When dealing with spillways, we might define the effective length (L) of spillways in several ways. If we want to define the effective length of spillways (L in the equation Q=C.L.H^1.5), how should we do it? I mean how we can determine (define/assume) the effective length of stepped spillways?
Lspillway=1.15[(Q flood- Q gross)/(C(H flood –H spillway)^1.5)]
15% additional length can be taken as Factor of Safety.
Dear Sajan,
Thanks. Would you please give (introduce) me a reference (which includes this formula) so that I can cite it in paper.
Regards,
Adam Harvey- Micro Hydro Design Manual
https://onedrive.live.com/view.aspx?resid=B0F99B6A459CF147!124&cid=b0f99b6a459cf147&app=WordPdf&wdo=2&authkey=!AFI8GF_CXN_dL1k
When you must calculate effective length you have to consider that that dimensión depends on contraction pier coefficient and contraction abutment coeficiente, which are both depending on the geometry and the relationship He/Hd , where He es the hydraulic head and Hd is the design head.
If you have a stepped spillway with transition steps from the smaller ones to the typical step, you musta analyze if discharge coeffcient of your spillway would eventually decrease compared to a conventional Creager profile.
I recommend you to see Hydraulic of Open Channels, by Ven Te Chow, a classic book that involves the analysis of spillways, or Hydraulic Design Criteria by United States Corps of Engineers (USACE). You can look for performance of stepped spillways in some publication, for instance one of Hubert Chanson. (University of Queensland, Australia).
Best regards,
Claudio A. Fattor
Hydraulics Laboratory
National Institute of Water
Buenos Aires - Argentina
e-mail: [email protected]
thanks. the latest reference, I do not know it. would you please guide more about its full title.
Kind Regards,
I am not sure that I know exactly what the concern is that is being addressed in the question, but I will relate an experience that I had something over ten years ago. On stormwater detention pond discharge structures, outflow is typically controlled by an orifice. King County Washington also suggested the use of what they called "notch weirs" which is essentially a rectangular orifice that flows as a sharp-crested weir at low heads, i.e. it is a rectangular slot for which the crest length is often less than the height of the opening. In their design manual, they referred to an old method by Francis that suggestion you account for contraction at the sides of the weir by reducing the crest length by L - 0.2H where L is the actual crest length and H is the weir head. You can see the logic trap here if H is large enough in that a negative effective crest length can be achieved. If you examine the original documentation, this dilemma would have been avoided since the equation is being used out of the recommended range from the original work, but this is a common problem where all the restrictions on application get forgotten and only the equation is remembered.
I got some data from an old study at Georgia Tech that had been collected for suppressed sharp crested weirs that were installed in flumes and for which the weir head to crest length ratio could be fairly large. I quickly discovered that the King County equation as recommended did an extremely poor job of fitting the data. A careful comparison of the data revealed that no end contraction effects were required, i.e. the actual crest length is what you should use in the equation. There was one other issue in the context of the original application that should not be relevant to you. That is that the notch weir cut into a circular culvert wall is not a flat plate. By our own experiments, it seems that the crest length at larger weir heads should more appropriately be the straight line distance between the two edges rather than the value measured around the culvert circumference
Effective length is the net length minus contractions
Le=Ln-2*He*(Nkp+Ka), which Le is effective length and Ln is the net length, He is Head of energy above crest, N is the number of piers, Kp and Ka are constants depends on shape of piers and abutments.
no differences between stepped spillway or Ogee ones when calculating the effective length.
Regarding the last answer, which is totally correct, I would point out that kp is the coefficient of half the pier (and obviously that the factor 2 multiplying everything). In my lab experience good results should be obtained with kp = 0.1 and ka = 0.01 or even negligible if the abutment is adequately designed (two or three circle arcs).
At this relation, L is the effective length of the crest which shows with Le. This is due to the presence of piers and abutments on the spillway. The following relation was proposed to calculate the effective length of the spillway:
Le=L-2(N.Kp+Ka)H0
In which L is actual length of the spillway, N is number of piers, Kp is pier contraction coefficient and ka is abutment contraction coefficient. The values of Kp and Ka depend on the geometry of piers and abutments. The following values are usually used for first estimation of Kp and Ka:
For piers:
Square nosed with rounded corners: Kp =0.02
Round nosed: Kp =0.01
Pointed nosed: Kp =0
And for abutments:
Square with sharp corners: Ka =0.2
Round entry corner: Ka =0.1
However, I think that more experiments on the physical models are needed for determining the real values of Kp and Ka. These values may be considerable affected the discharge coefficient of spillways.
What are the lower limits ( spillway lenghth) of this relationship? in the equation L = L′ − 2(NKp + Ka)H0 L tends to become zero and negative when L' is very small. any ideas? Literature for very small openings?
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