Session 1308

The Introductory Sophomore Course in Biological Engineering at North Carolina State University

John E. Parsons Department of Biological and Agricultural Engineering North Carolina State University, Raleigh, NC 27695-7625

Abstract

The trend in undergraduate Agricultural Engineering programs in the US is towards emphasizing the interactions between engineering and biology. At North Carolina State University, the undergraduate engineering curriculum was changed from a traditional Agricultural Engineering program to Biological Engineering in 1994. The first course in the program is a sophomore level introductory course. The course objectives are to provide an introduction to basic computer tools and an overview of the department. The changes in the curriculum dictated changes in most of the department's engineering courses including the introductory course. The intent of this paper is to discuss the content of the introductory course and how the course emphasizes the interactions between engineering and biology.

I. Introduction

Traditional agricultural engineering programs have always emphasized a strong basic engineering background. This background spans many engineering disciplines including civil, chemical, electrical, and mechanical engineering. As an applied engineering discipline, much of the junior and senior year engineering courses emphasize applications from the food and agricultural disciplines.

In the late 1980's, the traditional agricultural engineering program at North Carolina State University was experiencing declining enrollment. The department began a series of curriculum changes to better address the changing needs of our clientele. The initial objective of the curriculum changes was to enable students to select courses to show a concentration in an area of agricultural engineering. The initial concentration areas included: biological, environmental/soil and water, food, and power and machinery. Under this curriculum, students selected six courses from an approved list for each concentration area.

In 1994, the state legislature began reviewing undergraduate graduation rates and strongly encouraged each college and university to review their programs. The effect of this review was a reduction in the number of credit hours for many of the engineering programs. Our department replaced the curriculum with a biological engineering degree program that met the reduced hours. This program also includes agricultural, biomedical, bioprocess, and environmental engineering concentration areas. The students have a choice of four engineering electives and there was an increased emphasis on the biological sciences. In addition to selecting two biological science courses, many of our existing courses were changed to include biology. The Page 4.528.1 current curriculum is given in Table 1. Some of the Biological and Agricultural Engineering (BAE) and engineering science electives by concentration area are given in Table 2. In addition, the students select from an approved list of courses of biological sciences for each concentration area. The remaining elective courses in the Humanities and Social Sciences areas are selected from approved lists to meet the university's general education requirements.

Table 1. Biological Engineering Curriculum (128 credit hours). FRESHMAN YEAR Fall Semester Credits Spring Semester Credits CH 101, 102 General Chemistry I and Laboratory 4 CH 201, 202 General Chemistry II and Laboratory 4 E 100 Introduction to College of Engineering 0 ENG 112 Composition and Reading 3 E 115 Introduction to the Computing Environment 1 MA 241 Analytical Geometry & Calculus II 4 ENG 111 Composition and Rhetoric 3 PY 205 Physics for Engineers & Scientists I 4 MA 141 Analytical Geometry & Calculus I 4 Physical Education Elective - Activities Course 1 PE 1_X Fitness and Wellness 1 Humanities/Social Sciences Elective 3 Semester Total 16 Semester Total 16 SOPHOMORE YEAR Fall Semester Credits Spring Semester Credits BAE 101 Introduction to BAE & Computing 3 BAE 202 Intro. BAE Methods 3 MAE 206 Engineering Statics, MAE 208 Engineering Dynamics, 3 3 or CE 214 Engineering Mechanics - Statics or CE 215 Engineering Mechanics - Dynamics MA 242 Analytical Geometry & Calculus III 4 BAE (BIO) 235 Engineering Biology 3 PY 208 Physics for Engineers & Scientists II 4 MA 341 Applied Differential Equations 3 Humanities/Social Sciences Elective 3 MAE 301 Engineering Thermodynamics I 3 Semester Total 17 Semester Total 15 JUNIOR YEAR Fall Semester Credits Spring Semester Credits BAE 402 Transport Phenomena 3 ECE 331 Principles of Electrical Engineering I 3 CH 220 Organic Chemistry 4 MAE 314 Solid Mechanics 3 MAE 308 Fluid Mechanics 3 BAE Elective 3 BAE Elective 3 BAE 315 Properties of Biological Engr. Materials 3 Humanities/Social Sciences Elective 3 Biological Science Elective 4 Semester Total 16 Semester Total 16 SENIOR YEAR Fall Semester Credits Spring Semester Credits BAE 401 Bioinstrumentation 3 BAE 452 Engineering Design II 3 BAE 451 Engineering Design I 2 Biological Science Elective 3 Engineering Science Elective 3 Biological or Engineering Science Elective 3 Ethics Elective 3 Humanities/Social Sciences Elective 3 Humanities/Social Sciences Elective 3 Humanities/Social Sciences Elective 3 Communications Elective 3 Semester Total 17 Semester Total 15

The intent of this paper is to describe the impact of these changes on our introductory course, Introduction to Biological Engineering and Computing. A description of the course is presented along with information on the inclusion of the interaction of biology with engineering. Student feedback on the course is also presented. Page 4.528.2 Table 2. Typical course selections for BAE and Engineering Sciences Electives. Concentration Typical BAE Electives Typical Engineering Sciences Electives Agricultural BAE 361 Analytical Methods in Engineering BAE 462 Machinery Design and Applications Engineering Design (Required) BAE 472 Irrigation and Drainage Pick one additional course from the BAE BAE 578 Agricultural Waste Management Electives List MAE 435 Principles of Automatic Control Biomedical BAE 465 Biomedical Engineering BAE 495B BioElectricity Engineering Applications (Required) BAE 522 Mechanics of Biological Materials Pick one additional course from the BAE IE 441 Introduction to Simulation Electives List IE 765 Musculosketal Dynamics MAE 435 Principles of Automatic Control Bioprocess BAE 422 Introduction to Food Process FS (BAE) 585 Food Rheology Engineering Engineering (Required) MAE 435 Principles of Automatic Control Pick one additional course from the BAE Electives List Environmental BAE 471 Land Resources Environmental BAE 473 Water Quality Modeling Engineering Engineering (Required) BAE 573 Agricultural Waste Management BAE 472 Irrigation and Drainage BAE Electives List BAE 361 Analytical Methods in Engineering Design BAE 422 Introduction to Food Process Engineering BAE 465 Biomedical Engineering Applications BAE 471 Land Resources Environmental Engineering BAE 481 Structures and Environment

II. Course Content and Description

The first course in our department is BAE 101 - Introduction to Biological Engineering and Computing (Table 1). The main objectives of this sophomore-level course include introductions: 1) to the concentration areas through examples and case studies, and 2) to the computer tools used throughout their undergraduate programs. The course replaces the introductory programming course required during the freshman year by many of the engineering curricula. A programming textbook (Nyhoff and Leestma, 1997) is used along with supplemental material provided via the web-based course home page (Parsons, 1998a). The course contact hours is 3 credit hours (semester) which includes two lectures and one two-hour problem session per week.

A general outline of the course content is given in Table 3. The course presentation concentrates on engineering problem solving. Each topic is presented as a case study or problem that requires evaluation, synthesis, and analysis of the important information. Many of the problems are selected from the concentration areas. The problems are selected to build on basic mathematical and physical science principles that the students have been exposed to in their freshman year. All of the problems require analysis using computer tools and many are solved using different computer tools or multiple tools.

Each year, the actual computer tools may vary. In the Fall 1998 semester, all of the student work was done on the NC State campus-wide network of Unix workstations. Programming was done using Fortran 90. The equation solver used was TK Solver (UTS, 1998 and Parsons, 1998b). The spreadsheet on the Unix workstations is NExS, a spreadsheet developed for scientific and engineering applications (NExS, 1998). In the freshman year, students take a 1 credit hour Page 4.528.3 (semester) course that introduces the campus-wide computing network along with topics such as basic system commands, word processing, and home page development (Table 1). In the past, other tools have been selected and presented in the introductory course. This selection depends on the student's experience in the freshman course.

Early in the semester, we develop an approach to problem solving that is patterned after one used in many programming textbooks (Nyhoff and Leestma, 1997). For each problem, the steps for solving the problem are:

1. Definition of what constitutes a solution 2. Determination of the parameters, required inputs and outputs 3. Develop an example solution - usually by working the problem by hand 4. Generalize the example solution into a detailed algorithm 5. Test the algorithm using the inputs and parameters for the example solution 6. Implement the algorithm with computer tools 7. Test and solve the problem with the computer tools

In general, the student always has a starting point and procedure to attack any problem. The procedure is done for all problems including those requiring solutions with programming, equation solvers and spreadsheets. The approach emphasizes the importance of understanding how to solve the problem.

Table 3. Course Content. Topic Percent of Effort Programming - Fortran 90 40% Equation Solvers and Spreadsheets 35% Overview of Concentration Areas 25%

The programming section of the course covers the basics of Fortran 90. Topics include variable types and arrays, input and output, conditional branching, and repetitive execution. Approximately 50% of the problems are selected from the textbook exercises (Nyhoff and Leestma, 1997). The remaining problems are selected from the concentration areas.

Spreadsheets are introduced as a method to quickly and easily develop problem solutions. The topics include the concepts of spreadsheets, entering formulas, and developing graphs to display results. The development of spreadsheet solutions is integrated in the programming section by using the graph capabilities to plot tabular data and solutions from the Fortran 90 programs. The capabilities of spreadsheets, such as generating graphs, are emphasized.

TK Solver is used to demonstrate another approach to problem solving. TK Solver is a general equation solving package for mathematics, science, and engineering problems. One of the strengths of TK Solver is the ability to handle equations in engineering problems that require iteration. In TK Solver, equations are entered as rules much the same way they are written. Variables are determined from the rules and the student specifies the inputs and outputs. In situations where an output can not be determined directly, iteration is used to generate a solution. Multiple solutions can be generated using lists similarly to the use of arrays and DO loops in Page 4.528.4 Fortran 90. Plots demonstrating relationships can be done easily. III. Problem Selection and Integration of Biological Sciences

One of the differences between our introductory course and a general introductory programming class is the selection of problems and the inclusion of biological content. Each of the concentration areas is introduced via problems and guest presentations. During each presentation, the importance of biology and its linkage to the engineering is emphasized. Introductory engineering problems are presented and students are able to see the types of problems engineers work on in the area. Guest presenters are solicited at the start of each semester from the faculty. Generally, there are usually 8 guest presentations selected to represent a balance among the concentration areas. I work with about 4 of the presenters each semester to develop problems from their areas. A portion of their presentation presents the background for their problems. Additional background material is presented as needed by the instructor in the problem sessions and lectures. This represents an additional commitment by the faculty of less than 0.1 full-time equivalent, which is spread over 8 faculty members.

The agricultural engineering concentration includes applications ranging from power and machinery to structures and environment. An example problem is from the structures and environment area. The problem involves evaluating the effect of forced air ventilation and external loads on the heat balance of chickens in a poultry house. A faculty member from this area presents the problem. During the presentation, the background of the problem is presented along with the necessary equations. The presentation also includes a discussion of the biology of the chickens as related to heat transfer. The students develop a Fortran 90 computer program to simulate the effect of ventilation on the heat balance of the chickens. The results are graphed using the spreadsheet. The students do a short write-up explaining their results.

Our broadest area is the biomedical engineering concentration. This is also the area that attracts over 50% of our students. Guest presentations by faculty members include overviews of biomechanics and bioinstrumentation. In both of these presentations, the faculty members present overviews of the biology and how it relates to engineering devices in these areas. Assignments from biomedical engineering are also selected to illustrate the importance of biological sciences in this area. One assignment concentrates on analyzing ventricular fibrillation data from a swine heart. The data is part of research project comparing normal sinus rhythm with ventricular fibrillation. The students analyze the data using both spreadsheets and a Fortran 90 program. Another sample problem from Fall, 1998, analyzing a hypothetical problem on chilling blood for an operation is given in Appendix 1.

Guest presentations and example problems from the environmental engineering concentration also show the integration of biological and engineering concepts. Some faculty guest presentations include water management interactions with surface water quality and the effects of watershed land use on off-site water quality. An example problem from this area evaluates the relationship between watershed size and land use and storm runoff on sizing grassed waterways. The problem is introduced to the students by discussing the impact of peak runoff on off-site water resources. The relationship between surface water ecology and losses of chemical and nutrients in runoff is introduced enabling the students to recognize the interaction with the biology of the surface water system. A description of this problem is given in Appendix 2. Page 4.528.5 The concentration area of bioprocess engineering includes work from both marketing and handling of agricultural products to food engineering. An example of a guest presentation from this area is the effect of storage and transport of fruits and vegetables on quality. This presentation discusses the engineering concepts along with the biological concepts. Respiration by fruit and vegetables is related to storage temperatures to illustrate the interactions of biology and engineering design. During the Fall-1998 semester, the bioprocessing faculty arranged a field trip to a local microbrewery to introduce the students to food processing. The tour included demonstrations and explanations of brewing process from raw material to finished product. It also enabled the students to see the use of engineering via the level of automation and computer- based controllers used in modern food production.

IV. Course Reviews and Student Acceptance

College course and instructor evaluations are completed at the end of the course. In addition, student input on the course content is solicited on the final exam. Both of these measures provide feedback on the student's perceived value of the course. The interpretation of these should be done carefully since this is the first course in their major and most of the courses up to this point have contained well-defined content and problems. In addition, about 30% of the students use the course to decide if they want to continue in Biological Engineering.

Overall, the college course evaluations have ranged from 3.6 - 4.4 (out of 5) since the incorporation of biological content in 1995. Student enrollment during this period has ranged from 38 - 54 with approximately 80% of these continuing in the Biological Engineering curriculum.

Almost all of the students have indicated that they enjoy the guest presentations and material that introduces the concentration areas of Biological Engineering. Some comments indicate that the diversity of the curriculum also presents challenges. Some of the students concentrating in Biomedical Engineering have shown a lack of interest in problems and presentations from traditional Agricultural Engineering. The students interested in traditional Agricultural Engineering sometimes lack interest in the Biological and Biomedical Engineering presentations. This makes the selection of topics and the introductions to the concentrations more challenging to make connections with such a broad audience.

V. Summary

The introductory course in biological engineering at North Carolina State University covers the fundamental computer tools by solving problems from each of the concentration areas. Problems are selected to introduce the students to both the department and the interaction of engineering with the biological sciences. Problems and guest presentations are selected from each of the concentration areas to demonstrate that biological engineering is different from other engineering disciplines. Page 4.528.6 VI. References

NExS, 1998. X Engineering Software Systems Corporation Home page. http://www.xess.com/

Nyhoff, Larry R. and Sanford C. Leestma. 1997. Introduction to Fortran 90 for Engineers and Scientists. Prentice Hall, Inc. Upper Saddle River, NJ 07458. 359 pp.

Parsons, J. E. 1998a. Introduction to Biological Engineering and Computing. http://www3.bae.ncsu.edu/bae101/

Parsons, J. E. 1998b. Introductory Guide to TK!Solver for BAE 101. http://www3.bae.ncsu.edu/info1/courses/Gen- Handouts/tk-solver.f96/tk-man-color.html

UTS. 1998. Universal Technical Systems TK Solver home page: http://www.uts.com/

JOHN E. PARSONS John E. Parsons is an Associate Professor of Biological and Agricultural Engineering at North Carolina State University. He received his B.Sc. in Mathematics from Salisbury State College in 1973, his M.Sc. in Mathematics from the University of South Carolina in 1975, and his Ph.D. in Agricultural Engineering from North Carolina State University in 1987. His appointment is 65% research and 35% academic. He teaches the introductory course and an advanced undergraduate/entry graduate level course in environmental engineering. Page 4.528.7 Appendix 1. Sample Biomedical Engineering Problem.

Biomedical/Biological Engineering Case Study - BAE 101 - Fall, 1998

The following problem is extracted from the notes of a short course I attended in 1996 (Introduction to Biomedical Engineering Problems, ASAE 1996 Summer Meeting Short Course). The instructor was Dr. Arthur T. Johnson from the University of Maryland. I reference him for the original problem; however, I take responsibility for any errors or misinterpretations. The problem is hypothetical and may or may not be representative of what is actually done in an operating room.

You are now employed with a Biomedical Engineering firm that provides blood chillers for hospitals. The blood chillers are used to lower a transplant patient's body temperature during surgery. The surgery team routes the patient's blood through the chiller. The chiller is controlled such that blood temperature can be lowered to at most 29 degrees C. The blood then moves through the patient's body. The net effect is a reduction of the patient's body temperature. The desired body temperature for operating is 30 degrees C. Your task is to develop equations to track the patient's body temperature. Once you have the equations, your company would like to incorporate these into some control algorithms for the chiller.

You can assume that the normal body temperature for the patient is 37 degrees C. Also, assume that the blood enters the body at 25 degrees C (temperature of the blood exiting the chiller) and leaves at the current body temperature. As one might expect the body temperature will decline exponentially as we circulate the chilled blood. The rate of decline will depend on the exchange of blood through the body. The temperature difference between the blood and the body will tend to equilibrate (reach the same temperature).

Some of our assumptions:

1. The volume of fluid pumped with each stroke of the heart ranges between 70 to 80 ml. 2. The heart rate can range from 50 to 100 beats per minute with an average of 70 beats per minute. 3. The mass density of blood is approximately 1 mg/cm3. 4. The heat capacity for blood is the same as the head capacity for the body. The heat capacity is the change in degrees C in the media per unit change in heat. In this problem, we assume that the change in heat is represented by the temperature gradient across the boundary between the blood and the body.

As an example, assume that the patient weighs 70 kg, has a heart rate of 70 beats/min. Then, for each minute, the heart pumps 70 beats/min * 70 ml/beat = 4900 ml/min. The mass would be 4.9 kg/min (mass density * volume). We also assume that cp (related to the heat capacity) for blood and the body is the same (0.87). Then one can do a balance (assuming that heat and temperature behave similarly), 16qq- nn+1 f c =-heart 27qq - [1] p D n+1 chiller t mbody where: cp = exchange factor between the blood and body q n+1 = the body temperature at the next time step (degrees C) q n = the body temperature at the last time step (degrees C) fheart = mass flow rate of the heart (kg/min) mbody = mass of the body (kg) q chiller = temperature of the blood exiting the chiller (degrees C)

Using the following values for our parameters, a hand example for the first couple of time steps is given below. Page 4.528.8 Parameter Value Description mbody 70 kg Body weight fheart 5 kg/min Mass flow rate of blood = heart rate*mass of blood pumped per stroke q chiller 25 degrees C Temperature of blood exiting the chiller q160 37 degrees C Initial body temperature

cp 0.87 (dimensionless) See above

From time=0 minutes to 1 minute (where n=1 corresponds to time=0 and n=2 corresponds to time=1 minute)

16q - 37 5 087. 2 =-16q -25 10- 70 2 qq+= + 0.. 8722 0 071 0 .*.* 87 37 0 071 25 3397. q ==36. 09 2 0. 941

Now for time=1 minute (n=2) to time=2 minutes (n=3)

16q - 36. 09 5 087. 3 =-16q -25 10- 70 3 qq+= + 0.. 8733 0 071 0 .*..* 87 36 09 0 071 25 3317. q ==35. 25 3 0941. q The difference equation to solve for n+1 is:   Dtf* c *qq+ heart *   p n m chiller  q = body n+1   [2] Dtf*  + heart  cp   mbody 

This solution procedure is very similar to the mixing problem from early in the semester. As with the earlier mixing problem, an alternative to the above approach is to find a function that solves the differential equation. Form equation 1, we can derive a differential equation by taking the limit as Dt – 0. The differential equation is: q d =-fheart qq - cp 27chiller [3] dt mbody Page 4.528.9 That is, we want a function q16t that satisfies equation 2. For this type of equation, we need an initial condition, that is, q16t at t=0. In this case, the q160 = initial body temperature. This equation can be solved to find q16t using techniques you will learn in your differential equations class. The solution is:   f - heart t  cm  qq27=+- qq   p body  techiller 490 chiller  [4]

For the example, Eq. 3 becomes:   - 5 t q27=+ -  08770.* te2549 37 25 [5] q2te7 =+25 12* -0.* 082 t

Using the Numerical approach (eq. 2) and the Actual solution (eq. 5), the temperature response is given Figure 1.

40 35 30 25 (degrees C) Temperature 20 0 102030 Time (minutes)

Solution - Diff. Eq. Numerical SetPoint

Figure 1. Comparison of the Different Solution Procedures for Body Temperature versus Time.

Problems:

1. Develop a spreadsheet solution to produce a plot similar to Figure 1. You should use a time step of 1 minute and compare the solution to the differential equation, Eq. 5, to the numerical approximation, Eq. 2. Make your spreadsheet so that you can easily change the parameters. (3 points) (Expected Time: 20 minutes) 2. How does body weights change the solution? (Note you must prove this with a graph showing the time to reach 30 degrees C versus body weight. (3 points) (Expected Time: 20 minutes) 3. One could develop a control algorithm for the chiller. Assume that the chiller would be cycled on and off to keep the body temperature at 30 degrees C. Since the room temperature in the operating room is usually cold (say 20 degrees C), assume that the body tends to chill even further when the chiller is off, requiring the use of a blood heater. Suppose the heater warms the blood to 34 degrees C and is turned on when the chiller is off. Also, the heater is off when the chiller is on. Develop an algorithm to control the heater/chiller combination. Implement your algorithm in Fortran 90 and plot the results of a typical operation (assume the operation lasts 2 hours). (10 points) (Expected time: 3 hours) Page 4.528.10 Appendix 2. Sample Problem from Environmental Engineering.

GRASSED WATERWAY DESIGN FOR WATERSHED DRAINAGE SOIL AND WATER/ENVIRONMENTAL CASE STUDY GROUP PROJECT (2 per group) – FALL 1998

Surface water occurs during heavy rainfall. Water on the surface can infiltrate into the soil or may be drained from the site via surface drainage. Uncontrolled surface drainage can cause off-site environmental problems including sedimentation of streams, lakes, and rivers, and nutrient enrichment. Sedimentation and nutrient enrichment can cause many problems in waterways such as increased turbidity, algal growth, and oxygen deficits. One approach to controlling surface water flow from an area is to route the water through surface waterways lined with grass. The grass increases the resistance to surface flow. The increased resistance acts to decrease the velocity of runoff delaying the flow peaks and volumes that are carried off-site. As you might expect, one must design grassed waterways to carry expected runoff volumes and peak runoff rates.

Problem: This problem requires that you develop a Fortran 90 program that calculates the required waterway design for varying rainfall rates for any given watershed. The problem can generally be broken down into two phases: 1) Calculate the peak runoff flow rate expected from a given watershed for a given storm event, and 2) Find the design parameters for the waterway that will carry the computed flow rate.

Phase 1: Calculate the peak flow rate from a watershed for a given rainfall intensity.

The method you can use for this phase is the Rational Method. This method is commonly used in the US. The equation for this method is:

QCiA= 0.*** 00278 where: Q = peak runoff rate, m3/s C = runoff coefficient for the watershed (See Table 1) i = rainfall intensity, mm/h A = effective watershed area Steps to Calculate Q:

1. To calculate Q, you must find the runoff coefficient that represents the entire watershed. Since watersheds tend to have mixed land uses based on vegetation, slope, etc, you must find an average C that is weighted by the areas. That is,

no−− of areas

∑ ACii = i=1 C no−− of areas

∑ Ai i=1 where Ci = runoff coefficient of subarea i from the Table Ai = area of subarea i in acres

2. Next calculate the watershed area, A. 3. Next, find the estimate of the peak flow rate using the rational equation based on the rainfall intensity. Page 4.528.11 Table 1. Runoff Coefficient (C) based on Soil type and Land Use Topography and Open Sandy Loam Clay and Silt Loam Tight Clay Vegetation

Woodland Flat 0-5% slope 0.10 0.30 0.40 Rolling 5-10% slope 0.25 0.35 0.50 Hilly 10-30% slope 0.30 0.50 0.60

Pasture Flat 0.10 0.30 0.40 Rolling 0.16 0.36 0.55 Hilly 0.22 0.42 0.60

Cultivated Flat 0.10 0.30 0.40 Rolling 0.16 0.36 0.55 Hilly 0.52 0.72 0.82

Urban 30% of area 50% of area 70% of area impervious impervious impervious Flat 0.40 0.55 0.65 Rolling 0.50 0.65 0.80

Phase 2: Calculate the Waterway design parameters to carry the peak flow from the watershed

There are many different shapes of waterways. For this problem, we assume that the shape will be that of a trapezoid. See below.

Side Slope Rise/Run y 1 z b

For the trapezoidal channel given above, the area and the wetted perimeter are given by:

=+2 Abyzyd ** Pb=+21** y + z2

The formula for calculating the flow rate capacity of the waterway is Manning’s Equation and given by:

2 1 1 Page 4.528.12 QR= 3 *** S2 A d n where: Q = flow rate, m3/s (this is your runoff rate from the Rational method) A R = hydraulic radius, m, and is given by R = d P P = wetted perimeter given above S = slope of the ditch, m/100m n = Manning’s roughness coefficient

Input Information for Your Sample Run:

Watershed Characteristics:

Area 1: 65 ha Wooded Area Hilly Grade 10% Soil – Silt Loam

Area 2: 35 ha Pasture Flat Grade – 0.1% Soil – Silt Loam

Area 3: 30 ha Housing subdivision Rolling – 30% impervious Slope 4% Soil – Clay and Silt Loam

Ditch Characteristics: b (bottom width) = 1.0 m z (side slope) = 1.5:1 n = 0.045 S = 1% (slope of channel – subject to change depending on your hand calculations)

Requirements for Turn In:

For the watershed described above, your Fortran 90 program should estimate the flowrate from the watershed Q for rainfall intensities (i) from 10 to 60 mm/h by steps of 5. Once the flowrates are estimated, then you should determine the ditch design parameters for each of the 11 rainfall intensities. You hold the ditch bottom width, the side slope and n constant. You are only solving for y. The results should be written to a file such that you can import the data into Nexs (spreadsheet) and make two plots: 1) Peak flowrate (Q) versus Rainfall intensity (i), and 2) Ditch Depth (Y) versus Rainfall intensity (i) . Your program should use a function to calculate the Q, call this function Rational. Your program should be general enough to accept up to 5 watershed subareas along with the necessary inputs.

Assignment Requirements (Summary): Before you begin to program, you must work a hand example using the rainfall intensity 10 mm/h. (Turn this in). Then develop a detailed algorithm based on your hand example (Turn this in). Write your program (turn in

a hard copy). Finally, turn in your graphs (hard copy). Page 4.528.13