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OVERFLOW SPILLWAY CREST, SHEETS 111-1 to 111-2/1

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HYDRAULIC DESIGN CRITERIA
SHEETS 111-1 to 111-2/1
OVERFLOW SPILLWAY CREST

1. Previous Crest Shapes. Some early crest shapes were based on a simple parabola designed to fit the trajectory of the falling nappe. Bazin’s experiments of the 19th century were the basis of many early designs. The Bureau of Reclamation conducted extensive experiments on the shape of the nappe over a sharp-crested weir (reference 2). Numerous crests have been designed using the coordinates of the lower surface of the nappe for the shape of the crest, without resort to an equation. The Huntington District has used an equation involving the 1.82 power of
X and the Nashville District has used the 1.88 power of X.

2. Standard Shape, Downstream Quadrant. A comparison of the Bureau of Reclamation data with those of other experimenters was made by the Office, Chief of Engineers. On the basis of this study, Circular Letter No. 3281 was issued on 2 September 1944, suggesting the use of the 1.85 power of X. This equation is given in Hydraulic Design Charts 111-1 and 111-2 and was adopted to define the downstream quadrant shape.

3. Point of Tangency. The slope function graph of the tangents X and Y to the downstream quadrant is shown in Chart 111-1 to facilitate the location of the point of tangency a. Although it is realized that the tangent point will often be determined analytically for the final design, this graph should be of value in the preliminary layouts in connection with stability analyses and cost estimates. The downstream tangent points can be computed from

X/Hd = 1.096(1/a)^1.176 ---------------- (1)

and

Y/Hd = 0.592(1/a)^2.176 ---------------- (2)

where Hd is the design head.

4. Standard Shape, Upstream Quadrant. The upstream quadrant shape of circular arcs originally defined in Chart 111-1, dated 4-1-52(revised 8-60), resulted in a surface discontinuity at the vertical spillway face. A third, short-radius arc (R = 0.04Hd) incorporated in this design has been model tested (reference 1) and found to result in improved pressure conditions and discharge coefficients for heads exceeding the design head. Chart 111-2/1 (revised 9-70) presents this upstream crest quadrant design. A table of coordinates in terms of X/Hd and Y/Hd is included as Chart 111-2 for design convenience.

5. Recent model studies have verified the elliptical upstream quadrant design also presented in reference 1. This method, depicted in Hydraulic Design Charts 111-20 through 111-25/1, should be used for future spillway design. The Standard Shape Criteria will be retained for reference purposes.

6. References.

(1) U. S. Army Engineer Waterways Experiment Station, CE, Investigations of Various Shapes of the Upstream Quadrant of the Crest of a High Spillway; Hydraulic Laboratory Investigation, by E. S. Melsheimer and T. E. Murphy. Research Report H-70-1, Vicksburg, Miss., January 1970.

(2) U. S. Bureau of Reclamation, U. S. Department of the Interior, Boulder Canyon Project, Hydraulic Investigations; Studies of Crests for Overfall Dams. Part VI, Bulletin 3, Denver, Colo., 1948.

----------------------------

From the relation of formula (1) and (2), following formula can be obtained.

Y = X^1.85 / (2*Hd^0.85)

*** 참고문헌[References] ***

USACE, Hydraulic Design Criteria, SHEET 111-1 to 111-2/1, OVERFLOW SPILLWAY CREST

Y = X^1.85 / (2*Hd^0.85)

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현재 위치

OVERFLOW SPILLWAY CREST, SHEETS 111-1 to 111-2/1

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