS) taught in the Final year of Civil Engineering under Savitribai Phule Pune University Curriculum (SPPU).

Ditching the traditional method of too much writing and tapping on the calculator we came up with a method to simplify the task by employing technology to do it for us, rest assured; I'm a big fan of automation though it may kill a number of Jobs!

I did complete the design but with a few moderations and alterations as I learned by referring literature from a number of reference books and a few works of literature online such as NPTEL, et cetera.

Let's Get Started!
Commonly though we consider a problem wherein the specifications are provided and we're supposed to design a suitable spillway profile and the other necessary appurtenances for a conditioned hydraulic flow.

Here are the Problem and the Manually derived solution

A few pages might be disoriented as we used our smartphone to scan those pages!
As you might have seen above a few pages were the direct printouts, that's where I just used excel to reiterate the stuff and give me an output instead of me manually tapping each variable into my programmed calculator.


Ogee spillway is also known as the overflow spillway and as the name suggests, water overflows from the top and so the crest is so designed that it retains the hydraulic stability and also at the bottom a curve is provided which helps in dissipating the excess energy. The bottom curve helps in protecting the bottom from scouring and erosion, so the bottom curve is defined by a relation with respect to its height of fall and an inclination of 60 degrees is provided along with the perpendicular from the lower tangent point. 

The problem was that after you take a 60-degree line from the perpendicular and cast an arc of magnitude R, the arc wasn't touching the bottom. Instead of using the traditional graph paper method I used AutoCAD for plotting the graph which I later scale and just copy the graph from the readings AutoCAD gives me. But since I was using AutoCAD, I had access to a bunch of other tools that could seriously enhance my accuracy and now I could measure the minute difference and the angle that the perpendicular dropped from the 60-degree line would make with the bottom line.

First I tried with my own problem and then I checked the solutions provided by other college students and to no surprise even they had the same error but due to the limited precision of human abilities, the differences just aren't visible. So I was on my quest to find the solution!

Hard-work Pays Off

A few pages might be disoriented as we used our smartphone to scan those pages!
I tried jotting a few geometric relationships to derive an equation that could work out the solution. While preparing and re-iterating the geometric models I realized that angle formed by the straight line and the angle with the perpendicular are same. Try it yourself, Its a Challenge!

I tried another formula suggested by the book, "Irrigation and Water Engineering" by Dr. B.C. Punmia but the solution I found was not appropriate.

So here, I was with no solution to the problem...

Now, Deep in the thoughts, we deduced a relationship between the slope of the line joining the two tangent points and the arc along with the angle. so now I decided to change the slope of the line to 60-Degrees so that the angle now can be same and we can get the lower profile correct. This was possible because the problem required us to select the angle, again the question is that most problems on the design of spillways prefer having slopes of 0.7-0.8 so how is it that my slope of 0.577~0.6?

I would love to learn more to get an appropriate explanation for the problem, I recently faced!

Thanks for Reading, please feel free to leave your comments below..

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