The Discharge of Water in the Design of the Channel - Statistics Project Example

April 26, 2009 Storm Drainage Design Project Introduction In the study of storm drainage, the analysis of hydrographs are important. A hydrograph plots the river discharge as a function of time. Measurements are done at a certain point in a river. Rainfall is the input used to a watershed and the stream flow is also considered as the output of the watershed. A hydrograph also represents how a watershed reacts to rainfall. The response of a watershed to rainfall depends on several factors which affects the shape of a hydrograph. This represents the effect of rainfall on a particular basin. This is a hypothetical response of a watershed to the input of rainfall. This will allow calculations of the response to any input(rainfall). Hydrographs are often affected by factors of soil saturation and the surroundings. The vegetation type and the steepness of the surrounding lands, with the drainage density. Very dry weather, normally creates a crust on river beds and wet winters would increase the discharge. Sand and clay produces a flashy hydrographs but there could be a difference between the two. Fig 1 Cynon River Hydrograph, Time over rain fall Cynon River Hydrograph Time over river height In the analysis of the graphs, the bar graph would indicate that the amount of rainfall in the river would cause the river water to rise. We can notice that there is almost a steady flow of water until after a rainstorm. The amount of rainfall is indicated in the bar graph while the rise of water in the river is indicated in the line graph. As the water rises in the river, the height of water is recorded, and the amount of rainfall is computed. Normally the rise of water in a river occurs after a storm rainfall. The discharge is measured at a certain point in a river and is typically time variant. As the line graph is plotted, the part of the hydrograph rises up to its peak and the discharge is seen. The term given to this process in the hydrograph is the rising limb. The decrease of water discharge comes after the rising limb and it is defined as the falling limb. The peak discharge is when water reaches its highest point and there is greatest amount of water in the river. The period of time that is recorded between the peak rainfall and peak discharge is called the lag time. In the study of Cynon River that was performed, a total of 96 hours was consumed. The reading in the river height was taken every hour until the end of the 96th hour. At the end of the 96th hour, a hydrograph was plotted taking into considerations the result of the river height readings. A bar graph was plotted for the rainfall, and a line graph was plotted for the discharge. From the hydrograph, we can see the how the water in the river had risen. The graph showed that the rise of water started on the 44th hour. The peak point was reached on the 56th hour. After the water reached the peak point, it started to fall down. This stage is called the falling limb. It took 40 hours for the water to recede. In all hydrographs, the falling limb always take a longer time to recede, than the rising limb. In the computations for a channel design and the design load of a pump, we will take into consideration the amount of water needed to satisfy the channel design that will be computed. Channel design Given Data Note: apply the Manning formula to be able to get a suitable Q = 1.0 m3/s breadth b, of a channel with depth d n = 0.014 S = 0.0003 d = 0.5 Formula /Equations v = R2/3S1/2n where: v = velocity Q = Av R = Hydraulic Radius Q = AR2/3S1/2n S = slope A = bd n = Manning's coefficient R = Awetted perimeter Q = discharge Solutions A = db = 0.5(b) Q = AR2/3S1/2n R = 0.5b1.0+b 1.0 = 0.5b0.5b1.0 + b2/3(0.0003)1/20.014 1.0(0.014) = 0.5b0.5b1.0+b2/30.00031/2 0.014 = 0.5b 0.5b1.0+b23(0.0171) 0.0140.0171 = 0.5b0.5b1.0+b2/3 0.8187 = 0.5 b0.5b1.0+b23 0.81870.5 = b0.5b1.0+b23 1.6374 = b0.5b1.0+b23 (1.6374)3 = b30.5b1.0+b2 4.3899 = 0.25b51.0+b2 4.3899 = 0.25b21.0+2b+b2 4.3899 (1.0 + 2b + b2) = 0.25b5 4.3899 + 8.7998b + 4.3899b2 = 0.25b5 4.3899 + 8.7998 + 4.3899 - 0.25b5 = 0 b = 3.1293 m. In order to achieve for the value of the discharge in the river, the first computations will be: to solve for the value of depth d: Computations; Q = Av where: A = cross-sectional area v = velocity = 4.0 m/s A = bd b = 15 m. A = 15(d) R = areawetted perimeter R = 15d15 + 2d v = R2/3S1/2n v = 15d(15+2d)2/30.00031/20.014 4.0 = 15d(15+2d)2/30.00031/20.014 4.0(0.014) = 15d15+2d2/30.0171 0.056 = 15d15+2d2/30.0171 0.0560.0171 = 15d15+2d2/3 3.2748 = 15d15+2d2/3 (3.2748)3 = (15d)2(15 + 2d)2 35.1199 = 225d2(225 + 60d + 4d2) 35.1199(225 + 60d + 4d2) = 225d2 7,901.9775 + 2,107.194d +140.4796d2 = 225d2 7,901.9775 + 2,107.194d + 140.4796d2 - 225d2 = 0 7,901.9775 + 2,107.194d - 84.5204d2 = 0 By quadratic equation; solve for the value of d, d = -bb2-4ac2a where a = -84.52044 b = 2,107.194 c = 7,901.9770 d = -2,107.194(2,107.194)2-4-84.5204(7,901.9770)2(-84.5204) d = -2,107.1944,440,266.5536 + 2,671,516.3571-169.0408 d = -2,107.1947,111,782.9107-169.0408 d = -2,107.1942,666.7926-169.0408 d = 559.5986169.0408 d = 3.310 m Obtaining a result for d in the river which is 28.2416 m. and 3.310 m. we must use the value the lower numerical result for d. The reason for this is that the open channel is to located between 3.0 meters and 12.0 meters We can now solve for the value of the discharge Q Solving for the discharge Q Q = Av Q = 15(3.310) (4) Q = 198.6 m3/s = discharge of water in the river Since we have already solved for the discharge of water in the river, we can now compare discharge of water in the river with the discharge of water in the open channel. The river will be able to supply water to the open channel. A pump will be required to lift water from the river to the open channel. The design of pump will depend on the discharge of water in the open channel, as stated by Young and Freemen, 2000. The design load of the pump must be equal to the discharge of water in the open channel. Computations for the design of a water pump: HP = Q x H3960 where Q = discharge H = total head 3960 = constant H = v22g +d Q = Av A = bd A = 3.1293 (.5) A = 1.5646 m2 Q = Av 1.0 = 1.5646 x v v = 1.01.5646 v = 0.6391 m/s H = v22g + d where H = total head v = velocity H = 0.639122(9.81) + 0.5 g = 9.81 = gravitational constant d = depth = 0.639119.62 + 0.5 HP = design load 3960 = constant value H = 0.0325 + 0.5 1.0m3/s = 15850.323141489gallons/min 0.5325 m = 1.7470472440945 feet H = 0.5325 m HP = Q x H3960 HP = 15850.323141489 x 1.74704724409453960 HP = 6.9927432733195 horsepower The design load of the pump that was computed is safe and would be able to draw water from the river to the open channel. With the computed load design of the pump which is 6.9927432733195HP, a 7.0 HP pump will be used. The water that is pumped to the open channel will not overflow. The amount of water will of constant volume as it reaches the reservoir in the nearby area. Sketch of Pump Operation The sketch of the pump operation will show the direction of water. As seen, the water is coming from the river. The red arrows denotes that water is being drawn from the river, passing thru the pump and goes to the open channel. The design load of the pump is 7.0 HP. The design load of the pump is such that it will be able to pump water to the open channel. The discharge capacity of the pump is enough to maintain the volume of water passing thru the open channel. The open channel is directed towards a reservoir. The reservoir in turn will supply water to the end users. Conclusion In designing an open channel, it is very important that the location of the channel is to be considered. The water source is also a factor. The source of water must be plentiful so that there would be no shortage of water in the process of drawing water from the source. The factors to be taken into account are the discharge of water in the source and the discharge of water in the design of the channel. References Flooding, BBC - GCSE BITESIZE - Flooding, BBC April 12, 2009,. King, Wisler, and Woodburn, 1988, Hydraulics, John Wiley and Sons, Inc. New York. Pump Equation and Formula Calculation, 2007, AJ Designs, April 10,2009, . Stott, Tim, Flood Hydrographs, Fluvial Geomorphology, Learning and Research Technology University of Bristol, April 19,2009. . Vesilind, P. Aarne, Pierce, Jeffrey J. and Weiner, Ruth F. 1994, Environmental Engineering Butterworth Heinemann. 3rd Edition Waugh D. 1995. Geography: An integrated Approach, Walton-on-Thames, Nelson. Chapter 3 Drainage Basins and Rivers, 48-52. Weyman DR. 1975. Runoff Processes and Streamflow modelling, London, Oxford University Press, 54 pp. Young and Freedman, 2000, University Physics, Addison-Wesley Publishing Company, Inc. Singapore Read More