Assignment - Gradually Varied Flow Profiles and Numerical Solution of the Kinematic Equations
Objectives
1. Evaluate and apply the equations available for the description of open channel flow
2. Solve the equations governing unsteady open channel flow
3. Apply the equations of unsteady flow to practical flow problems
Special Instructions
a. Computer programs or spreadsheets must be the work of the individual student.
b. Assignments submitted without adequate proof of program validation will not be eligible for greater than a C grading.
c. A proportion of the marks is allocated to the communication aspects of the assignment. Marks will be deducted for untidy and poorly presented work, poor English expression, and failure to cite sources of information.
d. Plagiarism is taken seriously in this course, as such your assignment report will be checked using Turnitin and your spreadsheets (if you have chosen to use Excel or equivalent) will be checked for plagiarism using Excel-Smash
Question 1 - Gradually Varied Flow Profile
Your task:
a) Use the direct step method, and the equation below to compute the water surface profile downstream of the change of slope. The water level will gradually end up at normal depth.
Δy/Δx = S0 - S‾f/1 - F‾2R where FR = √αV/√(gy‾)
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 and corrected for height of the bed e.g. Fig 5.22 Chadwick)
d) Include sample hand calculation in the report
Hints:
- The size of the step is up to you.
- Use of computers for this task (Matlab, Excel etc is encouraged)
- When computing the water surface profile you should stop just short of normal depth
- The Froude number and critical depth for a triangular channel are different to that of a rectangular channel (e.g. need average depth ( y ) instead of max depth ( y ) in FR )
Question 2 - Kinematic Wave Model
Background
You have been asked to investigate the flow behaviour of a sporting field subjected to a short duration high intensity storm rainfall event.
As part of the process you will develop a computer program of the water depths and flow rates for a specified rainfall pattern. The kinematic wave approximation is a simple form of one dimensional flow model, which is deemed sufficient for this task.
Your Task
1) Complete the tutorial problems 5.1, 5.2, 5.3 and 5.4 in Module 5. You will find full solutions of first three questions in the study book that will help you to solve 5.4. The solution of 5.4 will be used to develop your own computer model.
2) OPTIONAL: If you are not confident about your answer to 5.4 you may submit your working (formulas/equations) to the examiner using the link provided on studydesk before proceeding with the numerical scheme. Your examiner will be able to guide you through.
3) Build your model (using any programming language or spreadsheet) for solving the kinematic wave equations for computing depth and flow rate resulting from the storm events. You must configure your model according to the specifications above.
4) Validation is important part for any model development. To validate your mathematical model, you need to compute the runoff resulting from steady rainfall (assume constant rainfall depth for sufficient period) and compare results with the analytical results for steady rainfall. The analytical procedure has been discussed at the end of this problem (The section Model Validation). You are required to check all three conditions
5) Modify the model to accommodate the design inflow, which you will use as upstream boundary condition in the model. The model should run for sufficiently long period to show the recession in the outflow hydrograph. You don't need to account lateral inflow as you may assume that this has been accounted in the given inflow data, which is deemed acceptable for the purpose of this assignment.
6) Write up all equations, model development, validation, results and discussion in a report format
Note: Only required question 2
Attachment:- Assignment.rar