Lecture 07: Open Channel Controls, Transitions and Afflux - Tutorial

School of Civil Engineering/Linton School of Computing, Information Technology & Engineering

Lecture 07: Open Channel Controls, Transitions and Afflux - Tutorial

CEM001 Hydraulic Structures, Coastal and River Engineering

River Engineering Section

Dr Md Rowshon Kamal

[email protected]

H/P: 0126627589

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Example 01

Q1: Compare different types of transitions connecting a lined channel carrying a maximum flow rate of 6 m3/s. Depth of flow is 1.53 m, side slopes 1.5:1 and a rectangular bridge crossing 10 m long. The overall head loss is 0.1 m between u/s and d/s canal reaches. The u.s. canal bed level is at datum 10 m. Assume the same type for inlet and outlet transitions. Width of the channel= 2.4 m.

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Solution for Example 01

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A bridge opening has details as listed below. Use the d’Aubuisson formula with a value of K = 0.9 to calculate the afflux caused by a flow rate of 46 m3/s. Give your answer to the nearest mm, and state the assumptions for the application of this formula to be valid in this situation.Upstream and downstream of bridge: rectangular channel with width 20 m

Bridge opening: rectangular with width 18 mDownstream water depth 2.2 m

Discuss measures involving fluming of a bridge that could be taken to enable higher flows to pass without excessively increasing upstream levels.



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Assuming that the bridge soffit is not submerged and that the flow remains subcritical throughout, d’Aubuisson gives: 46 = 0.9 x 18 x 2.2 (2gh + V1

2)1/2 (1) V1 = 46/ (20 (2.2 + h)) (2) Iterate to find solution to nearest mm, probably easiest by tabular method as below, but could use Newton Raphson h [m] V1 from (2) [m/s] h from (1) [m] 0 initial value 1.045 0.029 0.029 1.032 0.031 0.031 1.031 0.031 So afflux is 31 mm. (Critical depth may be checked at the bridge opening yc = ((46/18)2/9.81)1/3 = 0.873 m so depths are suitably above this.)



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Channel transitions streamlining the approach and the exit (in particular) will reduce local losses (see example values below) and hence the afflux (the effect is to raise the K in d’Aubuisson so that a given Q produces lower h). Main types of transition are : Sharp, Cylindrical, Wedge, Warped (see Al Naib or Chow for sketches). The latter are preferable at higher velocities and are in order of decreasing energy loss. Typical figures for energy loss as K times (V2/2g) are: Type of Transition Ki for Inlet or Entrance Ko for Outlet or Exit Cylinder 0.2 0.4 Wedge shaped 0.15 0.3 Warped 0.1 0.2 The above would improve conveyance up to a point, but a limiting factor as flow rate increases may become the value of critical depth at the bridge opening. A possible design approach to overcome this involves lowering the bed level at the bridge, with appropriate fluming, to enable the flow to remain subcritical throughout.


Example 03

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After a flood, the following measurements were taken at a bridge, with the water levels

deduced from marks left by debris:

Average bed level at bridge = + 0.00 m

Soffit level of bridge = + 4.90 m

Water level upstream of bridge = + 3.11 m

Water level downstream of bridge = + 2.99 m

Width of bridge opening = 13.8 m

Width of upstream channel = 19.7 m

Use the d’Aubuisson formula (see data sheet at end of paper) with K=1.02 to calculate

the flood discharge. Give justification why this formula is appropriate in this situation.



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From the information given in the question A = b2y3 = 13.8 x 2.99 K = 1.02 H = 3.11 – 2.99 = 0.12 m V1

2 = (Q/by1)2 = (Q/(19.7 x 3.11))2

Squaring the d’Aubuisson formula gives Q2 = K2A2(2gh + V1

2) Substituting for V1 and gathering terms of Q2 yields (Q/(1.02 x 13.8 x 2.99))2 - (Q/(19.7 x 3.11))2 = 2 x 9.81 x 0.12 0.0005645 Q2 – 0.0002664 Q2 = 2.3544 Q = (2.3544/0.0002981)1/2 = 89 m3/s From the data in the question, it is clear that the bridge soffit is not submerged (which would have led to an orifice type equation rather than d’Aubuisson), and it is also necessary to check that the flow is subcritical throughout (or else the opening behaves like a Venturi flume with critical depth at the bridge opening and a higher upstream head), in order for the use of the d’Aubuisson formula to be justified. From critical depth formula (on data sheet) applied at the bridge opening yc = ((89/13.8)2/9.81)1/3 = 1.6 m so depths are suitably above this. Alternatively check Fr2 =(89/(13.8 x 2.99))/(9.81 x 2.99)1/2 = 0.4 1


Describe different forms of channel transition, with details of where these are required, and discuss the design criteria that would apply to these situations. 03

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Channel transitions are required when fluming a bridge, or to move between trapezoidal and rectangular channels. Main types are : Sharp transition, Cylindrical transition, Wedge transition, Warped transition The latter are preferable at higher velocities and are in order of decreasing energy loss. Typical figures for energy loss as K times (V2/2g) are Type of Transition Ki for Inlet or Entrance Ko for Outlet or Exit Cylinder 0.2 0.4 Wedge shaped 0.15 0.3 Warped 0.1 0.2 Note these are for subcritical flow and supercritical poses additional problems. The function is to reduce energy loss, with due regard to construction cost and space constraints. Sketches encouraged of the different types of transition (see for example Al Naib, or Chow)


Thank You

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Lecture 07: Open Channel Controls, Transitions and Afflux - Tutorial