代做CVEN90051 CIVIL HYDRAULICS Module 1: CHANNEL HYDRAULICS AND HYDRAULIC STRUCTURES Topic 4代做留学生SQL 程

日期：2024-08-28 06:36

CVEN90051 CIVIL HYDRAULICS

Module 1: CHANNEL HYDRAULICS AND HYDRAULIC STRUCTURES

LEARNING GUIDE Topic 4

Topic 4:  Culverts and broad crested weirs

And throated flumes

Learning objectives

· To familiarise with other hydraulic structures such as culverts, broad crested weirs and throated flumes

· To design culvert structures

· To design broad crested weirs

· To design throated flumes

Introduction

Topic #3 introduces other types of hydraulic structures: culverts bread crested weirs and throated flumes. The focus of this last topic is on culverts (see an example in Figure 1 below). These are covered channel of relatively short length designed to pass water through an embankment (e.g. highway, railroad and dam). It is a hydraulic structure and it may carry flood waters, drainage flows, natural streams below earthfill and rockfill structures. From a hydraulic aspect, a dominant feature of a culvert is whether it runs full or not. Broad crested weirs and throated flume, on the contrary, are structures that are used to measure discharge in river and channels.

FOOD-FOR THOUGHT: Is the culvert a bridge?

FOOD-FOR-THOUGHT: Can a culvert be used to force a river underground? Do exist examples of river forced to flow underground?

Figure 1: Example of culvert.

Questions to guide your reading

· What are culverts, broad crested weirs and throated flumes?

· What are the main design objectives for these three structures?

Reading guide

The reading material is the primary source to understand the subject. The reading material for Topic #4 is available through “Reading Online” in LMS. The material is extracted from Hamill, L., 2011, Understanding hydraulics, Macmillan International Higher Education -- Read pp. 331-349. For more details on the design process, you may refer to Chanson, H., 2004, Hydraulics of open channel flow, Elsevier (also through reading online – see link in Reading online for Topic 3).

The reading material starts a general description of culverts and their components (Section 9.4); see Figure 2 below. The structure comprises of: an inlet, which has the function of allowing a smooth transition from the river/channel into the culvert; a barrel, which is the main component of the culver and it basically is a channel; and an outlet, which has the purpose to facilitate a smooth transition back into the river/channel. The barrel can be a single (wide) channel or a composite of a few adjacent channels (multi-cell box) with circular, squared or rectangular cross sections

NOTE: The invert is the base of the barrel, while the obvert is its ceiling. (I think these two components are not clearly introduced in the reading material)

Figure 2: A schematic of a culvert and basic definitions

Section 9.4.1 discusses the different 6 different types of flow in the culvert. A key characteristics that influence the flow in the culvert is whether the inlet/outlet is submerged/free. Beside the descriptive text, the key information in this section is its figure 9.25 (or a textual summary in table 9.7. These types can be summarized as follows:

· channel flow with unsubmerged inlet (types 1, 3 and 4);

· submerged inlet, but barrel only part full (type 2);

· submerged inlet, barrel full, but free discharge at the outlet (type 5);

· submerged inlet and outlet (type 6).

Interestingly, culverts are often described as operating under inlet control or outlet control. Therefore, the identification of the control point (CP) is crucial. This is the point that has the lowest discharge capacity.

NOTE: Most culverts are designed to operate as open channel systems with critical flow conditions occurring in the barrel in order to maximize the discharge per unit width and to reduce the barrel cross-section (and hence its cost).

Section 9.4.2 introduces basic concepts for the analysis of flow in the culvert. There is a basic relation to understand whether the inlet is submerged or free. Specifically, the inlet is submerged when the ratio of water depth at the inlet (H₁) to the height of the culvert (Y) is greater than 1.2 (H₁/Y ³ 1.2); submergence is more certain when H₁/Y ³ 1.5, though.

NOTE: If the inlet and outlet are free, the barrel is a standard open channel.

If the inlet is submerged, the inlet is similar to a sluice gate and the discharge can be computed with the same equation (see equation 9.10 in the reading material). This expression depends on the discharge coefficient C_D. An alternative expression is presented in equation 9.11 of the reading material.

NOTE: Which equation should you use when verifying the discharge in the culvert? A wise approach is to use both.

Equations 9.10 and 9.11 assumes that the inlet is submerged, but the barrel and outlet are free. So, what if the barrel/outlet are full/submerged? Solving the flow in these circumstances requires an energy balance that includes all related losses. The process is summarized in equations 9.12-17. Interesting to note, however, that these equations represents a general approach. Therefore, “these equations can be applied in both submerged and open channel flow. However, if the tailwater level (H₂ – water depth downstream) is below the top of the culvert outlet, when calculating the headwater level the total head loss should be added to the larger of H₂ or 0.5(D_C + Y) where D_C is the critical depth at the flow rate in question.”.

Sections 9.4.3 and 9.4.2 introduce basic design concepts. Beside the 6 points state in section 9.4.3, some design constraints can be summarised as follows:

· the cost must be (always) minimum;

· the afflux (the rise of water level above normal free-surface level on the upstream side of the culvert) must be small and preferably minimum;

· eventually the embankment height may be given or may be part of the design;

· a scour protection may be considered, particularly if a hydraulic jump might take place near the culvert outlet.

The design process is well explained in the example 9.5. Note that the optimum size is the smallest barrel size allowing for inlet control operation. Nonetheless, the design depends strongly on the input conditions, which are normally imposed by the client. In the example, the maximum headwater level is imposed. In this respect, the last note at the bottom of the example is interesting: “Note IF a higher headwater level and inlet control was acceptable then the culvert could be made smaller”. This to say that design constraints may lead to non-ideal structure.

Section 9.5 describes another type of hydraulic structure: the broad crested weir (see example in Figure 3 below). This is generally a concrete structure that spans the full width of the channel used to measure the discharge of rivers. Broad crested weirs are much more suited for this purpose than the relatively flimsy sharp crested weirs. Section 9.5.1 discusses the head-discharge relationship. A key feature of the broad crested weir is that, if the structure is sufficiently “broad”, critical depth is reached somewhere near the downstream edge.

NOTE: How broad is “broad”? The weir is broad enough when the crest (L) is greater than about three times the upstream head (H₁). Because the weir generates a change of water depth in the channel, this may generate some confusion about the datum. The reading material considers the head from the weir’s crest.

Section 9.5.1 shows how to compute the discharge (e.g. equation 9.19). Theoretical equations may not be idea, so a general expression based on the discharge coefficient is suggested as well (equation 9.20). Note that the weir will operate satisfactorily up to a submergence H_D/H₂ = 0.66 (where H_D is the head downstream). This threshold is known as the modular limit.

The reading continues with a discussion on crump weirs. I left them in the reading material for completeness. However, we will not discuss crump weirs during lectures/workshops.

Figure 3: Example of broad crested weir.

Section 9.5.2 provides details of design and specifically provides guidelines for the calculation of the minimum height of the broad crested weir.

Section 9.6 describes the throated flume. The discussion is similar to the broad crested weir (see an example in Figure 4 below). Please note that this last content may be a bit marginal in the lecture, but still be the subject of questions and exercises in the exam.

Figure 4: Example of throated flume.

Practice problems

1. The design discharge for a culvert is 13.8m³/s when the normal depth in the rectangular river channel is 1.9m. The channel has a bankful width of 4.2m, a slope of 1 in 300 and a Manning’s n of about 0.040s/m^1/3. The maximum permissible upstream depth is 2.2m (i.e. 2.5m minus 0.3m free- board). The culvert will have a length of 35m. Design a single barrel, rectangular culvert that will operate with outlet control. The site is environmentally sensitive so allow for the invert being 0.15m below existing bed level, thus enabling a layer of stones and gravel to be provided on the channel bottom.

2. (a) With respect to a broad crested weir, what is meant by the ‘submergence ratio’ and why is it important? (b) Water flows along a rectangular channel in which there is a broad crested weir with a horizontal crest. The channel is 9.0m wide, and upstream of the weir the depth of flow measured from the channel bed is 1.1m when the dis- charge is 8.24m³/s. Ignoring any loss of energy, what is the minimum height of the weir that will allow it to function with critical depth on the crest? (c) If a broad crested weir has a coefficient of discharge, C, of 1.65, and if it completely spans a 17.4m wide rectangular channel, what would be the head over the weir when the discharge is 6.8 m³/s?

3. (a) List the advantages and disadvantages of a throated flume compared to a broad crested weir when used to measure the discharge in an open channel. (b) A flat bed throated flume is to be constructed at a position in a rectangular open channel where the normal depth is 0.55m, the channel width is 7.5m, the channel slope is 1/250 and the channel has a Manning n value of 0.035 s/m^1/3. Assuming that the flume has a typical coefficient of discharge of 1.65, what is the maximum throat width that will still induce critical flow in the flume?