الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
A theoretical relation between the Harmonic Mean Distance and the velocity is deduced. Based on this relation, an analytical technique for drawing the dimensionless isovel contours for any open channel cross section is proposed. The model takes into consideration the composite roughness, the section geometry, and the effect of the free surface. The model is based on a simple idea but is engaged with three calibrating parameters. In this study, HMD equation is modified to be appropriate to any open channel cross section with segments of different roughness. Other modification is added also to control the semblance of HMD contour lines. Denominators of both sides of HMD equation are raised to a power Cf, which is named by the contour factor.
New two 2-D velocity distribution equations are developed, one is based on the power law, and the other is based on the logarithmic law. Each equation of them has a new calibrating parameter, m1` for the power law based equation, and m2` for the logarithmic law based equation. Both parameters are considered the third degree of freedom in the proposed model.
The proposed model is first verified with measured velocity profiles of a present experimental work in Irrigation and Hydraulics laboratory (Mansoura University, Faculty of Engineering, Egypt). The proposed model is then verified with measured velocity profiles from previous works (Maghrebi and Rahimpour, 2005; and Maghrebi and Ball, 2006). 11 measured velocity profiles of rectangular cross sections are used in the verification. 8 of them are for cross sections that have composite roughness.
The software presented in this study is written by Microsoft Professional Visual Basic 6.0 language. It includes many features such as drawing options, save and load options, and the contour levels adjustment. Data can be easily introduced through the interface, and also results can be easily produced through it. For every run, it produces all main and minor related results. It calculates the velocity factors (α andβ), the location of the maximum velocity, and the ratio of the maximum to the mean velocity (umax / V). It can produce a series of values along a vertical or a horizontal line in the cross section. It can compute the discharge by the known of a velocity value at a single point. A complete illustration is done for introducing data, producing results, and the analytical procedure of the main subroutine. The main subroutine contains many complex operations based on the fundamentals of analytical geometry. The variables in this subroutine are defined carefully to avoid overflow as possible, and to avoid errors caused by numerical approximations in loops. It is also provided by a timer to calculate the run time.