Title page
Table of Content
Abbreviation and Symbols

1.1       Introduction
1.2       Aim and Objectives of the Study
1.3       Statement of Research Problem
1.4       Justification
1.5       Scope of Study

2.1       Theoretical Consideration
2.2       Discharge Equation
2.3       Dimensional Analysis of a Sharp Crested Weir
2.4       Weir Equation
2.5       Previous Studies on Weir Equations
2.6       Previous Studies on Oblique Weirs
2.7       Previous Studies in Labyrinth Weirs

3.1       Materials
3.1.1    Experimental models
3.1.2    Laboratory Flume
3.1.3    Point gauge
3.1.4    Weighing scale
3.1.5    Stop watch
3.1.6    Pitot tube
3.2       Methods
3.2.1    Experimental setup
3.2.2    Weir Equation
3.2.3    Discharge coefficient
3.2.4    Hydraulic Weir Performance
3.2.5    Surface Profile Study
3.2.6    Dimensional Analysis for the Semi-Circular Weir

4.1       Results
4.2       Water surface Profile
4.3       Measured flow parameter on the semi-circular broad crested weir
4.4       Hydraulic performance of the semi-circular weir models
4.5       Developed Model Equations
4.6       Cost Implication

5.1       Conclusions
5.2       Recommendation

The overflow characteristics of semi-circular crested weir models were investigated. Twelve models were fabricated and tested. The models were categorized into two groups; normal weirs and oblique weir models. Both group of model had constant weir height and had the crest radius varied three times; 5cm, 7.5cm and 10cm. However, for the oblique weir, the oblique angle was varied three times; 60o, 30o and 15o. From experimental results, it was observed that for normal weirs, the coefficient of discharge (Cd) increases with corresponding increase in head to crest height ratio (h/P). There were increases in Cd by 3.75%, 3.11% and 3.12% for 5cm, 7.5cm and 10cm normal weirs respectively. However, the oblique weirs showed corresponding increases of (Cd) with the increase of (h/P) values; while the highest Cd values were obtained with weirs of small oblique angle (α =15o) for all crest radius tested. There were increases in Cd values by 0.4%, 4.8% and 4.86% as the oblique angle was varied from 900 to 600, 600to 300 and 300 to 150 respectively. For normal weirs, the performance in terms of the discharge magnification factor (Qac/QNS) increases as (h/P) values increases. Hence, for all values of crest radius tested, normal weirs of semicircular crests had performance better than those of sharp crested weirs. While, for oblique weirs the performance in terms of the discharge magnification factor (Qac/QNS) increases with the increases in (h/P) values for all oblique weirs tested, hence, Weirs of small oblique angles give high discharge magnification factor and performance. Therefore, the model with radius 5cm and oblique angle 15o was selected as the most efficient with a discharge coefficient and magnification factor of 0.885 and 1.326 respectively. Expression for determining the flow rate over the semi-circular weir was developed through dimensional and regression analysis respectively. Similarly, linear and non-linear equations for estimating the discharge coefficients of the weir models were developed. It was found that the flow rate equation developed had correlation coefficient of 0.986 with maximum error of 1.4%. Also, the linear and non-linear equations developed had correlation coefficients of 0.664 and 0.574 with maximum errors of 33.5% and 42.6% respectively. Finally, the mathematical models developed for computing the discharge coefficient can be used for design of normal and oblique semi-circular crested weirs.

Weirs are stable over flow structures built across rivers or channels to spill or divert water. Weirs are the most primitive, easiest and most accurate flow structures that have various uses (Nawzad et al., 2004). Weirs are often used for diversions and regulations of flow as well as discharge analysis and depth control in various field of engineering involving applications of canals, rivers and reservoirs. They are often used for free-flow conditions. A normal linear weir is commonly used in canal applications as a diversion structure, and is positioned normal to the direction of flow (Tingey, 2011).

Forms of weirs include; sharp-crested, broad crested, ogee crest and circular weirs respectively. However, the curvature for circular weirs gives it some outstanding characteristics over other forms of weir such as stable overflow pattern, passing of floating debris easily, lower cost of construction and easily designed when compared to ogee weir (Chanson and Montes, 1997).

In engineering applications (canal), a linear weir may not be able to convey the required discharge due to insufficient freeboard (difference between water height and channel depth). Discharges can be increased without a corresponding increase in upstream head by merely increasing the weir length. However, increasing the weir length is often difficult since increasing the channel width in most engineering applications is impractical. Therefore, the use of oblique weir is a reasonable solution (Tingey, 2011).

Furthermore, the discharge may also be influenced by the crest configuration. A quarter round broad crested weirs may give higher discharge for a given head than a sharp crested weir; a half.....

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