SPILLWAY DESIGN FOR A COMPOSITE DAM

Size: px
Start display at page:

Download "SPILLWAY DESIGN FOR A COMPOSITE DAM"

Transcription

1 Vlume: 03 Issue: 04 April p-issn: SPILLWAY DESIGN FOR A COMPOSITE DAM Arun Jji 1, Nithya Thmas 2, Reshma Jse 3,Yapung Chije 4, Dr. Slly Gerge 5 1Arun Jji, Unde graduate, Dept. f Civil Engineering,MACE Kthamangalam 2Nithya Thmas, Unde graduate, Dept. f Civil Engineering,MACE Kthamangalam 3Reshma Jse, Unde graduate, Dept. f Civil Engineering,MACE Kthamangalam 4Yapung Chije, Unde graduate, Dept. f Civil Engineering,MACE Kthamangalam 5Dr.Slly Gerge,Prfessr, Dept. f Civil Engineering,MACE Kthamangalam,Kerala, India *** Abstract - Spillways are prvided fr strage and detentin dams which may nt fail with slight vertpping fr a dams t release surplus fldwater, which cannt be small perid f time. cntained in the alltted strage space. In this paper we have This dcument is template. We ask that authrs fllw sme designed a spillway fr a cmpsite dam prpsed at simple guidelines. In essence, we ask yu t make yur paper Kanthallr as a part f Pattiserry irrigatin prject. lk exactly like this dcument. The easiest way t d this is Pattiserry irrigatin prject envisages cnstructin f 140 m simply t dwnlad the template, and replace(cpy-paste) lng and 23m high cmpsite dam, earthen bund with the cntent with yur wn material. Number the reference cncrete verflw sectin, acrss the river chengalar a items cnsecutively in square brackets (e.g. [1]). Hwever tributary f Pambar river, lcated in Kanthallr village. The the authrs name can be used alng with the reference prject aims at irrigating 240 Ha f land in Marayr area, number in the running text. The rder f reference in the thrugh 8 km lng unlined canal. The prpsed dam is lcated running text shuld match with the list f references at the 5m dwnstream f the existing weir which is 20m lng and 5m end f the paper. high, cnstructed during The prpsed dam cmprises, 15m lng cncrete verflw sectin at the centre and 25m lng nn-verflw sectin n the right and 15m lng n the left. The cncrete sectin is flanked by earthen dam, 50 m lng 2. FACTORS AFFECTING SPILLWAY DESIGN in the left and 35m in the right. In the prpsed dam spillway is at the cncrete verflw sectin. We chse an gee type spillway fr the dam prpsed. a. Safety cnsideratins cnsistent with ecnmy: Key Wrds: Cmpsite dam, Ogee Spillway, Spillway prfile, Safety against sliding, Trajectry bucket. 1.INTRODUCTION Pambar river basin is faced with severe drught situatin during summer seasn when the crps grwn in Kanthallr village need water fr irrigatin. The sil is highly fertile fr paddy, sugarcane, vegetables and varieties f fruits. In rder t cater t the irrigatin needs, the pssible slutin in this catchment is t stre water during the mnsn mnths and als t facilitate fr strage f water frm rainfall received during summer. This cncept lead t the prpsal f cnstructin f dam at Kanthallr. Spillway is ne f the mst imprtant cmpnent f a dam. Many failures f dams have been reprted due t inadequate capacity r imprper design f spillway, especially fr earthen and rckfill type dams which are likely t be destryed,if vertpped,unlike cncrete Many failures f dams have resulted frm imprperly designed spillway r spillways f inadequate capacity. Prperly designed structure f adequate capacity may be fund t be nly mderately higher in cst than a structure f inadequate capacity. b. Hydrlgical and site cnditins: The spillway design and its capacity depend n Inflw discharge, its frequency, and shape f hydrgraph Height f dam Gelgical and ther site cnditins Imprtant tpgraphical features, which affect spillways design, are Steepness f terrain Amunt f excavatin and pssibility f its use as embankment material. The pssibility f scur Stability f slpes, safe bearing capacity f sils. Permeability f sils. 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2557

2 Vlume: 03 Issue: 04 April p-issn: c. Type f Dam The type f dam influences the design fld and spillway. Fr earth and rckfill dam gee r chute spillway is preferred. 3. DESIGN OF SPILLWAY Full Reservir Level (FRL) = M Maximum Water Level (MWL)= M Height f Dam=23 m Tp Level= M Crest Level= M Deepest rck level= M Therefre, Head = MWL Crest level = = 4.00 m Maximum fld discharge = m 3 /sec H d (design head) = (IS: ) = 3.6 m P/ H d = (spillway crest level deepest level)/ H d = ( ) = m > Upstream prfile u/s quadrant f the crest may cnfirm t ellipse X 12 /A Y 12 /B 1 2 =1 (IS: 6934, cl ) Fr P/H d > 2, A 1/H d = 0.28 (frm fig 2, IS 6934) B 1/H d = Where, P= height f spillway crest frm river bed H d = Design head A 1 = 0.28 H d = =1.008 m B 1 = = m Therefre, X 12 /A Y 12 /B 2 1 =1 X 12 / (1.008) 2 + Y 12 /(0.5904) 2 = 1 X 12 = {1- Y 1/(0.5904) 2 } X 2 1 = Y 2 1 Table -1: Upstream prfile c-rdinates Y 1 X Dwnstream prfile d/s prfile f the crest may cnfirm t the equatin IS: 6934, cl X = K 2 H 0.85 d Y , IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2558

3 Vlume: 03 Issue: 04 April p-issn: K 2 = 2 (IS 6934, FIG 2) P/H d = > 2 Therefre, X = Y 2 X 2= 2.62 Y Table -2: Dwnstream prfile c-rdinates Y 2 X Figure 1: Upstream prfile 3.3 Tangent pint X = 2.62Y dx/dy = Y = Y Adpt a slpe f 0.75 (slpe varies frm 0.7:1 t 0.8:1) 0.75= dx/dy = Y Figure 2: Dwnstream prfile Y = /0.75 Y = At tangent pint, Y 2 = m X 2 = = m 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2559

4 Vlume: 03 Issue: 04 April p-issn: Table-3: Frces and Mments Figure 3: Spillway Prfile 3.4 Cmputatin f frces and mments The entire area f spillway prfile was divide int rectangles and triangles numbered frm 1 t 38. Vertical frce = Area x Unit weight f cncrete Mment = Frce x Lever arm 3.5 Water Pressure At MWL all shutters will be pen. Hence the water abve crest i.e, at t MWL(1582) will flw ver the crest. 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2560

5 Vlume: 03 Issue: 04 April p-issn: Hence, the pressure develped abve the crest will be wh i.e, wh= 1 ( )= 4 Pressure diagram will be rectangle frm base t crest level and triangle frm base f dam up t MWL. a) Water at MWL Table- 4: Frces and Mments Descriptin Frce, KN Lever Arm Mment, KNm Rectangle Triangle Ttal Silt pressure( IS ) Bed level= Silt height is taken as 2m As per IS vertical pressure, r s = =0.925 t/m 3 Hrizntal pressure, r s = =0.36 t/m 3 Vertical frce = 1/ = t Hrizntal frce = /2 = 0.72 t Table-8: Lads/mments at base f te Descriptin Frce, t Lever Arm Mment, tm Vertical b) Water at FRL Shutter clsed Hrizntal Table- 5: Frces and Mments Descriptin Frce, KN Lever Arm Mment, KNm Triangle Uplift Pressure a) Water at MWL Table- 6: Frces and Mments Frce Lever arm Mment, tnne b) Water at FRL Table- 7: Frces and Mments Frce Lever arm Mment, tnne Weight f water Lads/mments f base f te due t water a) Water at MWL Table- 9: Frces and Mments Descriptin Frce, t Lever Arm Mment, tm Rectangle Triangle b) Water at FRL Table- 10: Frces and Mments Descriptin Frce, t Lever Arm Rectangle Mment, tm Triangle , IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2561

6 Vlume: 03 Issue: 04 April p-issn: L O A D 3.9 Lad cmbinatin DESCRIPTION H V M 0 M x A area under cnsideratin F ɸ partial safety factr f reactin F c partial safety factr f chesin P ttal hrizntal frce A Weight f structure B Weight f structure COMBINATION B F = ((w - u) tan ɸ / F ɸ + C A / F c) / P F = ((( ) tan25 ) / / 4.5 ) / Water pressure Uplift pressure Silt pressure Water lad = 2.1 kn>1 Hence safe COMBINATION C F = ((w u ) tan ɸ / F ɸ + C A / F c ) / P = ((( ) tan25 ) / / 4.5 ) / = 2.17 kn>1 Hence safe C Weight f structure Water pressure Uplift pressure HYDRAULIC DESIGN OF TRAJECTORY BUCKET TYPE ENERGY DISSIPATOR ( IS 7365:2010) a) Bucket shape Fr practical cnsideratin, a circular shape f trajectry bucket is prpsed fr the design. Silt pressure Water lad b)bucket invert elevatin Available data Ttal discharge = 88 m 3 /s H- Hrizntal Frce M verturning mment V- Vertical Frce M x resisting mment 3.10 Check fr sliding Factr f safety against sliding F = ((w-u) tan ɸ /F ɸ + CA/F c)/p w ttal mass f dam u ttal uplift pressure tan ɸ cefficient f internal frictin ɸ= 25 Width f bucket = 10 m Max. reservir pl elevatin = 1582 m Crest level f spillway = 1578 m Max. tail water level = 1562 m S assume bucket invert elevatin = m c) Radius f bucket H 1 = reservir pl elevatin bucket invert elevatin = = m 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2562

7 Vlume: 03 Issue: 04 April p-issn: H = reservir pl elevatin crest level = = 4 m H 5 = reservir pl elevatin jet surface elevatin = = As per IS 7365: 2010 cl: Radius f bucket = 0.6 t 0.8(H.H 5) 0.5 = 0.6 t 0.8(4 x 18.44) 0.5 = 5.15 t 6.87 Prvide radius f bucket as R = 6.00 m d) Lip elevatin and exit angle In rder t minimize the sub-atmspheric pressure n lip prvide a lip angle f 30 R R cs ϕ = 6 6 cs (30) f) Estimatin f scur dwnstream f spillway ( IS 7365:2010) Depth f scur, d s = m (q H a ) 0.5 m = 0.36 (minimum expected scur) q = 17.9 m 3 /s H 4 = reservir pl elevatin bucket lip level = = m Therefre d s = 0.36 ( ) 0.5 = 6.58 m g) The shape and width f lip As per IS 7365:2010,cl ,width f lip is prvided 1/10 f radius f bucket. 6/10 = 0.6 m = S lip level = = m Therefre tail water level is lwer than lip level. Lip shall be made flat. (As per IS 7385:2010, cl:5.2.4) e) Trajectry length Actual velcity f jet at lip f bucket V a = m/s ɣ= Lip level Tail water level = = m H γ = V a2 /2g = / = m X/H γ = sin 2ϕ + 2 cs ϕ sin 2 ϕ+ ɣ/h ɣ X/ = sin cs30 sin (1.304/14.574) X = m Vertical distance f thrw as per IS 7365 cl a= V 2 a sin 2 ϕ /(2g) = sin 2 30/ (2 9.81) = 3.64 m Figure 4: Trajectry Bucket 5. CONCLUSIONS The verflw sectin f the dam is f cncrete where spillway is lcated. S the design f the spillway f cmpsite dam was based n the spillway design criteria f a gravity dam. Ogee type spillway was adpted because f high discharging efficiency. Fr energy dissipatin and the preventin f dwnstream scur, trajectry bucket is als included in the design. REFERENCES [1] IS 6934:1998, Hydraulic design f high gee verflw spillways- Recmmendatins [2] IS 7365:2010, Criteria fr hydraulic design f bucket type energy dissipatrs 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2563

8 Vlume: 03 Issue: 04 April p-issn: [3] IS 10137:1982, Guidelines fr selectin f spillways and energy dissipatrs [4] IS 6512:1984, Criteria fr design f slid gravity dams [5] United States Bureau f Reclamatin, Design f small dams [6] Dr. P N Mdi, Irrigatin and water pwer engineering [7] S K Garg, Irrigatin engineering and hydraulic structures BIOGRAPHIES 1 B Tech Graduate, Civil Engineering Department, Mar Athanasius Cllege f Engineering, Kthamangalam, Kerala, India, mail2arunjji@gmail.cm 2 B Tech Graduate, Civil Engineering Department, Mar Athanasius Cllege f Engineering, Kthamangalam, Kerala, India, nithyamarythmas@gmail.cm 3 B Tech Graduate, Civil Engineering Department, Mar Athanasius Cllege f Engineering, Kthamangalam, Kerala, India, reshma.k.jse@gmail.cm 4 B Tech Graduate, Civil Engineering Department, Mar Athanasius Cllege f Engineering, Kthamangalam, Kerala, India, yapung2010@gmail.cm 5 Prfessr, Civil Engineering Department, Mar Athanasius Cllege f Engineering, Kthamangalam, Kerala, India, sllygerge@mace.ac.in 2016, IRJET Impact Factr value: 4.45 ISO 9001:2008 Certified Jurnal Page 2564

Sediment Basin (SB) Description. Appropriate Uses. Design and Installation

Sediment Basin (SB) Description. Appropriate Uses. Design and Installation Descriptin A sediment basin is a temprary pnd built n a cnstructin site t capture erded r disturbed sil transprted in strm runff prir t discharge frm the site. Sediment basins are designed t capture site

More information

3. Design of Channels General Definition of some terms CHAPTER THREE

3. Design of Channels General Definition of some terms CHAPTER THREE CHAPTER THREE. Design f Channels.. General The success f the irrigatin system depends n the design f the netwrk f canals. The canals may be excavated thrugh the difference types f sils such as alluvial

More information

Aircraft Performance - Drag

Aircraft Performance - Drag Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce

More information

Exam #1. A. Answer any 1 of the following 2 questions. CEE 371 March 10, Please grade the following questions: 1 or 2

Exam #1. A. Answer any 1 of the following 2 questions. CEE 371 March 10, Please grade the following questions: 1 or 2 CEE 371 March 10, 2009 Exam #1 Clsed Bk, ne sheet f ntes allwed Please answer ne questin frm the first tw, ne frm the secnd tw and ne frm the last three. The ttal ptential number f pints is 100. Shw all

More information

Drought damaged area

Drought damaged area ESTIMATE OF THE AMOUNT OF GRAVEL CO~TENT IN THE SOIL BY A I R B O'RN EMS S D A T A Y. GOMI, H. YAMAMOTO, AND S. SATO ASIA AIR SURVEY CO., l d. KANAGAWA,JAPAN S.ISHIGURO HOKKAIDO TOKACHI UBPREFECTRAl OffICE

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Exam #1. A. Answer any 1 of the following 2 questions. CEE 371 October 8, Please grade the following questions: 1 or 2

Exam #1. A. Answer any 1 of the following 2 questions. CEE 371 October 8, Please grade the following questions: 1 or 2 CEE 371 Octber 8, 2009 Exam #1 Clsed Bk, ne sheet f ntes allwed Please answer ne questin frm the first tw, ne frm the secnd tw and ne frm the last three. The ttal ptential number f pints is 100. Shw all

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

Assume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected.

Assume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected. 1 HW #3: Cnservatin f Linear Mmentum, Cnservatin f Energy, Cnservatin f Angular Mmentum and Turbmachines, Bernulli s Equatin, Dimensinal Analysis, and Pipe Flws Prblem 1. Cnservatins f Mass and Linear

More information

Figure 1a. A planar mechanism.

Figure 1a. A planar mechanism. ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,

More information

Chapter 2 GAUSS LAW Recommended Problems:

Chapter 2 GAUSS LAW Recommended Problems: Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating

More information

erosion&sedimentcontrol

erosion&sedimentcontrol Auckland Reginal Cuncil Sediment Cntrl: 2 1 ersin&sedimentcntrl Guidelines fr Land Disturbing Activities in the Auckland Regin 2.1 Sediment Retentin Pnd Plate 2.1.1 Sediment Retentin Pnd Shwing Decant

More information

Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm

Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm Faculty f Engineering and Department f Physics Engineering Physics 131 Midterm Examinatin February 27, 2006; 7:00 pm 8:30 pm N ntes r textbks allwed. Frmula sheet is n the last page (may be remved). Calculatrs

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

Review for the final exam (Math 127)

Review for the final exam (Math 127) . Evaluate 3 tan tan 4 3 (b) (c) cs cs 4 7 3 sec cs 4 4 (d) cs tan 3 Review fr the final eam (Math 7). If sec, and 7 36, find cs, sin, tan, ct, csc tan (b) If, evaluate cs, sin 7 36 (c) Write the csc in

More information

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle? Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes

More information

PHYSICS Unit 3 Trial Examination

PHYSICS Unit 3 Trial Examination STAV Publishing Pty Ltd 005 PHYSICS Unit 3 Trial Examinatin SOLUTIONS BOOK Published by STAV Publishing Pty Ltd. STAV Huse, 5 Munr Street, Cburg VIC 3058 Australia. Phne: 6 + 3 9385 3999 Fax: 6 + 3 9386

More information

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle? Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which

More information

Math 0310 Final Exam Review Problems

Math 0310 Final Exam Review Problems Math 0310 Final Exam Review Prblems Slve the fllwing equatins. 1. 4dd + 2 = 6 2. 2 3 h 5 = 7 3. 2 + (18 xx) + 2(xx 1) = 4(xx + 2) 8 4. 1 4 yy 3 4 = 1 2 yy + 1 5. 5.74aa + 9.28 = 2.24aa 5.42 Slve the fllwing

More information

TRWD Stream Trailer Demonstration Guide

TRWD Stream Trailer Demonstration Guide TRWD Stream Trailer Demnstratin Guide Objectives: The Student Will Observe and interact with an evlving river and wetland. Understand the three cmpnents f a river system Understand the rle ersin plays

More information

ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vector Functions Page 2-01 ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

More information

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?

Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string? Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)

More information

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3 ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at

More information

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support. ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

Surface and Contact Stress

Surface and Contact Stress Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated

More information

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

More information

39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution

39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution 39th Internatinal Physics Olympiad - Hani - Vietnam - 8 Theretical Prblem N. /Slutin Slutin. The structure f the mrtar.. Calculating the distance TG The vlume f water in the bucket is V = = 3 3 3 cm m.

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972

ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972 115 ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972 B.Gauir SUMMARY On 16 September, 1972 at 04 15 09.8 UT an earthquake f magnitude ML 5.0 ccurred in sutheast Papua within abut 20

More information

Lecture 5: Equilibrium and Oscillations

Lecture 5: Equilibrium and Oscillations Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if

More information

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed

More information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax .7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical

More information

Comparison of two variable parameter Muskingum methods

Comparison of two variable parameter Muskingum methods Extreme Hydrlgical Events: Precipitatin, Flds and Drughts (Prceedings f the Ykhama Sympsium, July 1993). IAHS Publ. n. 213, 1993. 129 Cmparisn f tw variable parameter Muskingum methds M. PERUMAL Department

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)? THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,

More information

CHAPTER 8b Static Equilibrium Units

CHAPTER 8b Static Equilibrium Units CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but

More information

MOCK CBSE BOARD EXAM MATHEMATICS. CLASS X (Paper 1) (AS PER THE GUIDELINES OF CBSE)

MOCK CBSE BOARD EXAM MATHEMATICS. CLASS X (Paper 1) (AS PER THE GUIDELINES OF CBSE) MOCK CSE ORD EXM MTHEMTICS CLSS X (Paper 1) (S PER THE GUIDELINES OF CSE) Time: 3 Hurs Max. Marks: 80 General Instructins 1. ll the questins are cmpulsry. 2. The questin paper cnsists f 30 questins divided

More information

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1 Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

More information

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter). Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)

More information

1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?

1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south? 1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is

More information

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY Unit 43: Plant and Prcess Principles Unit cde: H/601 44 QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY 3 Understand static and namic fluid systems with

More information

CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,

More information

Compressibility Effects

Compressibility Effects Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

SOLUTION OF THREE-CONSTRAINT ENTROPY-BASED VELOCITY DISTRIBUTION

SOLUTION OF THREE-CONSTRAINT ENTROPY-BASED VELOCITY DISTRIBUTION SOLUTION OF THREECONSTRAINT ENTROPYBASED VELOCITY DISTRIBUTION By D. E. Barbe,' J. F. Cruise, 2 and V. P. Singh, 3 Members, ASCE ABSTRACT: A twdimensinal velcity prfile based upn the principle f maximum

More information

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the

More information

Q x = cos 1 30 = 53.1 South

Q x = cos 1 30 = 53.1 South Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is

More information

Lornshill Academy. Geography Department National Revision Physical Environments Rivers

Lornshill Academy. Geography Department National Revision Physical Environments Rivers Lrnshill Academy Gegraphy Department Natinal Revisin Physical Envirnments Rivers Revisin Ntes fr Rivers What yu need t knw: 1. Hw rivers erde, transprt and depsit. 2. The Upper Curse: Frmatin f a V-shaped

More information

1 Course Notes in Introductory Physics Jeffrey Seguritan

1 Course Notes in Introductory Physics Jeffrey Seguritan Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

UNIT 1 COPLANAR AND NON-COPLANAR FORCES

UNIT 1 COPLANAR AND NON-COPLANAR FORCES UNIT 1 COPLANA AND NON-COPLANA FOCES Cplanar and Nn-Cplanar Frces Structure 1.1 Intrductin Objectives 1. System f Frces 1.3 Cplanar Frce 1.3.1 Law f Parallelgram f Frces 1.3. Law f Plygn f Frces 1.3.3

More information

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007

CS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007 CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is

More information

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology

Technical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)

More information

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential

More information

Higher Mathematics Booklet CONTENTS

Higher Mathematics Booklet CONTENTS Higher Mathematics Bklet CONTENTS Frmula List Item Pages The Straight Line Hmewrk The Straight Line Hmewrk Functins Hmewrk 3 Functins Hmewrk 4 Recurrence Relatins Hmewrk 5 Differentiatin Hmewrk 6 Differentiatin

More information

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs

Admissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs Admissibility Cnditins and Asympttic Behavir f Strngly Regular Graphs VASCO MOÇO MANO Department f Mathematics University f Prt Oprt PORTUGAL vascmcman@gmailcm LUÍS ANTÓNIO DE ALMEIDA VIEIRA Department

More information

ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels

ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION Instructins: If asked t label the axes please use real wrld (cntextual) labels Multiple Chice Answers: 0 questins x 1.5 = 30 Pints ttal Questin Answer Number 1

More information

Analysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network

Analysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:

More information

Design and Analysis of Gas Turbine Blade by Potential Flow Approach

Design and Analysis of Gas Turbine Blade by Potential Flow Approach V. Vijaya kumar et al Int. Jurnal f Engineering Research and Applicatins RESEARCH ARTICLE OPEN ACCESS Design and Analysis f Gas Turbine Blade by Ptential Flw Apprach V. Vijaya Kumar 1, R. Lalitha Narayana

More information

WYSE Academic Challenge Regional Mathematics 2007 Solution Set

WYSE Academic Challenge Regional Mathematics 2007 Solution Set WYSE Academic Challenge Reginal Mathematics 007 Slutin Set 1. Crrect answer: C. ( ) ( ) 1 + y y = ( + ) + ( y y + 1 ) = + 1 1 ( ) ( 1 + y ) = s *1/ = 1. Crrect answer: A. The determinant is ( 1 ( 1) )

More information

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS On cmpletin f this tutrial yu shuld be able t d the fllwing. Define viscsity

More information

Chapter 6. Dielectrics and Capacitance

Chapter 6. Dielectrics and Capacitance Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges

More information

Trigonometric Ratios Unit 5 Tentative TEST date

Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

More information

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu

More information

N umerical analyses such as the finite element method

N umerical analyses such as the finite element method TUNNELS AND DEEP SPACE P: 80886-7798(98) 00004-2 Lessns Learned frm Field Measurements in Tunnelling S. Sakurai Abstract-- Over the past tw decades, varius numerical methds f analysis have becme ppular

More information

M thematics. National 5 Practice Paper B. Paper 1. Duration 1 hour. Total marks 40

M thematics. National 5 Practice Paper B. Paper 1. Duration 1 hour. Total marks 40 M thematics Natinal 5 Practice Paper B Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain

More information

SPH3U1 Lesson 06 Kinematics

SPH3U1 Lesson 06 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

More information

Kinematic transformation of mechanical behavior Neville Hogan

Kinematic transformation of mechanical behavior Neville Hogan inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

More information

1/2 and e0 e s ' 1+ imm w 4 M s 3 πρ0 r 3 m. n 0 ktr. .Also,since n 0 ktr 1,wehave. 4 3 M sπρ 0 r 3. ktr. 3 M sπρ 0

1/2 and e0 e s ' 1+ imm w 4 M s 3 πρ0 r 3 m. n 0 ktr. .Also,since n 0 ktr 1,wehave. 4 3 M sπρ 0 r 3. ktr. 3 M sπρ 0 Chapter 6 6.1 Shw that fr a very weak slutin drplet (m 4 3 πr3 ρ 0 M s ), (6.8) can be written as e 0 ' 1+ a r b r 3 where a σ 0 /n 0 kt and b imm w / 4 3 M sπρ 0. What is yur interpretatin f thecnd and

More information

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )

[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y ) (Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

3. Classify the following Numbers (Counting (natural), Whole, Integers, Rational, Irrational)

3. Classify the following Numbers (Counting (natural), Whole, Integers, Rational, Irrational) After yu cmplete each cncept give yurself a rating 1. 15 5 2 (5 3) 2. 2 4-8 (2 5) 3. Classify the fllwing Numbers (Cunting (natural), Whle, Integers, Ratinal, Irratinal) a. 7 b. 2 3 c. 2 4. Are negative

More information

Loads, Structures & Mechanisms Team C3

Loads, Structures & Mechanisms Team C3 Lads, Structures & Mechanisms Team C3 Dylan Carter Siddharth Paruchuru Kenneth Hart Michael Hamiltn Overview f Lads Crew Vehicle - Earth Launch - Pressurizatin Lads - Dcking Lads - Earth EDL Lunar Landing

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.

More information

Concept Category 2. Trigonometry & The Unit Circle

Concept Category 2. Trigonometry & The Unit Circle Cncept Categry 2 Trignmetry & The Unit Circle Skill Checklist Use special right triangles t express values f fr the six trig functins Evaluate sine csine and tangent using the unit circle Slve tw-step

More information

Module 4: General Formulation of Electric Circuit Theory

Module 4: General Formulation of Electric Circuit Theory Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

More information

Charge of an Electron

Charge of an Electron Charge f an Electrn EX-9929 Page 1 f 12 EQUIPMENT Charge f an Electrn 1 Millikan Oil Drp Apparatus AP-8210 1 Basic Digital Multimeter SE-9786 1 High Vltage Pwer Supply SF-9585A 1 Large Rd Base ME-8735

More information

Lab 1 The Scientific Method

Lab 1 The Scientific Method INTRODUCTION The fllwing labratry exercise is designed t give yu, the student, an pprtunity t explre unknwn systems, r universes, and hypthesize pssible rules which may gvern the behavir within them. Scientific

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical

More information

SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR 11

SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR 11 SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR Cpyright Schl Curriculum and Standards Authrity, 08 This dcument apart frm any third party cpyright material cntained in it may be freely cpied,

More information

When a substance heats up (absorbs heat) it is an endothermic reaction with a (+)q

When a substance heats up (absorbs heat) it is an endothermic reaction with a (+)q Chemistry Ntes Lecture 15 [st] 3/6/09 IMPORTANT NOTES: -( We finished using the lecture slides frm lecture 14) -In class the challenge prblem was passed ut, it is due Tuesday at :00 P.M. SHARP, :01 is

More information

OTHER USES OF THE ICRH COUPL ING CO IL. November 1975

OTHER USES OF THE ICRH COUPL ING CO IL. November 1975 OTHER USES OF THE ICRH COUPL ING CO IL J. C. Sprtt Nvember 1975 -I,," PLP 663 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.

More information

3. Mass Transfer with Chemical Reaction

3. Mass Transfer with Chemical Reaction 8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,

More information

CLASS XI SET A PHYSICS

CLASS XI SET A PHYSICS PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the

More information

The standards are taught in the following sequence.

The standards are taught in the following sequence. B L U E V A L L E Y D I S T R I C T C U R R I C U L U M MATHEMATICS Third Grade In grade 3, instructinal time shuld fcus n fur critical areas: (1) develping understanding f multiplicatin and divisin and

More information

Solution to HW14 Fall-2002

Solution to HW14 Fall-2002 Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

More information

Kinetic Model Completeness

Kinetic Model Completeness 5.68J/10.652J Spring 2003 Lecture Ntes Tuesday April 15, 2003 Kinetic Mdel Cmpleteness We say a chemical kinetic mdel is cmplete fr a particular reactin cnditin when it cntains all the species and reactins

More information

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents

WRITING THE REPORT. Organizing the report. Title Page. Table of Contents WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive

More information

Function notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property

Function notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property Functin ntatin & cmpsite functins Factring Dividing plynmials Remainder therem & factr prperty Can d s by gruping r by: Always lk fr a cmmn factr first 2 numbers that ADD t give yu middle term and MULTIPLY

More information

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions

Guide to Using the Rubric to Score the Klf4 PREBUILD Model for Science Olympiad National Competitions Guide t Using the Rubric t Scre the Klf4 PREBUILD Mdel fr Science Olympiad 2010-2011 Natinal Cmpetitins These instructins are t help the event supervisr and scring judges use the rubric develped by the

More information

The calculation method of small-scale water injection multiple in water drive reservoirs

The calculation method of small-scale water injection multiple in water drive reservoirs Available nline.jcpr.cm Jurnal f Chemical and Pharmaceutical Research, 04, 6(5):04-09 Research Article ISSN : 0975-7384 CODEN(USA) : JCPRC5 The calculatin methd f small-scale ater injectin multiple in

More information

E-Waybill in Tally.ERP9. V e r s i o n : 1. 0 g s a n t r a w e b. c o m w w w. t a l l y h e l p. c o m

E-Waybill in Tally.ERP9. V e r s i o n : 1. 0 g s a n t r a w e b. c o m w w w. t a l l y h e l p. c o m E-Waybill in Tally.ERP9 V e r s i n : 1. 0 g s t @ a n t r a w e b. c m w w w. t a l l y h e l p. c m 022-4 0 8 6 4 0 8 6 Cntents Electrnic Way Bill... 3 E-Way Bill under GST... 3 Wh shuld generate the

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

Matter Content from State Frameworks and Other State Documents

Matter Content from State Frameworks and Other State Documents Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with

More information

Types of Gear Pg xxx. Spur Gear Teeth is parallel to axis of rotation Can transmit power between parallel shaft The simplest form for gear

Types of Gear Pg xxx. Spur Gear Teeth is parallel to axis of rotation Can transmit power between parallel shaft The simplest form for gear [Pg / 2] Gears Objectives. 2. 3. 4. 5. Cmpute the frces exerted n gear teeth as they rtate and transmit pwer. Use apprpriate stress analyses t determine the relatinships amng the applied frces, the gemetry

More information