2 nd Semester TRANSITIONS STRUCTURES 1 of 9 A transition is a local change in cross-section which produces a variation of flow from one uniform state to another due to the change in cross sections of channels. Also, In many hydraulic structures such as bridges, aqueducts, culverts, syphon, falls, head regulators and many others, the original cross-section of flow is reduced so as to economize the construction costs, that is need accordingly to design and construction a transitions structures. All transitions may be classified as either contraction or expansion. However, the transitions can be classified according to a state of flow through, subcritical transitions or supercritical transitions. Almost applications in practice is need to use a subcritical transitions, both in contraction and expansion flow fields. 1-Contracting Transitions The contracting transition should be tangential to the wall at throat (contracted section) where velocity is high. The geometric shape may be made of an elliptical quadrant or any cylindrical surface with center laying on throat section. (see figures below)
2 nd Semester TRANSITIONS STRUCTURES 2 of 9 2-Expansion Transitions The same shapes as illustrated in contracted sections can be used in expanding sections, but with the expansion the feature of flow will be differs, such that, due to curved surface profile in a transition the pressure distribution is not hydrostatic. In the contacting zone the pressure gradient is negative, and in expanding zone the pressure gradient is positive, as the flow is subcritical, according to this difference in flow field it will be expected that the losses coefficients should be differs. 3-Types of Transitions Various types of transitions can be used to connect between channels when vary in cross sections and shapes is need, or to connect between channel and hydraulic structure or vice versa. The engineer to be select an appropriate type according to the following :- - Important - Economy - Amount of head loss needs. Straight Line Headwall ; It is suitable for small short structures and where head loss is not a problem. It is cheap and easy to construct. See Fig. 1 (a) it is also used on small pipe culverts as shown in Fig. 2. Note that, both inlet and outlet takes this form. Broken Back (Dog Leg) ; It is used for discharge ranges from 0.5 to 5 m 3 /s. It is used for inlets and outlets. See Fig. 1 (b). It is also suitable for transitions to pipes as shown in Fig. 2.
2 nd Semester TRANSITIONS STRUCTURES 3 of 9 Cylinder Quadrant ; It gives slightly lower loss coefficients than broken back and is suitable for distributary canals. See Fig. 1 (c). Straight Warp ; It is suitable for discharge ranges of 2.5 to 5 m 3 /s. It is preferred on branch and distributary canals. See Fig. 1 (d). Stream-line warp ; It is suitable for canal discharges exceed 5 m 3 /s especially for inlet. See Fig. 1 (e). Note that, For a well-designed inlet transition the optimum angle between the channel center-line and a line joining the channel sides at the water line between the beginning and the end of transition is about 14 o. The mentioned angle should not exceed 27.5 o in any case. R.S. Chaturvedi s Semi-Cubical Parabolic Transition ; R.S. Chaturvedi (1960), proposed the following shape and relation for design the contraction or expansion transition :-
2 nd Semester TRANSITIONS STRUCTURES 4 of 9 Where ; x= Distance from throat, where velocity Vx, Lf= Length of flume (transition), Bc= Bf= Bx= Normal width of channel, where mean velocity is Vc, Width of throat, where mean velocity is Vf, and Width of flume at distance x from throat. The Chaturvedi presented the following formula to determining the transition sections ; x= Lf Bc1.5 Bc 1.5 -Bf Bf [1-( 1.5 Bx )1.5 ].. (1) Mitra s Hyperbolic Transition ; Mitra assumed the following, that used to formulate his formula to be used for transition design : 1. The rate of change of velocity along the length of transitions remains constant. 2. The depth of flow remains constant in the direction of flow (this may be achieved by gradually lowering the bed in the constriction transitions and raising it in the expansion). From the above assumptions the final derived Mitra s Equation is :- Bx= Bf Bc Lf Lf Bc-x[Bc x[bc-bf] Bf] (2) This transition has a satisfactory field performance. These transitions are useful for constrictions less than 50%.
2 nd Semester TRANSITIONS STRUCTURES 5 of 9 Morris and Wiggert Warped Transition ; These authors suggested that the length (L f )of warped transition connect between rectangular channel (flume) and trapezoidal channel or vice versa or the shape of two channel sections is rectangular, must be :- L f >= 2.25 ΔT... (3) Where ΔT is a difference in top width of channels connected. Vittal and Chiranjeevi warped Transition ; These authors obtain the following formula to for transition design connect a rectangular channel with a trapezoidal channel having a side slope 1: Z c, where:- L f =2.35 (B c - B f ) + 1.65 Z c Y c. (4) Note that B c is a bottom width of a trapezoidal channel, and Y c is the flow depth at a trapezoidal channel. At any sections within a transition the side slope (Z x ) and bottom width (B x ) can be calculated using the following formulas :- Zx= Zc-Zc Zc(1 (1- x Lf )0.5 0.5 0.5 (5) Bx= Bf+ (Bc-Bf) Bf) x [1-(1 (1- x Lf Lf )e ] (6) e= 0.8-0.26 0.26Zc 0.5.. (7) The Figure below illustrate the Vittal and Chiranjeevi warped Transition.
2 nd Semester TRANSITIONS STRUCTURES 6 of 9 L F x B f Bx Bc
2 nd Semester TRANSITIONS STRUCTURES 7 of 9 Fig.(1) : Different shape of Transitions
2 nd Semester TRANSITIONS STRUCTURES 8 of 9
2 nd Semester TRANSITIONS STRUCTURES 9 of 9 Table: Loss coefficients for transitions in Fig.1 Transition Pipe Rectangular type Full flow Partial flow Full flow Partial flow Fig. 1 Inlet Outlet Inlet Outlet Inlet Outlet Inlet Outlet K 1 K 2 K 1 K 2 K 1 K 2 K 1 K 2 (a) 0.5 1.0 0.4 0.8 0.5 1.0 0.3 0.75 (b) 0.4 0.7 0.3 0.6 0.4 0.7 0.3 0.6 (c) - - - - 0.3 0.6 0.25 0.5 (d) 0.2 0.4 0.2 0.4 0.25 0.5 0.2 0.4 (e) 0.2 0.4 0.1 0.2 0.2 0.4 0.1 0.2