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Fluid Dynamics - Free surface profiles in an open channel.

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Introduction

Fluid Dynamics Laboratory Investigation 2: Free Surface Profiles in an Open Channel. Summary The objectives of this laboratory experiment are to analyse the flow of water past a Sluice gate. Flow through a horizontal rectangular channel partially obstructed by a gate has been used to establish a hydraulic jump. Experimental measurements for upstream and downstream depths determining the free surface profile is compared to that predicted by theory for free surface profiles for the horizontal bed and Chezy's roughness coefficient for the channel. This experiment enables design implications for many real civil engineering problems to be solved, or examined critically. Introduction Open channels are frequently encountered, "Natural Streams and rivers, artificial canals, irrigation ditches and flumes are obvious examples; but pipelines or tunnels which are not completely full of liquid also have essential features of open channels."1 Predicting the free surface profile and the ability to control fluid levels especially the control of water levels and regulation of water discharge is necessary for purposes such as "irrigation, water conservation, food alleviation and inland navigation"2. This lab examines the rapid increase of depth from super-critical flow to sub-critical flow in a hydraulic jump. A hydraulic jump can occur downstream of a sluice gate (as will be the case in this lab), after a decrease in channel slope, due to an increase in roughness or channel width, or upstream of an obstacle located in a channel. It is an important energy-dissipating phenomenon; practical applications include the dissipation of energy below a spillway for the prevention of scouring farther downstream in the channel. ...read more.

Middle

Using this value for the Chezy, the constant K1 is - 5.11103 m. The profile of the Super-Critical flow can be given mathematically as, The Theoretical profile of the Supercritical flow is represented by the graph below. X is considered the independent variable and Y to be the dependent Variable. The theoretical profile is visibly different from the experimental data plot. The theoretical profile does not consider all real variables, whilst the experimental data is real engineering and the result of multiple data measurements. However, the experimental profile is a representation of the flow at that moment in time, whilst the theoretical profile may be considered as a general profile of the flow and as such is a valid generalisation of the flow. The sub critical part of the flow is located after the hydraulic jump and is where the flow reaches a steady height (Sequent Depth) and velocity. The sequent depths are related to the distance X, by the equation The Chezy coefficient has been determined as 36 and therefore the value of K is 6.718003 m, therefore the mathematical equation for sub-critical flow is, Using this equation, a plot of the theoretical and experimental profile of the sub-critical part of the flow can be determined. Initially the theoretical graph looks a very poor fit for the experimental plot. The Chezy coefficient seems too high as the gradient is too steep and the corresponding K constant is too high; however when 1.5<x<2.0 the graph is a good approximation for the laboratory data. ...read more.

Conclusion

0.0443 0.7 0.2306 0.4761 0.5142 0.5547 0.5976 0.6430 0.6909 0.0446 0.8 0.2334 0.5009 0.5424 0.5865 0.6333 0.6828 0.7350 In order to compare which Chezy coefficient best fits the laboratory conditions, the graph below has been produced. As can be seen the Chezy Coefficients alters the gradient of the graph. The line with a Chezy Coefficient of 36 matches the experimental plots the best. Using this value for the Chezy, the constant K1 can be calculated as - 5.11103 m. The profile of the Super-Critical flow can now be given mathematically as Appendix E The initial depths of fluid (Yinitial) are related to the sequent depths by the equation, Where, is called the Froude number, determined by The initial Equation therefore becomes, Appendix F Part I: Head loss due to the Hydraulic jump The head loss caused by the hydraulic may be calculated by the formula Where the values y1 and y2 are the depths of water just before and after the hydraulic jump. Substituting values, y1 = 0.073m and y2 = 0.1604m, = 0.01425m (1.425cm) Part II: Head loss due to Friction in the Channel The formula for calculating head loss due to friction is equivalent to calculating the specific energy head at a specific location and subtracting this from a value obtained upstream. The head loss due to friction is therefore, Where, The equation therefore becomes, Substituting values, y1 = 0.152m, y2 = 0.159m and q = 0.08744m2s-1. =5.547 x 10-3 m (0.5547cm) 1 Mechanics for fluids B.S. Massey 2 Fluid mechanics for Civil Engineers, N.B. Webber 1971 Rubinder Singh Virdee 1 ...read more.

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