5. Reinforced Concrete Sewer, Harlem Creek, St. Louis, Eng. News, Vol. 60, p. 131.
6. U-Shaped Section, San Francisco, Eng. News, Vol. 73, p. 310.
Fig. 23.
Equivalent sections are sections of the same capacity for the same slope and coefficient of roughness. They have not necessarily the same dimensions, shape, nor area. The diameter of the equivalent circular section in terms of the diameter of each special section shown is given in Table 18. The inside height of a sewer is spoken of as its diameter.
For example let it be required to determine the rate of flow in a 54–inch egg-shaped sewer on a slope of 0.001 when n = .015. First convert to the equivalent circle. From Table 18 the diameter of the equivalent circle is 1
1.295 times the diameter of the egg-shaped sewer, which becomes in this case 43 inches. From Fig. 16 the capacity of a circular sewer of this diameter with S = 0.001 and n = .015 is 28 cubic feet per second, which by definition is the flow in the egg-shaped sewer.
As an example of the reverse process let it be required to find the velocity of flow in an egg-shaped sewer flowing full and equivalent to a 48–inch circular sewer. Both sewers are on a slope of 0.005 and have a roughness coefficient of n = .015. It is first necessary to find the quantity of flow in the circular sewer, which by definition is the quantity of flow in the equivalent egg-shaped sewer. The velocity of flow in the egg-shaped sewer is found by dividing this quantity by the area of the egg-shaped section. As read from the diagram the quantity of flow is 90 cubic feet per second. From Table 18 the area of the egg-shaped sewer is 0.51D2 where D is the diameter of the egg-shaped sewer, and D = 1.295d where d is the diameter of the equivalent circular sewer. Therefore the area equals (0.51) × (1.295 × 4)2 = 13.5 square feet and the velocity of flow is 90
13.5 = 6.7 feet per second. This is slightly less than the velocity in the circular section.
Some lines for egg-shaped sewers have been shown on Fig. 17 by which solutions can be made directly. For other shapes, and for sizes of egg-shaped sewers not found on Fig. 17 the preceding method or the original formula must be used for solution. Problems in partial flow in special sections are solved similarly to partial flow in circular sections, by converting first to the conditions of full flow or by working in the opposite direction.
40. Non-uniform Flow.—In the preceding articles it is assumed that the mean velocity and the rate of flow past all sections are constant. This condition is known as steady, uniform flow. In this article it will be assumed that conditions of steady non-uniform flow exist, that is, the rate of flow past all sections is constant, but the velocity of flow past these sections is different for different sections. Under such conditions the surface of the stream is not parallel to the invert of the channel. If the velocity of flow is increasing down stream the surface curve is known as the drop-down curve. If the velocity of flow is decreasing down stream the surface curve is known as the backwater curve. The hydraulic jump represents a condition of non-uniform flow in which the velocity of flow decreases down stream in such a manner that the surface of the stream stands normal to the invert of the channel at the point where the change in velocity occurs. Above and below this point conditions of uniform flow may exist.