UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2007

Similar documents
First Semester Review Calculus BC

The heat budget of the atmosphere and the greenhouse effect

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

Example. Have precipitation and streamflow data, need to estimate losses

Year 12 Mathematics Extension 2 HSC Trial Examination 2014

Vadose Zone Hydrology

The Fundamental Theorem of Calculus, Particle Motion, and Average Value

Mathematics Extension 1

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon

SAINT IGNATIUS COLLEGE

Distance And Velocity

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40

Physics 220. Exam #1. April 21, 2017

Sections 1.3, 7.1, and 9.2: Properties of Exponents and Radical Notation

Mathematics Extension Two

5.1 How do we Measure Distance Traveled given Velocity? Student Notes

Physics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:

200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes

Mathematics Extension 2

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction

Mathematics Extension 2

Student Session Topic: Particle Motion

AB Calculus Review Sheet

Vadose Zone Hydrology

( ) as a fraction. Determine location of the highest

Operations with Polynomials

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

TImath.com Algebra 2. Constructing an Ellipse

6.2 CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS

A sequence is a list of numbers in a specific order. A series is a sum of the terms of a sequence.

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs

Ph2b Quiz - 1. Instructions

MATH SS124 Sec 39 Concepts summary with examples

Scientific notation is a way of expressing really big numbers or really small numbers.

Math 113 Exam 1-Review

A formula sheet and table of physical constants is attached to this paper. Linear graph paper is available.

Physics 24 Exam 1 February 18, 2014

MA Exam 2 Study Guide, Fall u n du (or the integral of linear combinations

Estimation of Global Solar Radiation at Onitsha with Regression Analysis and Artificial Neural Network Models

Predict Global Earth Temperature using Linier Regression

Warm-up for Honors Calculus

Math Calculus with Analytic Geometry II

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Flow in porous media

A-Level Mathematics Transition Task (compulsory for all maths students and all further maths student)

2 b. , a. area is S= 2π xds. Again, understand where these formulas came from (pages ).

Math Sequences and Series RETest Worksheet. Short Answer

Physics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15

Advanced Algebra & Trigonometry Midterm Review Packet

Continuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom

Math 31S. Rumbos Fall Solutions to Assignment #16

MA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1

Sample Problems for the Final of Math 121, Fall, 2005

Session Trimester 2. Module Code: MATH08001 MATHEMATICS FOR DESIGN

List all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.

Physics 1402: Lecture 7 Today s Agenda

Main topics for the First Midterm

Algebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1

Unit Six AP Calculus Unit 6 Review Definite Integrals. Name Period Date NON-CALCULATOR SECTION

10.2 The Ellipse and the Hyperbola

3.1 Exponential Functions and Their Graphs

Total Score Maximum

Spring 2017 Exam 1 MARK BOX HAND IN PART PIN: 17

Precalculus Spring 2017

Unit 1 Exponentials and Logarithms

Sample Exam 5 - Skip Problems 1-3

COMPUTER SCIENCE TRIPOS

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA

Edexcel GCE Core Mathematics (C2) Required Knowledge Information Sheet. Daniel Hammocks

MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS

Physics 2135 Exam 1 February 14, 2017

Math 1B, lecture 4: Error bounds for numerical methods

The Properties of Stars

approaches as n becomes larger and larger. Since e > 1, the graph of the natural exponential function is as below

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is:

Mathematics for Physicists and Astronomers

Pre-Session Review. Part 1: Basic Algebra; Linear Functions and Graphs

Advanced Functions Page 1 of 3 Investigating Exponential Functions y= b x

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

0.1 THE REAL NUMBER LINE AND ORDER

4.4 Areas, Integrals and Antiderivatives

4.1 One-to-One Functions; Inverse Functions. EX) Find the inverse of the following functions. State if the inverse also forms a function or not.

Physics Honors. Final Exam Review Free Response Problems

CBE 291b - Computation And Optimization For Engineers

UNIT 3 Indices and Standard Form Activities

APPROXIMATE INTEGRATION

Trigonometric Functions

Math 116 Final Exam April 26, 2013

Generating Australian potential evaporation data suitable for assessing the dynamics in evaporative demand within a changing climate

Time in Seconds Speed in ft/sec (a) Sketch a possible graph for this function.

Chapter 5. , r = r 1 r 2 (1) µ = m 1 m 2. r, r 2 = R µ m 2. R(m 1 + m 2 ) + m 2 r = r 1. m 2. r = r 1. R + µ m 1

Week 10: Line Integrals

Physics 2135 Exam 3 April 21, 2015

Review of Calculus, cont d

Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions

Math 42 Chapter 7 Practice Problems Set B

Designing Information Devices and Systems I Spring 2018 Homework 7

AQA Chemistry Paper 2

AP Calculus AB Unit 5 (Ch. 6): The Definite Integral: Day 12 Chapter 6 Review

Minnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017

Transcription:

EXAMINATIONS: SUBJECT, COURSE AND CODE: HYDROLOGY 20 DURATION: HOURS TOTAL MARKS: 00 Internl Exminer : Ms ML Wrburton : Prof RE Schulze : Ms KT Chetty : Mr MJC Horn Externl Exminer : Prof PJT Roberts STUDENTS ARE REQUIRED IN THEIR OWN INTERESTS, TO WRITE LEGIBLY NOTES: This pper consists of 5 pges of questions. Plese see tht you hve them ll. Answer ll questions. Clcultors my be used. QUESTION : Rinfll (5 mrks) () Currently in South Afric three techniques of rinfll mesurement re used, viz. ringuges, wether rdr nd stellite. (i) Briefly discuss the use of wether rdr in mesuring rinfll, giving both the dvntges nd disdvntges. (4) (ii) With the id of sketch, explin the differences between hydrologicl nd meteorologicl rinfll. () (iii) Nme two fctors of ringuge s exterior which ffect its ccurcy, giving short resoning for ech fctor nmed. (2) (b) Does the rel reduction fctor (ARF) increse or decrese with (i) re? (ii) storm durtion? (iii) storm intensity? () Discuss the three () bsic ssumptions behind design rinfll studies. ()

QUESTION 2 : Interception nd Systems (5 Mrks) () Why, for given durtion of rinfll event, is the interception loss higher for higher rinfll intensities? Answer with the id of n nnotted sketch. (6) (b) Prepre sketch of the interctions of n ecosystem nd for ech component, explin how ech of the interctions is importnt in hydrology. (9) QUESTION : Evportion (20 Mrks) () When considering vegettion fctors which ffect totl evportion, explin the importnce of reflectivity, nd how it vries with plnt colour, wetness, seson nd time of dy. (6) (b) Both the Blney-Criddle nd the Thornthwite equtions for the estimtion of reference potentil evportion contin correction fctors for dylength. How, respectively, re the correction fctors clculted? (4) In the shortwve eqution of the Penmn formul for reference potentil evportion, clculte wht frction of extrterrestril rdition would rech the erth on dy when the sun shines for hlf the time, given n lbedo of 20%. Show ll working steps. (5) (d) In the versions of the Lincre eqution for n extended wter surfce nd wet vegetted surfce, wht re the differences between the equtions nd why do the respective constnts used chnge in the wy they do? (5) [20] 2

QUESTION 4 : Soil Wter (5 mrks) () Derive n expression for prticle density, P s, given lbortory setup where you re provided with four identicl flsks, some soil, some wter nd scle. Use digrms to explin your derivtion. (4) (b) Explin the processes of sorption nd desorption in the hysteresis effect. (2) (d) Explin, with the id of digrm, how one would mesure verticl flow in cylindricl smple. Add in your explntion how you would clculte sturted hydrulic conductivity nd the verge velocity. (5) If the bulk density of the soil smple is mesured s 600kg.m -, the prticle density is 2650 kg.m - nd the wter content is 0.2, determine the percent sturtion of the smple. (4) QUESTION 5 : Runoff (5 mrks) () Criticlly discuss ny two ssumptions of Horton s runoff theory. (4) (b) Explin the two theories used to describe interflow contribution to the hydrogrph. (6) Briefly explin the impct of (i) Overgrzing on sediment yield nd, (ii) Afforesttion on bseflows (4) (d) Define the term rting curve. () QUESTION 6 : Wter Budget (20 Mrks) () (b) Complete the monthly wter budget tble on pge 4. (Hint: All the necessry informtion is contined in the tble) (7) Explin briefly how, in given month there my be more net precipittion (Pn) thn totl evportion (E) nd yet no runoff my be generted? (4) Knowing the Men Annul Precipittion of n re is of no vlue to wter prctitioner, frmer or home owner. Discuss this sttement with reference to the vrious spects of the wter budget you hve studied. (9) [20]

Do Not forget to hnd in this pge Student Number (mm) Jn Feb Mr Apr Pn 56 0 90 Em 85 70 60 4 Pe - Em 28 Actul SM 200 chnge 0 SM E 85 70 50 D 0 S 28 Avil Q 56 Q 28 Detention 28 4

EQUATION SHEET P % n 0 = ( n+ m) 00 n+ RH ed = 00 e P T t =.(0.27 lnt + 0.56)(0.54t 0.25-0.50)(4.5 + 0.55M 2 +.9L) = (0.5 lnt +0.76)(0.54t 0.25-0.50)(.M 0.6 R 0.20 ) E p = /γ Rn + E /γ+ P n - o = ( - / T) n r = R+ Rtn tn i cos( B W ) 2 V = 0. 46 + 5. 56 d. 02 d + 0. 068 d t5 50 50 d 50 =.28I 0.82 50 E = 7. 62 0 ( 60. 9 + u)( 00 RH ) e 7. 5T /( 27. + T) e = 60. 78 0 R = R ( α )( 0. 24 + 0. 5n / N) sw R = [ ε ( σt 4 )][ 0. 56 c( e RH ) 0.5 ][ f + ( f) n / N ] lw k E = 0.5mv 2 = 29.8-27.5 / I =.9 + 8.7log 0 I h= 2σ cos ά rρg A 0 = (π / 4) D 0 E p = [0.05+4x0-4 T +0-6 z][480(t +0.006z)/(84 - φ) - 40 + 2.u(T -T d )] = [0.05+4x0-4 T +0-6 z][80(t + 0.006z)/(84 - φ) - 40+ 4u(T - T d )] = [60(T +0.006z)/(84 - φ) - 60 +.6u(T - T d )] / [28.5+45(γ / ) ] where (T - T d ) = 0.002z+0.7T+0.5(T mx - T mn ) + 0.5T r - 0.9 f = 0. 94 + 0. 0026ψ cr / E s l r i m( i ) = E = k E FRAC If Ө (i-) > [(f s PAW ) + LL ], then FRAC = else A e = A 0 cos i FRAC = ( LL ) θ ( i ) PAW f s 5