Stone or brick aggregate filling. Brick chamber with dry joints. 1.5m

Size: px
Start display at page:

Download "Stone or brick aggregate filling. Brick chamber with dry joints. 1.5m"

Transcription

1 SERVICES FOR THE URBAN POOR Key poits about draiage The objective of draiage improvemets is to cotai ad limit floodig so that it causes miimal damage ad disruptio. The raisig of road surfaces above the plith levels of earby houses should always be avoided. Where off site draiage systems are iadequate, try to develop draiage schemes which retai water locally i order to reduce the rate of ruoff. Wherever possible, desig streets to act as drais. I geeral, the ru-off from areas up to about 5 hectares i area ca be carried o the street surface where the aual raifall is i the rage mm/yr. Draiage schemes i iformal areas should ormally be desiged for a retur period of 1 year or less. I the absece of local iformatio, a raifall itesity i the rage mm per hour ca be assumed. Both ope ad covered drais give rise to maiteace problems ad their total legth should be miimised. Ulied ditches have limited uses i upgradig schemes because of their eed for costat maiteace. Covered drais should ot be smaller tha about 500mm square i crosssectio. 4.4

2 4a: DRAINAGE Sectio 4a Draiage Tool D1 Draiage: Objectives ad optios Objectives The objective of draiage is to remove uwated water from the eighbourhood i a cotrolled ad hygieic maer i order to miimise public health hazards, icoveiece to residets ad the deterioratio of other ifrastructure. This requires: the removal of sullage, that is, household wastewater which has bee used for washig, cookig or cleaig purposes but which does ot cotai excreta; ad the removal of surface water, that is, water which rus off the lad ad buildigs as a result of raifall. More specifically, we eed to cosider: miimisig the icidece of floodig of houses; prevetig erosio ad the cosequet risk of damage to property; elimiatig stadig water ad the cosequet dager from mosquitocarried diseases; ad reducig the extet ad duratio of floodig of streets ad rights of way to acceptable levels. 4.5

3 SERVICES FOR THE URBAN POOR It is ecessary to defie what costitutes acceptable levels of floodig. Ideally, the draiage system should prevet floodig completely i all but the most severe storms. However, this ideal will be uattaiable i may iformal areas. I geeral, some floodig of streets ad public spaces ca be tolerated if: the floodig does ot prevet movemet of pedestrias ad vehicles; flood levels are below most house plith ad yard levels; the floodig clears quickly, say withi 30 miutes of the edig of heavy raifall; ad the flood water does ot iclude sewage. Sullage draiage systems The problems resultig from iadequate disposal of sullage ted to be idirect, rather tha due to the actual quality of the wastewater itself, although there is likely to be a sigificat amout of orgaic matter i water which has bee used for food preparatio ad cleaig cookig utesils. Pools of sullage become breedig grouds for flies; a geerally isaitary eviromet results, i which certai pathoges, such as worm eggs, ca survive. The quatity of sullage geerated varies with the quatity of water supplied ad local bathig practices; betwee 50 ad 80% of the water supplied may ed up as sullage. The provisio of idividual household water coectios sigificatly icreases the volume of sullage to be disposed of. The use of large quatities of water for bathig at commual stadposts or wells ca create highly isaitary coditios if the draiage is iadequate. There are three optios available for the disposal of sullage: o-plot; surface water drais; ad sewerage. O-plot disposal O-plot disposal of sullage ca be through garde waterig, or by allowig percolatio through the soil by meas of a soakage pit. Key factors are the quatity of sullage, the plot size, ad the permeability of the groud. Garde waterig is oly appropriate if plots are large. If the groud is very sady ad highly permeable, it may be feasible to dispose of household sullage ito a 4.6

4 4a: DRAINAGE Turf Stoe or brick aggregate fillig Brick, stoe or cocrete block liig with mortar joits Ilet 300mm thick coarse sad outer casig Brick chamber with dry joits 1.5m Figure D1. Soakage pit (after Idia Stadards Istitutio) soakage pit; such a pit could hadle the sullage arisig from a household of about six people havig a per capita water supply of approximately 40 litres per day. A example is show i Figure D1. If the groud is oly slightly permeable, or is waterlogged durig the wet seaso, soakage pits will ot work. O-plot disposal may be feasible where water is beig fetched from a public water supply poit. However, where the houses have idividual water coectios it is ulikely to be appropriate uless the groud is very permeable or the plots are very large. Surface water drais It is very commo for sullage to be disposed of to surface water drais; however, there is a health risk associated with this as sullage ofte cotais high umbers of disease-causig orgaisms. The surface water drais must satisfactorily carry: the high flows resultig from itese raifall; ad very low flows of sullage at a velocity sufficietly high to prevet depositio of solids. 4.7

5 SERVICES FOR THE URBAN POOR Sewerage If a sewerage system exists, sullage should be discharged ito it. This is probably the most coveiet optio for the householders ad geerally creates the least problems o the site as a whole, although it is likely to be expesive. Surface water draiage systems There are several differet approaches to the desig of a surface water draiage system: rapid removal of surface water usig a etwork of ope chaels, or occasioally buried pipelies; storage o site; ad temporary retetio. Rapid removal This is by far the most commo method; the surface ruoff resultig from a particular raifall evet is calculated ad the drais are desiged to be able to carry this flow away from the site as rapidly as possible. The mai problems with this approach are: it depeds upo the existece of a adequate secodary draiage system, off-site; it requires a high degree of coordiatio ad plaig to esure compatibility with the secodary system, particularly if commuity actio is evisaged; ad maiteace is a problem ad blockages ca cause the system to cease to fuctio. Storage o site Storage o site holds water ad allows it to percolate away through soakaways or evaporate from holdig areas after a storm. Whilst it is ot depedet o off-site facilities it has the followig serious limitatios: systems will ot deal with more tha oe storm i quick successio; they are ot suitable if combied sullage ad surface water flows exist; the capacity of the system reduces with time as the surfaces clog with silt; ad lad is required for holdig areas. 4.8

6 4a: DRAINAGE Temporary retetio Temporary retetio allows some water to be held ad allows the remaider to drai away i a cotrolled maer. The advatage is that the storage reduces the magitude of the peak flows ad therefore the capacity of the off-site draiage system is less critical. The mai drawback is that lad is required for the storage. Storage o site is ulikely to be feasible i most circumstaces; the possibility of temporary retetio i cojuctio with removal by surface water drais is attractive ad should be ivestigated. Removal of surface water The total system The draiage problems of a small area caot be solved i isolatio. As with sewerage there is a importat hierarchy i draiage systems: Tertiary drais are those drais at the eighbourhood level which collect ad deliver draied water to oe or more outfall poits at the site boudary, as show i Figure D2. Secodary drais ruig past the site ito which the tertiary site drais discharge. Primary drais such as a large draiage caal, stream or river ito which the secodary drais discharge. There are two mai causes of floodig by stormwater: iudatio from a surroudig area, for example from a river or caal which is flowig at a abormally high level; ad iability of the draiage system to remove the required quatity of stormwater resultig from itese raifall. It is importat to realise that the draiage problem does ot ed oce a draiage etwork has bee desiged for the site i questio. The draiage water which has bee collected from the site discharges ito a earby secodary drai; if this has isufficiet capacity to cope with the additioal flows, its water level rises, ad water caot escape from the site drais. Floodig occurs o the site, ad the fudametal problem has ot bee solved. Cosideratio must always be give to that part of the mai draiage system which is dowstream of the outfall poit of the site drais. 4.9

7 SERVICES FOR THE URBAN POOR Site Tertiary drais Secodary drai O 'Outfall' of the site draiage Figure D2. Site draiage outfall 4.10

8 4a: DRAINAGE Ope chael draiage etworks are relatively simple to costruct ad maitai. They occupy space ad pose a hazard to road users, especially if the drai is very wide or deep, or passes alog a busy thoroughfare. I such cases the drais ca be covered with removable slabs. Road-as-drai. I some desely populated settlemets, paved roadways ad alleys are used to carry stormwater short distaces to draiage chaels; that is, water is deliberately allowed to flow alog the paved surface ad there are o chaels alogside (see Figure D3). This works where the surfaces are fully paved ad well maitaied ad is oly applicable if adequate sullage disposal facilities exist. It is cost effective ad is recommeded wherever possible. Buried pipelie systems have regularly spaced ilets or gullies alog the roadside, through which surface water eters the drais. This optio, which is commoly used i may wester tows ad cities, requires the roads to be costructed ad surfaced to a high stadard. Serious problems arise if the pipelies become blocked. Difficult Situatios. The pricipal problems i the desig ad implemetatio of draiage relate to the slope of the groud. Difficulties are ecoutered o groud which is either flat or excessively steep. Figure D3. Road as drai 4.11

9 SERVICES FOR THE URBAN POOR Flat groud. Positive draiage by gravity implies that all drais must slope dowhill; this is achieved by followig atural cotours. O low-lyig or flat sites which are beig redeveloped it is difficult to create the required gradiet, groud preparatio must esure adequate cotourig of the groud to permit positive draiage to occur. The available optios iclude: fillig ad cotourig; movig the outfall closer to the site by meas of a caal; ad costructig the outfall drai as a buried pipelie. Steep groud. Hydraulic problems occur if drais are very steep. O steep sites it is likely that the groud will be terraced for housig costructio. Drais should follow a path parallel to the cotours for short distaces to help reduce the flow velocity. Where the drais ru steeply dowhill, a series of dowward steps ca be built. 4.12

10 4a: DRAINAGE Tool D2 Draiage: Plaig Iitial appraisal The aim of iitial appraisal is to establish the extet ad capacity of existig facilities ad to idetify problems ad their causes. A pla of the area uder cosideratio is required at a scale betwee 1:2000 ad 1:5000. Overall draiage plas should be cosulted where they are available. A visual survey of the site should be made i order to: establish existig draiage routes ad boudaries; idetify the places where floodig is a problem; ad idetify ay restrictios ad ecroachmets that restrict the capacity of mai draiage routes. I the case of floodig, it will usually be ecessary to obtai iformatio by talkig to local people ad officials. This may be doe formally usig idepth iterviews ad focus group discussios. The likely causes of floodig are likely to be foud amog the followig: iadequacy of mai drais; reduced capacity of mai drais due to ecroachmets, restrictios or lack of maiteace; uplaed developmet which allows storm ad foul water drais to flow ito low lyig areas; ad iadequacies i local draiage. I may cases, this iitial survey will provide a clear idicatio that existig mai drais are iadequate. I other cases, it will be ecessary to produce calculatios to determie their capacity i relatio to desig flows. The importat thigs from the poit of view of upgradig are to establish whether a problem exists ad to esure that appropriate actio is take by the cocered agecy. As far as local problems are cocered, the liks betwee causes ad effects will usually be fairly obvious ad so there should be a basis for decidig o remedial actio. 4.13

11 SERVICES FOR THE URBAN POOR Draiage layout The draiage layout may be affected by the approach adopted; for istace, a layout that icorporates local storage/ifiltratio basis may be differet from that for a covetioal system. Nevertheless, the priciples that follow ca be employed for all but the most self-cotaied draiage systems. The draiage layout is largely determied by topography. A good guide to the likely draiage layout ca be obtaied from existig draiage routes but it is preferable to base layout decisios o survey levels, particularly i flat areas. Logitudial sectios should be draw alog the routes of collector drais. Typical scales for these sectios should be i the rage 1:1000-1:2500 horizotally with a 10 to 20 times vertical exaggeratio. (Normal practice is to use a vertical exaggeratio of 10 but a greater amout may be justified i flat areas). There will be some places, for istace where a existig iadequate drai rus i a arrow right of way betwee plots, where a ew drai caot be located alog the lowest possible route. I such cases, it should be located as closely as possible to the lowest route. The legth of drais should be reduced as far as is possible by allowig water to be held ad/or drai o the surface for some distace before eterig the drai. I places with aual raifalls betwee 500mm ad 1000mm, it is reasoable to assume that drais will oly be required for areas greater tha about 5ha. This assumes that streets ca be graded to provide a slope, o matter how small, to the drais ad that some temporary floodig of access streets ad laes is permissible. It is reasoable to allow larger areas without formal drais i dryer areas, providig that streets ad laes are desiged to deal with stormwater. To avoid erosio problems, this approach should be used with some cautio where ot all the right of way is paved ad average falls are greater tha about 1:100. Ay low-lyig areas which might be retaied ad used to hold stormwater ad thus reduce ru-off should be idetified at the plaig stage. The scope for providig temporary storage i shallow ditches, ifiltratio treches ad depressed areas should also be assessed. The decisio o the approach to be adopted will deped o both the topography ad the adequacy or otherwise of mai drais. Where either the average groud slope is less tha about 1:500 or mai drais are iadequate, the aim should be to hold stormwater withi the area for as log as possible. 4.14

12 4a: DRAINAGE Pumpig of stormwater should be avoided except where there is absolutely o other optio. Where it caot be avoided, stormwater should be collected i a holdig pod coected to the pumpig statio sump. This will have two beefits; it will balace flows so that the required pumpig rate ca be less tha the peak discharge rate ad it will settle ay solids ad thus reduce the likelihood of pumps beig blocked. Preparig plas for draiage schemes Iformatio o the route ad levels of drais should be provided o drawigs, each showig a pla of a legth of drai uder which is a logitudial sectio of that legth. It is importat to show pla ad sectio o the same drawig. By providig stadard cross-sectios, icludig both the drai ad the street surface, it will ofte be possible to use oe drawig to show levels for both the drai ad the street. The ormal procedure will be first to costruct the drai to the levels show o the drawigs ad the to relate levels across the street cross-sectio to the drai levels. Additioal levels may be show o the pla at poits where the arragemet diverges from a simple cross-sectio, for istace where the drai crosses from oe side of the street to the other. Figure D4 shows a typical pla ad sectio for a legth of drai. Costructio details for drais are provided by stadard cross-sectios ad details of features such as access arragemets for covered drais. These should ormally be produced at a scale of about 1:

13 SERVICES FOR THE URBAN POOR Drai Juctio with mai stormwater drai 9" (228mm) diameter RCC pipe bedded ad surrouded i Class C cocrete PLAN Drai o: 7 Drai uder street Width 450mm Shallow drai o both sides of street Gradiet 1:300 Datum Existig G.L Proposed ivert level of drai Proposed top of slab/road level Chaiage LONGITUDINAL SECTION Horizotal Scale 1: Vertical Scale 1: Figure D4. Typical pla ad sectio drawig for secodary drai 4.16

14 4a: DRAINAGE Tool D3 Draiage: Desig Estimatig surface water ruoff The desig procedure ivolves calculatio of the quatity of surface water or ruoff which is likely to result from raifall. Draiage catchmet The boudaries of draiage catchmets ca be defied usig a cotoured pla of the site, give that i a gravity flow draiage system water flows dowhill from a higher elevatio to a lower elevatio. This is illustrated i Figure D5. Site boudary Fall Fall High poit Fall Cotour Fall Key:... Catchmet boudary Site boudary Figure D5. Idetifyig catchmet boudaries from site cotours 4.17

15 SERVICES FOR THE URBAN POOR Calculatio of ruoff The simplest way of calculatig the ruoff from a give catchmet is by the ratioal method which states that: Q = 2.78 CIA where Q = ruoff i litres per secod C = volumetric ruoff coefficiet I = raifall itesity of the storm i mm per hour A = total area draied i hectares ( 1 hectare = m 2 ) Table D1 gives appropriate values for C. It is assumed that the area is fully developed, that road surfaces are impermeable ad that plots are geerally above the level of the roads. A reductio of 20% ca be applied to these values if the road surfaces are semi-permeable (such as sad-grouted bricks or blocks, or uboud gravel). Note that we are usig populatio desity as a idicator of housig desity, which i tur affects the impermeable area of a settlemet. Table D1 Ruoff coefficiets Average Populatio Average Typical plot size per hectare groud slope ru-off coefficiet < 100m ad over <1: :500-1: >1: m <1: :500-1: >1: m

16 4a: DRAINAGE Raifall itesity The raifall itesity represets a rate of raifall, ad its magitude depeds upo the storm duratio (that is, the legth of time for which rai is fallig i a particular storm) ad the retur period of the raifall itesity (that is, the umber of years o average betwee the raifall itesity beig greater tha or equal to a specified itesity). The selectio of a suitable retur period for the desig storm is usually arbitrarily take to be oce i oe year. Raifall itesity reduces as the duratio of the storm icreases; examples of itesity/duratio curves for several retur periods from Lahore are show i Figure D INTENSITY - IN / HOUR TIME - MINUTES 10 YEARS STORM 5 YEARS STORM 2 YEARS STORM 2 YEAR STORM BASED ON DATA COLLECTED FROM METEOROLOGICAL DEPTT. BY NESPAK (E & PHE. DIVISION) Figure D6. Raifall itesity-duratio curves for Lahore The ratioal method assumes that the storm duratio which is appropriate for a particular draiage catchmet equals the total time it takes for rai fallig o the most distat part of the catchmet to flow dow to the outfall poit of that catchmet. This is defied as the time of cocetratio, where time of cocetratio = time of etry + time of flow 4.19

17 SERVICES FOR THE URBAN POOR The time of etry is the time take for rai fallig o the groud or a buildig to flow ito the earest drai; the time of flow is the time take for that water to flow from its etry poit ito the drai to the outfall poit. time of flow = legth of drai velocity of flow The legth of the drai is obtaied from the proposed site draiage pla; the flow velocity ca be assumed to be 0.7 metres per secod as a first estimate, ad the time of cocetratio determied. The duratio of the storm appropriate to the catchmet is equal to the time of cocetratio; thus the appropriate raifall itesity ca be foud from the raifall itesity/duratio curve for the locatio i questio. The ruoff from the catchmet uder cosideratio is the calculated usig the ratioal formula. Desig itesities for small areas It ca be see from Figure D6 that desig raifall itesity decreases with icreased duratio. This meas i effect that the smaller the draiage area, the larger the itesity assumed i desig. I practice, the ru-off from short periods of raifall will usually be less tha that predicted usig the itesity obtaied from the itesity/duratio curve with a costat ru-off coefficiet. This is because water gathers i small depressios i the surface ad thus reduces the short-term ru-off coefficiet. To allow for this effect, a costat itesity ca be assumed for times of cocetratio of 15 miutes ad less. (I effect, the adjustmet for the reduced ru-off is the made i the itesity assumed rather tha the ru-off coefficiet). I practice, this geerally applies to catchmet areas of about 15ha. ad less, i other words for tertiary level facilities. Raifall itesity/duratio data is ofte ot readily available; a very useful guide to developig these curves from stadard raifall data is give by Kolsky (1998). I the evet of there ot beig ay iformatio, a reasoable value for a raifall itesity havig a oe year retur period is likely to be i the rage millimetres per hour; this could be applied to tertiary level catchmets. 4.20

18 4a: DRAINAGE Effect of storage o ru-off The Ratioal Formula is iteded for use with covetioal schemes i which the aim is to remove water from the site as quickly as possible. It does ot allow for storage of water i the draiage system ad therefore teds to overestimate ru-off, particularly i flat, slow-draiig areas. I areas with average slopes less tha about 1:250, the effect of storage o road surfaces will be sigificat but this effect caot be quatified simply. It is probable that the best way to deal with this situatio will be to use reduced ru-off coefficiets to compesate for storage ad this is the approach which is followed here. Table D1 gives suggested relatioships betwee ru-off coefficiets ad average groud slope. However, it must be emphasised that these figures are estimates oly ad more research is eeded o this subject. For wholly o-site ad hybrid systems that rely heavily o storage, the critical factor is ot so much the istataeous ru-off flow as the total volume of ruoff. Aalysis of these systems is complex, ideed the ecessary theory is ot available i ay simple usable form. If a site cotais a substatial area of potetial stormwater storage, for istace a low-lyig park or playig field area, the advice of a specialist draiage egieer should be obtaied. Estimatio of available falls The first step i estimatig available falls is to prepare logitudial sectios of the mai draiage routes, showig existig groud levels ad otig the bed levels ad top water levels of receivig drais or watercourses. Sectios already prepared whe decidig the draiage layout may be used. Possible drai profiles ca the be added to these sectios, together with road profiles where it is plaed that the road may occasioally carry stormwater. (This will be the case i most iformal areas.) Whe plaig street ad drai profiles, the followig rules should be observed: Raisig of road surfaces alog primary ad secodary draiage routes should be avoided. Variatios i logitudial fall that result i flat legths of street ad drai should be smoothed out. This will be particularly importat where a flat legth of street is located upstream of a legth with a good fall. This poit is illustrated i Figure D7. The aim should always be to slope tertiary streets towards draiage routes. 4.21

19 SERVICES FOR THE URBAN POOR Covered drais ad storm sewers should have sufficiet fall to esure selfcleasig velocities. This requiremet is less importat for ope drais sice they ca be cleaed more easily; evertheless, it should be achieved where possible. Existig road profile. Note lack of fall from to Maximum drop i level fixed by depth of house foudatios/ floor levels. Typically 300mm. Road profile lowered to improve draiage Drai ivert profile takes advatage of good fall from to Figure D7. Adjustmet of road ad drai profles to equalise logitudial fall Drai desig Tertiary draiage routes Specific desig calculatios are ot required for idividual tertiary draiage routes where the best optio is to use the road-as-drai, which has miimal maiteace requiremets. Tertiary areas up to about 15 hectares ca be treated i this way. The importat poit is to determie where water from differet parts of the site will drai to, so that the ruoff ito the secodary drais ca be correctly estimated. If covetioal ope chael drais are used i tertiary areas, the drai size is ofte determied by the available space ad access widths. Table D2 gives the capacity of differet drai sizes for differet logitudial slopes. 4.22

20 4a: DRAINAGE Table D2. Drai capacities i litres per secod = Bed slope S Drai Size (width * depth) i mm Width Depth : : : : : : : : : Primary/secodary drai capacity A suitable drai size must be specified which ca carry the required surface ruoff from tertiary areas. If the capacity of a existig drai is beig checked, the it is essetial to go to the site ad measure the width, available depth ad bed slope of the drai. Note that solids ad debris o the bed of the drai reduce the available depth of flow; the capacity should be calculated for two cases: assumig the depth ad slope measured to the chael ivert; ad assumig the depth ad slope measured to the solid deposits rather tha to the chael ivert (after Kolsky 1998). After doig these calculatios the importace of drai cleaig becomes readily apparet. 4.23

21 SERVICES FOR THE URBAN POOR The capacity of a ope chael ca be calculated from the Maig equatio. Q = 1000 * AR 0.67 S 0.5 where Q = capacity i litres per secod A = cross sectioal area of flow i metres squared S = logitudial bed slope of the chael = Maig s chael roughess coefficiet R = hydraulic radius of chael i metres where R = A Width + 2 * Depth for a rectagular chael. Table D3 gives some typical values. Table D3. Maig s roughess coefficiet Material Maig s coefficiet Earth Brick - uredered Brick - smooth redered Cocrete - smooth fiish Cocrete - very rough fiish Solids o bed ad smooth side walls approx The optimum shape for a rectagular cross sectio drai is for the width to be twice the depth; thus the capacity (Q) ca be calculated for a give drai size, slope ad roughess usig the Maig equatio. However, i practice restrictios o available width mea that the sectio may be square. The drai capacity is the compared with the ruoff which it is required to carry ad the size of the drai is adjusted util its capacity is withi say 10% of the ruoff. Calculate the velocity of flow i the drai usig Velocity = Capacity/Cross sectioal area 4.24

22 4a: DRAINAGE If it is ot equal to 0.7 metres per secod (that is, the value assumed i order to fid the time of cocetratio ad raifall itesity), recalculate the time of flow based upo this recalculated value of velocity. I practice it is usual to stadardise o a limited umber of drai sizes i order to simplify costructio. Small drais easily become blocked ad a miimum width of 300 mm is suggested. At the juctio of two drais, the ivert level of the mior drai should be above that of the major drai which it is joiig as show i Figure D8. This prevets backflow of water up the mior drai. Step Height = Depth i major drai - Depth i mior drai Note that for sheet flow o street pavemets, the value of the hydraulic radius (R) approximates to the average depth, measured i metres. It is ormal to carry out calculatios for secodary drais o stadard sheets such as that show i Figure D9. Colums 1-13 of the sheet are cocered with the calculatio of desig flows i the drai. Colums 8-12 are cocered with the calculatio of the raifall itesity, usig raifall itesity/ duratio curves such as that give i Figure D6. For areas up to about 15 ha, the procedure may be simplified by assumig a costat raifall itesity. Colums are cocered with the calculatio of the velocity ad quatity of flow i the drai. For each drai leg, startig at the head of the system, the desig flow is calculated, drai dimesios are assumed ad the drai full flow velocity ad quatity are calculated. Calculatio is a iterative process. If the velocity obtaied i colum 23 is too low, a greater drai slope must be assumed. If the capacity calculated i colum 24 differs by more tha 10% from that obtaied from colum 13, revised drai dimesios or slope should be tried. If the calculated velocity obtaied i colum 23 differs by more tha about 20% from that assumed i colum 9, it may be ecessary to recalculate the raifall itesity based o a revised time of cocetratio. Oce the desig of a drai leg has bee satisfactorily completed, the desiger iputs the data obtaied o time ad quatity of flow ito the desig of the ext dowstream leg. 4.25

23 / / / / SERVICES FOR THE URBAN POOR Icomig lateral drai Ivert level of the mai drai is lower tha that of the icomig drai Mai drai a: Low flow Icomig lateral drai Mai drai b: Maximum flow Figure D8. Drai ivert levels Drai leg Upstream ode Area cotributig over leg (ha.) Ru-off coefficiet Effective cotributig area (ha) Effective area at u/s ode (ha) Effective area at d/s ode (ha) Distace from previous poit (m) Assumed V (m/sec) Time from u/s ode (mi) Time of coc. (mi) I (mm/hr) Required drai capacity ( l /sec) Av slope o drai Drai width (mm) Drai height (mm) Cross-sectioal area, A (m ) Wetted perimeter P (m) R = A/P R 2 3 S 1 2 Maigs V = R S (m/sec) Q = VA x 1000 Figure D9. Typical calculatio sheet for secodary drais 4.26

24 4a: DRAINAGE Types of drai Ulied ditches Ulied ditches are the cheapest form of drai to costruct. However, they require costat maiteace ad this limits their usefuless i iformal areas. They are ot suitable for carryig sullage flows ad should therefore oly be cosidered i sewered areas. I practice, they will oly be a optio i the rare situatios i which streets are at least 7 metres wide. The slope o ulied drais should ot be greater tha about 1% (1 i 100) to avoid scourig. The side slopes should ormally be about 1 i 1.5 except i particularly sady soils where flatter side slopes are required. A example is show i Figure D10. Ope drais Brick-lied ope drais iteded to carry both storm ad sullage flows are widely used. Their mai disadvatage is that it is easy to throw rubbish ito them, reducig their capacity ad evetually blockig the flow. O the other had, they are much easier to clea tha covered drais ad the equipmet presetly used by muicipality sweepers is iteded for use with them. Ope drais over about 400mm deep are a hazard, particularly to childre who may fall ad ijure themselves. Large ope drais may be appropriate where space is available so that sides ca be pitched or where access ca be restricted. For mai drais, access may be restricted by providig walls o either side of the drai. The most commo cross sectioal shape is rectagular; this gives rise to very low flow velocities whe the discharge is small ad is thus usuitable for sullage flows. This ca be overcome by usig parabolic or half-roud ivert profiles as show i Figure D10, or the compoud sectio show i Figure D11. This esures that a acceptable velocity ad depth of flow are maitaied durig low flows, with the overall capacity sufficiet to carry the required storm discharges. Covered drais It is more difficult to gai access to covered drais tha to ope drais. This meas that it is more difficult to throw solid waste ito them so that they do ot become blocked as quickly. Coversely, it meas that they are more difficult to clea ad experiece shows that muicipalities are ofte ot equipped or prepared to clea them. 4.27

25 SERVICES FOR THE URBAN POOR Access required across ditch at etraces to plots Typically mm 1:1.5 1:1.5 Street surfacig Sewer coectio uder ditch (i) Possible arragemet of ope ditch i street (Usuitable where there are o sewers or for street widths less tha about 7m.) Note that ditch ca later be upgraded by liig sides with brick / stoe pitchig. Bricks laid flat o sad or cemet - mortar bed mm Stoe pitchig (alterative to brick) Max. 400mm (a) Pitched sides suitable for larger drais (b) Small brick-lied drai (for storm or strorm/sullage flows) (ii) Typical ope drai sectios. 1:2:4 cocrete kerb 150mm Road costructio Bechig to form parabolic sectio (a) Uder footpath Optio with miimal bechig (b) Uder road (iii) Typical covered drai details. Figure D10. Typical drai cross-sectios 4.28

26 4a: DRAINAGE Half-roud chael sized to take peak desig sullage flow Figure D11. Ivert arragemet for drai carryig both sullage ad storm flows A advatage of covered drais is that it is possible to use the area above them. This may be importat where the available right of way is limited. For larger covered drais, the cover slab ca have a importat structural effect, covertig the walls from catilevers to propped catilevers ad reducig the wall thickess required. This will partly offset the additioal cost of coverig the drai. As a geeral rule, drais smaller tha about 500mm x 500mm should ot be covered. Larger drais should be covered except where access to them ca be preveted. Road as drais Tertiary drais ca be elimiated by desigig streets ad laes to carry stormwater. This reduces both the capital cost of draiage ad the eed for maiteace ad the approach should therefore be used i upgradig schemes wherever possible. Most of the typical street ad lae cross-sectios give allow for stormwater to be draied o the surface. Where streets are desiged to act as drais, surfacig materials such as brick ad cocrete, which are ot damaged by stormwater, should be used. 4.29

27 SERVICES FOR THE URBAN POOR The most importat factor is to esure that the paved areas ad roads have a positive slope so that the water drais ito secodary drais at a kow umber of outfall poits. This requires attetio to detail at the plaig stage. The road should slope logitudially ad also have a cross-fall uless: the street is less tha about 2 metres wide; or the logitudial fall is less tha about 1 i 300. For arrow laes, the beefits derived from a cross-fall are ot great eough to justify its provisio. Where there is little logitudial fall ad the surface is impervious, irregularities i the surface will result i stadig water after rai, The water will remai for loger if it is cocetrated i oe spot by the crossfall, especially where ifrequet street cleaig allows dirt ad rubbish to gather at the low poit of the cross-sectio. With a flat cross-sectio, water will stad over a wider area but the depth will be less ad the speed with which the water will either evaporate or percolate away will be greater. I flat areas it may be permissible to allow streets to flood temporarily to a depth of say 150mm providig that the water drais away rapidly after the storm. Street levels must be sufficietly far below the plot levels to prevet floodig of properties. This retetio of floodwater will have importat beefits for the secodary drais, as it serves to reduce the peak outflow, thereby reducig the risk of overloadig these drais. Refereces Kolsky, P. (1998) Storm Draiage, Itermediate Techology Publicatios Lodo. 4.30

28 4a: DRAINAGE Tool D4 Draiage: Hady Tips Draiage: Some geeral operatio ad maiteace tips Costructio debris is a major problem; clea out all debris from the drais whe costructio is completed. Regular ublockig ad solid waste removal is required. Small drais may eed to be desilted o a mothly basis. Desiltig of primary ad secodary drais is essetial prior to the raiy seaso. Road crossigs ad culverts are subject to frequet blockages ad eed particular attetio. Proper tools are required for removal of waste from drais. Drai waste should ot be stacked alogside the drai; the maagemet challege is to orgaise desiltig ad liftig i oe operatio with subsequet removal to the disposal site. Muicipally maaged drai cleaig is labour itesive ad cosumes cosiderable resources; larger drais may icreasigly be cleaed usig mechaical plat. Cleaig of local drais ca be commuity-maaged. Regular sprayig of street drais with pesticides to reduce mosquito breedig is importat. 4.31

29 SERVICES FOR THE URBAN POOR Earth drais: where to use them Not geerally suitable for draiage chaels i desely populated areas. Do ot use for carryig sullage or foul sewage. Ofte used for large primary draiage chaels ad for ultimate disposal of stormwater. Durig the urbaisatio process, old earthe irrigatio chaels are used as tertiary ad secodary drais. For temporary purposes such as diversio or pumpig out of draiage water, e.g. where there are site disputes o the proposed permaet aligmet. Problems iclude: low velocity due to high roughess ad irregular shape; mosquito meace as there is a possibility of weed growth. Earth drai: costructio tips Iexpesive ad simple to costruct; lies ad levels eed careful settig out ad cotrol by a surveyor. Use trapezoidal sectios to miimise scour. O relatively steep groud, icrease the legth of the drai by followig a zig-zag route to reduce velocity - ultimately to reduce scourig by havig a flatter slope. Use excavated earth (spoil) for embakmets o larger drais. I certai cases, larger drais may eed approach roads for udertakig maiteace. Requires cohesive soils for greater stability of excavated sectio; ot good i sady soils. Suitable for commuity based works; excavatio ca be doe by uskilled labour. Earth drai: operatio ad maiteace tips See geeral operatio ad maiteace tips. Maiteace itesive compared with other optios. Frequet desiltig ad ublockig required; this may lead to the bed profile beig disturbed. Periodic realigmet is ecessary; depth, width ad slope are fixed iitially but chage i the course of time, as the chael flows i regime. Suitable for commuity based works. Care should be take whe there is a roadway o its embakmet, as slips are commo. Uexpected floodig from adjacet catchmets areas ca cause major damage. 4.32

30 4a: DRAINAGE Brick masory drai: where to use them Very commo ad appropriate for tertiary ad secodary drais usig bricks or cemet blocks. Resistat to settlemets ad associated cracks as the sectio is strog. A icreasigly expesive optio for larger drais due to the cotiuig rise i the cost of bricks. Brick masory drai: costructio tips Accurate measuremet of levels ad falls is essetial. A good quality smooth cemet plaster to cover the bricks is ecessary to esure good flow characteristics. Side walls have varyig depths govered by the logitudial bed slope ad the road levels. Use a template or former to produce the required cross sectioal profiles for orectagular sectios; half-roud ad parabolic bechig for small drais ca be produced i-situ usig a woode had-held former up to about oe metre log. Use good quality bricks which are well-burt ad have good water resistace. At road crossigs, side walls eed to be strog eough to take traffic loadig; i this situatio ad with deep sectios sidewalls are desiged as small retaiig walls. Cosider the type of tools used for drai cleaig whe specifyig the cross sectioal shape Requires skilled labour other tha for trech excavatio. Brick masory drai: operatio ad maiteace tips See geeral operatio ad maiteace tips. Suitable for commuity maagemet usig oly basic tools. 4.33

31 SERVICES FOR THE URBAN POOR Cemet cocrete drais: where to use them Coveiet if cemet cocrete pavig is used; costructio ca be doe at the same time. Costructio is relatively simple ad quicker tha brick liig. Cost comparisos deped primarily o the local costs of procurig materials ad their quality. Used mostly for tertiary street drais. For medium to large sized secodary ad primary drais cocrete reiforcemet is required. Useful if access is very restricted because the wall thickess is less tha for brick drais ad a margially wider pathway is available. Resistat to scour by high velocities such as occurs i steeply slopig areas. Good where raifall is high; cocrete deteriorates less tha brick uder submerged coditios. Cemet cocrete drais: costructio tips Accurate measuremet of levels ad falls is essetial; the bed aligmet eeds to be carefully prepared followig the required slope before cocretig. Good quality formwork is ecessary to obtai the desired cross sectio. Small drais may eed plasterig to esure good flow characteristics. Use coarse aggregate of less tha 20 mm size for small drais. Rectagular or box drais may eed tie beams at top betwee two walls to improve stability agaist collapse due to movig loads (such as traffic). Machie mixed cocrete is preferable. Costructio is more difficult whe the depth of the sidewall varies due to problems with formwork. Requires skilled labour other tha for trech excavatio. Cemet cocrete drais: operatio ad maiteace tips See geeral operatio ad maiteace tips. Loger life tha brick drais, but cracks develop if there is ay groud settlemet. Repair ad patchig cost is slightly less tha for brick lied drais. Durability of the surface meas that heavier tools ca be used for cleaig. 4.34

32 4a: DRAINAGE Precast cocrete drais: where to use them Appropriate for small tertiary drais. Useful as a temporary measure to relieve immediate problems. Relatively cheap to costruct but experiece shows that it is ot a log lastig solutio. Difficult to use i situatios where depths vary over short distaces ad where there are frequet chages i aligmet. Precast cocrete drais: costructio tips Accurate measuremet of levels ad falls is essetial i preparig the trech profile. Castig ca be cetralised, offerig the opportuity for closer quality cotrol. It is possible to remove ad refix sectios. Cocrete should be vibrated ad cured properly at the castig yard; care eeds to be take to avoid damage whe the uits are trasported to site. Take particular care whe makig cemet mortar joits; use a strog mortar mix. Suitable for small eterprise developmet. Precast cocrete drais: operatio ad maiteace tips See geeral operatio ad maiteace tips. Ueve joits pose problems whe movig cleaig tools alog the drai. Settlemet opes up joits ad subsequet leakage ca create localised pools of water. Refixig ad replacemet eed to be carried out o a regular basis as the pre-cast sectios are disturbed relatively easily. 4.35

33 SERVICES FOR THE URBAN POOR Stoe/block/rubble lied drais: where to use them Suitable for larger secodary ad primary drais ad mai outfalls; commoly used as a meas of improvig existig large ulied chaels. Provides a stable sectio by liig the sidewalls; the bed eed ot ecessarily be lied for larger mai drais. Cost effective if local materials such as stoes, stoe flags ad radom rubble are used for pitchig the sides. Difficult to provide ay coverig over drai for safety ad access. Susceptible to accidets through people, particularly childre, fallig i. Stoe/block/rubble lied drais: costructio tips Accurate measuremet of levels ad falls is essetial for ew drais; large drais ted to have flatter slopes. Simple to costruct; sidewalls ca be vertical, sloped or stepped ad should be desiged as retaiig walls allowig for earby traffic loadig. Requires a mix of uskilled ad skilled labour. Sidewall/revetmet liig ca be either mortar joited or without joitig material; ope joits allow some percolatio. Use a cemet cocrete cappig for the tops of side walls to impart extra stregth agaist wearig. Cross draiage works are complicated ivolvig culverts ad possibly bridges; plaig eeds to be itegrated with wider, log term draiage eeds. Adequate safety measures eed to be take durig costructio withi developed housig areas as walls of earby buildigs are proe to crackig or eve collapse. Water ad sewer lie crossigs create major problems if ecoutered durig costructio; it is essetial to work out what to do at the plaig stage. Stoe/block/rubble lied drais: operatio ad maiteace tips See geeral operatio ad maiteace tips. Stoes ad blocks have some salvage value. Settlemet ca cause cracks i the liig; some sectios may eed periodic refixig. Care must be take whe heavy equipmet is used for desiltig to avoid disturbig the stoe pitchig o the revetmet. Weeds such as water hyacith ca severely restrict flows; removal is a major operatio oce the weeds take hold. 4.36

34 4a: DRAINAGE 4.37

CVE 372 HYDROMECHANICS EXERCISE PROBLEMS OPEN CHANNEL FLOWS

CVE 372 HYDROMECHANICS EXERCISE PROBLEMS OPEN CHANNEL FLOWS CVE 72 HYDROMECHANICS EXERCISE PROBLEMS OPEN CHANNEL FLOWS ) A rectagular irrigatio chael of base width m, is to covey 0.2 m /s discharge at a depth of 0.5 m uder uiform flow coditios. The slope of the

More information

Flood Emergency Response Plan

Flood Emergency Response Plan Flood Emergecy Respose Pla This reprit is made available for iformatioal purposes oly i support of the isurace relatioship betwee FM Global ad its cliets. This iformatio does ot chage or supplemet policy

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature. Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

summary of cover CONTRACT WORKS INSURANCE

summary of cover CONTRACT WORKS INSURANCE 1 SUMMARY OF COVER CONTRACT WORKS summary of cover CONTRACT WORKS INSURANCE This documet details the cover we ca provide for our commercial or church policyholders whe udertakig buildig or reovatio works.

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

Using Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N)

Using Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N) INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - Usig Four Types Of Notches For Compariso Betwee Chezy s Costat(C) Ad Maig s Costat (N) Joyce Edwi Bategeleza, Deepak

More information

How to read A Mutual Fund shareholder report

How to read A Mutual Fund shareholder report Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

Amendments to employer debt Regulations

Amendments to employer debt Regulations March 2008 Pesios Legal Alert Amedmets to employer debt Regulatios The Govermet has at last issued Regulatios which will amed the law as to employer debts uder s75 Pesios Act 1995. The amedig Regulatios

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

Subject CT5 Contingencies Core Technical Syllabus

Subject CT5 Contingencies Core Technical Syllabus Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value

More information

Baan Service Master Data Management

Baan Service Master Data Management Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology

More information

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

ODBC. Getting Started With Sage Timberline Office ODBC

ODBC. Getting Started With Sage Timberline Office ODBC ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.

More information

Measuring Magneto Energy Output and Inductance Revision 1

Measuring Magneto Energy Output and Inductance Revision 1 Measurig Mageto Eergy Output ad Iductace evisio Itroductio A mageto is fudametally a iductor that is mechaically charged with a iitial curret value. That iitial curret is produced by movemet of the rotor

More information

FIRE PROTECTION SYSTEM INSPECTION, TESTING AND MAINTENANCE PROGRAMS

FIRE PROTECTION SYSTEM INSPECTION, TESTING AND MAINTENANCE PROGRAMS STRATEGIC OUTCOMES PRACTICE TECHNICAL ADVISORY BULLETIN February 2011 FIRE PROTECTION SYSTEM INSPECTION, TESTING AND MAINTENANCE PROGRAMS www.willis.com Natioal Fire Protectio Associatio (NFPA) #25 a mai

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

Determining the sample size

Determining the sample size Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich [email protected] [email protected] Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

Ekkehart Schlicht: Economic Surplus and Derived Demand

Ekkehart Schlicht: Economic Surplus and Derived Demand Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 2006-17 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät Ludwig-Maximilias-Uiversität Müche Olie at http://epub.ub.ui-mueche.de/940/

More information

The Forgotten Middle. research readiness results. Executive Summary

The Forgotten Middle. research readiness results. Executive Summary The Forgotte Middle Esurig that All Studets Are o Target for College ad Career Readiess before High School Executive Summary Today, college readiess also meas career readiess. While ot every high school

More information

HCL Dynamic Spiking Protocol

HCL Dynamic Spiking Protocol ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7

More information

Quadrat Sampling in Population Ecology

Quadrat Sampling in Population Ecology Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

Statement of cash flows

Statement of cash flows 6 Statemet of cash flows this chapter covers... I this chapter we study the statemet of cash flows, which liks profit from the statemet of profit or loss ad other comprehesive icome with chages i assets

More information

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

More information

Enhancing Oracle Business Intelligence with cubus EV How users of Oracle BI on Essbase cubes can benefit from cubus outperform EV Analytics (cubus EV)

Enhancing Oracle Business Intelligence with cubus EV How users of Oracle BI on Essbase cubes can benefit from cubus outperform EV Analytics (cubus EV) Ehacig Oracle Busiess Itelligece with cubus EV How users of Oracle BI o Essbase cubes ca beefit from cubus outperform EV Aalytics (cubus EV) CONTENT 01 cubus EV as a ehacemet to Oracle BI o Essbase 02

More information

Bajaj Allianz General Insurance Company Limited

Bajaj Allianz General Insurance Company Limited Bajaj Alliaz Geeral Isurace Compay Limited Regd. Office & Head Office : GE Plaza, Airport Road, Yerawada, Pue - 411 006. PROPOSAL FORM FOR OFFICE COVER Importat : This proposal for isurace will be the

More information

Pre-Suit Collection Strategies

Pre-Suit Collection Strategies Pre-Suit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process

More information

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find 1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.

More information

Systems Design Project: Indoor Location of Wireless Devices

Systems Design Project: Indoor Location of Wireless Devices Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 698-5295 Email: [email protected] Supervised

More information

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics

More information

Maintaining portable and transportable electrical equipment

Maintaining portable and transportable electrical equipment Health ad Safety Maitaiig portable ad trasportable electrical equipmet This is a free-to-dowload, web-friedly versio of HSG107 (Secod editio, published 2004). This versio has bee adapted for olie use from

More information

RISK TRANSFER FOR DESIGN-BUILD TEAMS

RISK TRANSFER FOR DESIGN-BUILD TEAMS WILLIS CONSTRUCTION PRACTICE I-BEAM Jauary 2010 www.willis.com RISK TRANSFER FOR DESIGN-BUILD TEAMS Desig-builD work is icreasig each quarter. cosequetly, we are fieldig more iquiries from cliets regardig

More information

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed Multi-Evet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

Making training work for your business

Making training work for your business Makig traiig work for your busiess Itegratig core skills of laguage, literacy ad umeracy ito geeral workplace traiig makes sese. The iformatio i this pamphlet will help you pla for ad build a successful

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS

COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread and Boxplots Discrete Math, Section 9.4 Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

Hypothesis testing. Null and alternative hypotheses

Hypothesis testing. Null and alternative hypotheses Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

More information

A guide to School Employees' Well-Being

A guide to School Employees' Well-Being A guide to School Employees' Well-Beig Backgroud The public school systems i the Uited States employ more tha 6.7 millio people. This large workforce is charged with oe of the atio s critical tasks to

More information

Chapter 7 Methods of Finding Estimators

Chapter 7 Methods of Finding Estimators Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of

More information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number. GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

More information

Hypergeometric Distributions

Hypergeometric Distributions 7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you

More information

FI A CIAL MATHEMATICS

FI A CIAL MATHEMATICS CHAPTER 7 FI A CIAL MATHEMATICS Page Cotets 7.1 Compoud Value 117 7.2 Compoud Value of a Auity 118 7.3 Sikig Fuds 119 7.4 Preset Value 122 7.5 Preset Value of a Auity 122 7.6 Term Loas ad Amortizatio 123

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

June 3, 1999. Voice over IP

June 3, 1999. Voice over IP Jue 3, 1999 Voice over IP This applicatio ote discusses the Hypercom solutio for providig ed-to-ed Iteret protocol (IP) coectivity i a ew or existig Hypercom Hybrid Trasport Mechaism (HTM) etwork, reducig

More information

Module 2. The Science of Surface and Ground Water. Version 2 CE IIT, Kharagpur

Module 2. The Science of Surface and Ground Water. Version 2 CE IIT, Kharagpur Module The Sciece of Surface ad Groud Water Versio CE IIT, Kharagpur Lesso 8 Flow Dyamics i Ope Chaels ad Rivers Versio CE IIT, Kharagpur Istructioal Objectives O completio of this lesso, the studet shall

More information

The control of fire-water runoff from CIMAH sites to prevent environmental damage

The control of fire-water runoff from CIMAH sites to prevent environmental damage Health ad Safety The cotrol of fire-water ruoff from CIMAH sites to prevet evirometal damage Guidace Note EH70 This is a free-to-dowload, web-friedly versio of EH70 (First editio, published 1995). This

More information

How to use what you OWN to reduce what you OWE

How to use what you OWN to reduce what you OWE How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.

More information

Assessment of the Board

Assessment of the Board Audit Committee Istitute Sposored by KPMG Assessmet of the Board Whe usig a facilitator, care eeds to be take if the idividual is i some way coflicted due to the closeess of their relatioship with the

More information

CREATIVE MARKETING PROJECT 2016

CREATIVE MARKETING PROJECT 2016 CREATIVE MARKETING PROJECT 2016 The Creative Marketig Project is a chapter project that develops i chapter members a aalytical ad creative approach to the marketig process, actively egages chapter members

More information

LEASE-PURCHASE DECISION

LEASE-PURCHASE DECISION Public Procuremet Practice STANDARD The decisio to lease or purchase should be cosidered o a case-by case evaluatio of comparative costs ad other factors. 1 Procuremet should coduct a cost/ beefit aalysis

More information

Comparing Credit Card Finance Charges

Comparing Credit Card Finance Charges Comparig Credit Card Fiace Charges Comparig Credit Card Fiace Charges Decidig if a particular credit card is right for you ivolves uderstadig what it costs ad what it offers you i retur. To determie how

More information

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the. Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

More information

Information about Bankruptcy

Information about Bankruptcy Iformatio about Bakruptcy Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea Isolvecy Service of Irelad Seirbhís Dócmhaieachta a héirea What is the? The Isolvecy Service of Irelad () is a idepedet

More information

Domain 1: Identifying Cause of and Resolving Desktop Application Issues Identifying and Resolving New Software Installation Issues

Domain 1: Identifying Cause of and Resolving Desktop Application Issues Identifying and Resolving New Software Installation Issues Maual Widows 7 Eterprise Desktop Support Techicia (70-685) 1-800-418-6789 Domai 1: Idetifyig Cause of ad Resolvig Desktop Applicatio Issues Idetifyig ad Resolvig New Software Istallatio Issues This sectio

More information

Chapter 1 INTRODUCTION TO MAINTENANCE AND REPLACEMENT MODELS

Chapter 1 INTRODUCTION TO MAINTENANCE AND REPLACEMENT MODELS 1 Chapter 1 INTRODUCTION TO MAINTENANCE AND REPLACEMENT MODELS 2 Chapter 1 INTRODUCTION TO MAINTENANCE AND REPLACEMENT MODELS 1.0 MAINTENANCE Maiteace is a routie ad recurrig activity of keepig a particular

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

Normal Distribution.

Normal Distribution. Normal Distributio www.icrf.l Normal distributio I probability theory, the ormal or Gaussia distributio, is a cotiuous probability distributio that is ofte used as a first approimatio to describe realvalued

More information

7.1 Finding Rational Solutions of Polynomial Equations

7.1 Finding Rational Solutions of Polynomial Equations 4 Locker LESSON 7. Fidig Ratioal Solutios of Polyomial Equatios Name Class Date 7. Fidig Ratioal Solutios of Polyomial Equatios Essetial Questio: How do you fid the ratioal roots of a polyomial equatio?

More information

Engineering Data Management

Engineering Data Management BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package

More information

Handling. Collection Calls

Handling. Collection Calls Hadlig the Collectio Calls We do everythig we ca to stop collectio calls; however, i the early part of our represetatio, you ca expect some of these calls to cotiue. We uderstad that the first few moths

More information

Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study. Normal and t Distributions. Density Plot. Normal Distributions Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

More information

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies.

More information

4.0 Deciding Which Method is Right for Your Home

4.0 Deciding Which Method is Right for Your Home 4.0 Decidig Which Method is Right for Your Home With the iformatio from Chapters 2 ad 3, you are ready to decide which retrofittig method is right for your home. Your decisio will be based primarily o

More information

AP Calculus BC 2003 Scoring Guidelines Form B

AP Calculus BC 2003 Scoring Guidelines Form B AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet

More information

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

Optimize your Network. In the Courier, Express and Parcel market ADDING CREDIBILITY

Optimize your Network. In the Courier, Express and Parcel market ADDING CREDIBILITY Optimize your Network I the Courier, Express ad Parcel market ADDING CREDIBILITY Meetig today s challeges ad tomorrow s demads Aswers to your key etwork challeges ORTEC kows the highly competitive Courier,

More information

The storage of flammable liquids in containers

The storage of flammable liquids in containers Health ad Safety The storage of flammable liquids i cotaiers This is a free-to-dowload, web-friedly versio of HSG51 (Secod editio, published 1998). This versio has bee adapted for olie use from HSE s curret

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity

More information

5 Boolean Decision Trees (February 11)

5 Boolean Decision Trees (February 11) 5 Boolea Decisio Trees (February 11) 5.1 Graph Coectivity Suppose we are give a udirected graph G, represeted as a boolea adjacecy matrix = (a ij ), where a ij = 1 if ad oly if vertices i ad j are coected

More information

A Guide to the Pricing Conventions of SFE Interest Rate Products

A Guide to the Pricing Conventions of SFE Interest Rate Products A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios

More information

Bank Secrecy Act. Job-specific BSA tracks Related case studies Suggested courses

Bank Secrecy Act. Job-specific BSA tracks Related case studies Suggested courses Bak Secrecy Act Whether your bak is big or small, Bak Secrecy Act (BSA) compliace ofte feels overwhelmig due to the complexities ad related processes ad procedures surroudig this ever-chagig legislatio.

More information

Valuing Firms in Distress

Valuing Firms in Distress Valuig Firms i Distress Aswath Damodara http://www.damodara.com Aswath Damodara 1 The Goig Cocer Assumptio Traditioal valuatio techiques are built o the assumptio of a goig cocer, I.e., a firm that has

More information

Configuring Additional Active Directory Server Roles

Configuring Additional Active Directory Server Roles Maual Upgradig your MCSE o Server 2003 to Server 2008 (70-649) 1-800-418-6789 Cofigurig Additioal Active Directory Server Roles Active Directory Lightweight Directory Services Backgroud ad Cofiguratio

More information

Semiconductor Devices

Semiconductor Devices emicoductor evices Prof. Zbigiew Lisik epartmet of emicoductor ad Optoelectroics evices room: 116 e-mail: [email protected] Uipolar devices IFE T&C JFET Trasistor Uipolar evices - Trasistors asic

More information

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

REFURBISHMENTS AND AUGMENTATIONS

REFURBISHMENTS AND AUGMENTATIONS INTRODUCTION TIER WORKING PAPER No. 0 REFURBISHMENTS AND AUGMENTATIONS Workig Paper No. How Water Prices are Set provided a overview of how water prices are set o the basis of lower boud costs. As oted

More information

How To Find FINANCING For Your Business

How To Find FINANCING For Your Business How To Fid FINANCING For Your Busiess Oe of the most difficult tasks faced by the maagemet team of small busiesses today is fidig adequate fiacig for curret operatios i order to support ew ad ogoig cotracts.

More information

Chapter 7: Confidence Interval and Sample Size

Chapter 7: Confidence Interval and Sample Size Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum

More information

2011 LTEA Threat-to-Water-Quality Examples

2011 LTEA Threat-to-Water-Quality Examples This appedix provides examples of the use of the Threat-to-Water Quality (TTWQ) methodology discussed i the 2011 Log-Term Effectiveess Assessmet (LTEA) Sectio 4. All of the examples preseted i this appedix,

More information

The deployment of EMRs and CPOE systems

The deployment of EMRs and CPOE systems FEATURE: Techology How to Select Ed User Cliical Data Etry Devices Rush Uiversity Medical Ceter Develops Tool to Idetify the Quatity of Devices Needed for the Implemetatio of a ew EMR ad CPOE System. Karl

More information

E-Plex Enterprise Access Control System

E-Plex Enterprise Access Control System Eterprise Access Cotrol System Egieered for Flexibility Modular Solutio The Eterprise Access Cotrol System is a modular solutio for maagig access poits. Employig a variety of hardware optios, system maagemet

More information

Preserving Your Financial Legacy with Life Insurance Premium Financing.

Preserving Your Financial Legacy with Life Insurance Premium Financing. Preservig Your Fiacial Legacy with Life Isurace Premium Fiacig. Prepared by: Keeth M. Fujita, Natioal Director, The Private Bak Specialty Fiace Group Life Isurace Premium Fiace. James Mosrie, Seior Wealth

More information