Homework answers / question archive / Question 1 – Gradually Varied Flow Profiles The water flows in a triangular channel shown in Figure 1 with a side slope 1 (Hor

Question 1 – Gradually Varied Flow Profiles The water flows in a triangular channel shown in Figure 1 with a side slope 1 (Hor

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Question 1 – Gradually Varied Flow Profiles The water flows in a triangular channel shown in Figure 1 with a side slope 1 (Hor.): 2.5 (Ver.) and manning roughness coefficient of 0.04. The downstream end of this channel is a channel of same cross section but of much higher slope. The sudden change in slope means that the depth at the downstream end of the channel of interest can be approximated as critical depth. Take alpha as being 1.1 (α=1.1). The channel is conveying a steady flow rate of ? = ( 1 0.2 + 1.5 × ?1) m3 /s The bed slope of the channel is ?? = ( 1 1000 + 0.0001 × ?2) Where, ??is the second last digit and ?? is the last digit in your student number. For example, if your student number is 105007675 then ? = ( 1 0.2 + 1.5 × 7) = 15.5 m3 /s ?? = ( 1 1000 + 0.0001 × 5) = 0.0015 Figure 1: Long prismatic channel of triangular cross section ENV3104 Hydraulics II 2022 Assignment 1 4 Your task: a) Use the direct step method, and the equation below to compute the water surface profile upstream of the change in slope. where b) Plot the water depth against distance. c) Plot the longitudinal bed, normal depth, critical depth, water surface and energy line over the length of this profile. (All on the same set of axis e.g. Fig 5.22 Chadwick, scanned copy of this page in provided on study desk) d) Include sample hand calculation in the report Hints: ? The size of the step is up to you. ? Use of computers for this task (Excel, Matlab, etc is encouraged) Marking Scheme for Question 1 Marks ? Initial Calculations Initial calculations to classify the gradually varied profile and help set up the direct step method 20 ? Direct step Method The method implemented correctly 20 ? Plots of profile Plots are shown correctly 20 ? Sample Calculations Showing sample calculation for at least one row of the table 10 Total 70 0 2 1 f R y S S x F ? − = ? − R V F g y ? = ENV3104 Hydraulics II 2022 Assignment 1 5 Question 2 – Kinematic Wave Model Background You have been contracted to investigate the behaviour of a large car park when subjected to a short duration high intensity storm rainfall event. As a first step you have decided to develop a computer simulation of the water depths and flow rates when subjected to a specified rainfall pattern. After making some reasonable assumptions you have decided that the kinematic wave approximation is sufficient for this task The Car Park For study purposes it has been deemed sufficient to represent the behaviour of the car park with a one-dimensional hydraulic model, in effect reducing the two-dimensional car park to a unit flow width running down the predominant slope direction. The specifications are as follows: The length of the carpark area is determined by the last digit of your student number: ? = 120 + (5 × ?????) For example, if your student number was 105007675 ? = 120 + (5 × 5) = 145 m Manning’s n = based on your research (assume a constant value of Manning’s roughness n across the carpark. You should justify your choice) Field Slope = Drop of 0.12 m over length L Freely draining at downstream end.