Methods Estimating Loads Plumbing Systems_Hunter 1940

7/29/2019 Methods Estimating Loads Plumbing Systems_Hunter 1940

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UNITED STATES DEPARTMENT OF COMMERCE Jesse H. Jones, SecretaryNATIONAL BUREAU OF STANDARDS Lyman J. Briggs, Director

BUILDING MATERIALSand STRUCTURES

REPORT BMS65

lVlethods of Estimating Loads in Plumbing Systems

byROY B. HUNTER

I S SUE D D E C E M B E R 16, 19 4 0

The National Bureau of Standards is a fact-finding organization;it does not "approve" any particular material or method of construction. The technical findings in this series of reports are to

be construed accordingly.

UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTONFOR SALF. BY THE SUPERINTENDENT OF DOCUMENTS, WASHINGTON, D. C. PRICE 10 CENTS


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ForewordFor many years, differences in the plumbing regulations or plulllbin~-('ode n'q uire

monts in different localities have been a source of annoyance to building owneIS, builders,and public health officials and have hindered the standardization, on a geneI'Dl or nationalscale, of plumbing materials and equipment, and of construction desi~n. The principalreasons for the existence of plumbing codes are the protection of the health of theoccupants of a building and of the inhabitants of the community or cit~Tin which thebuilding is located and the protection of property from dam:tge by water or Sl'wage.

The results sought by plumbing requirements and health regulations applying toplumbing are or should be the same for low-cost or expensive and for small or largebuildings, and may be covered by general regulations applying to all plumbing. Anysimplified or standardized form of plumbing construction which gives thesl' resultsthat is, which complies with 11eCeSsarygeneral regulations pertaining to snnit.ation orhealth-cannot be prohibitp


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Nlethods of Estimating Loads in Plumbing Systemsby

ROY B. HUNTER

CONTENTSPageForeword n nnn __ h II

r. Introduction n 1II. Purposc n 1III. Definitions and symbols_h n n 2IV, Basis of selection of pipe sizes n 3V. Character of fio\\' in plumbing systems_ 31. Cases of loading 5Statement of the problenL 5Development ofthe probability functiOlL 6Interpretation of the probability func-tion ~ ..__IX Proposcd uses of the probability function for making load estimates __..__1. Pcrtinent information obtainable

from the probability functiolL_

VI.VII,VIII, 777

PageIX, Proposed uses of the probability function for making load estimates-Con.2. Valucs of t, T, 7", and q.. ~_h 83. Prescntation of probability data 114. Derivation of fixture weights (fix-ture units) n __ n 135. Rclative load weights for diffcrentconditions of scrvice hh 166. Application of load chart andwcight tablcn n 18

X. Adcquacy of the mcthod 19XI. Estimates of sewagc loads_ n __ n _ n __ 20XII. Discussion n 21

XIII. Referencesn nn __ nn 21

ABSTRACTThis report describes a method of estimating thedemand and se\\'age loads for which provision should bemade in designing plumbing systems in order that theservice may be satisfacton'. The characteristics offlow through a plumbing system and of the operation ofsupply valves and plumbing fixtures are described, andtheir influence on the method of estimating the load to

be expected is discussed. The relath'e load-producingvalues of different kinds of commonly used plumbingfixtures are analyzcd, and a tablc is de\'elopcd givingrelati\ 'e load \veights in terms of a load factor called the"fixture unit." An estimate curve developed bymeans of the probability function is given, and its usein conjunction with the table of fixture units is illustrated.

1. INTRODUCTIONAside from the choicp of materials and equipment as regards quality, style, and quantity offixtures, simplification and standardization ofpiping layouts offer the principal opportunitiesfor reduct.ion in cost of plumbing systems.

Simplification and standardization in thisrespect must comply with accepted healthregulations and minimum rc'quirem~nts forplum bing, which in tUl'Jl should be based onscientific principles. This is true whpther thebuilding is small and "low-cost" or large and

[ 1 ]

expensive. Few, if any, existing plumbingcodes are based entirely on scientific principles;and they do not in general permit the simplification of plumbing piping layouts that couldbe accomplished well within the requirementsfor sanitation, and in many cases with moresatisfactory operation than can be obtained byinstallations under existing codes.This report deals with one of the factors onwhich minimum requirements should be based,the maximum load to be provided for in plumbing systems. Other reports are planned, dealing with the principles of water supply andwater distribution in buildings, the principlesof building drainage, and the principles ofventing. II. PURPOSEThe purpose of this series of papers is tocollcct in an organized form the mass of information obtained by the author over a number

of years, beginning with the investigation in1921 of plumbing of small dwellings, and including the current research (1937-40) on plumbingfor low-cost housing, together with the resultsof intervening experiments related to plumbingrt'quirements, and to interprpf, the results ofthese investigations in a form suitable for direct


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and practical application. It is hoped thatthis series of papers will supply the logicalanswer to many of the controversial questionspertaining to pipe sizes and design of plumbingconstruction.

III. DEFINITIONS AND SYMBOLSA number of terms employed in the plumbingindustry, and a few that are now introducedfor the first time, are here defined in the sense

in which they arc to be used in this and laterpapers of this series. Insofar as they areadequate and applicable, the definitions fromRecommended .Minimum Requirements forPlumbing [1]1 will be utilized.

The plumbing system of a building includesthe water-supply distributing pipes, the fixturesand fixture traps, the soil, waste, and ventpipes, the building drain and building sewer,and the storm-water drainage pipes, togetherwith their devices, appurtenances, and connections within or adjacent to the building.The building main is the pipe from the streetwater main or other source of supply to thebuilding served.The water-distributing system is the pIpmgby which the water is conducted from thebuilding main to its various places of use withinand adjacent to the building, consisting oflaterals, risers, and branches.The sanitary system of a building is the pipingsystem, including soil, waste, and vent pipes,that conducts waste water and water-bornewastes from the plumbing fixtures to the streetsewer or other place of sewage disposal.

A plumbing fixture is any receptacle throughwhich waste water or water-borne waste is discharged into the sanitary system.A drain is any pipe that carries waste wateror water-borne waste in either the storm orsanitary system.A fixture drain is the single drain from afixture-trap outlet to its junction with anotherdrain.

A waste pipe is any drain that carries thewaste water from one or more fixtures otherthan water closets.1 Figures in brackets indicate the l itera ture references a t the end of

this report.

[ 2 ]

A soil pipe is any drain that carries the wastewater from one or more water closets with orwithout the waste water from other fixtures.A stack is a vertical section of pipe extendingtwo or more stories with branches therefrom to

serve the stories through which it passes, aswaste stack, soil stack, or vent stacIeA horizontal branch is a drain, extendinglaterally from a sailor waste stack, with orwithout vertical sections, to which the fixturedrains in the same story are connected.A building drain is that part of a sanitarysystem which receives the sewage from soil

and waste stacks and conducts it to the buildingsewer.A building sewer is the main trunk of a sanitary, storm, or combined system from a point 5

feet outside the inner face of the building wallto the street sewer.A primary branch is the single drain line leading from the base of sailor waste stack to itspoint of connection with the building drain or

another branch thereof.A secondary branch is any branch of the building drain other than a primary branch.A vent or vent pipe is any pipe installed in asanitary system for the purpose of permitting acirculation of air through or within the system.A vent stack or main vent is a vent pipe paralleling a sailor waste stack to which the branchvents from the stack and its horizontal branchesare connected.Deman d loa d is the volume rate of demandfor water imposed on the water-distributingsystem or any branch thereof by the use ofwater, as by plumbing fixtures.

Sewage load is the load in volume or volumerate imposed on the sanitary system or anybranch thereof by the use of plumbing fixtures.Charging load is the volume inflow into thesanitary system from one or more plumbingfixtures, applicable when the capacity of thepipe receiving the load depends mainly on theinternal volume (cross section times length) ofthe pipe.Receiving capacity is the internal volume ofa section (drain) of the sanitary system, applicable when the total sewage load is an additivefunction of the separate volumes but not of theseparate rates.Terminal velocity is the constant velocity of


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flow that exists under fixed conditions whenequilibrium between the forces (gravitational)producing and the forces (frictional) opposingflow has been established.Design factor m is the particular value of rout of n fixtures that will be found in operationa selected fraction of the time under the assumed conditions of use.

Fixture unit, or load factor, is a numericalfactor which measures on some arbitrary scalethe load-producing effect of a single plumbingfixture of a given kind. The use of the fixtureunit makes it possible to reduce the loadproducing characteristics to a common basis.n= the total number of fixtures or supply

openings of a given kind in the system.r= the number of fixtures out of a total ofn which at any given instant of observation are found operating to impose a demand load on the supplysystem, or a sewage load on the drainage system.m=the design factor (see definition above).q=the average volume rate of flow, ingallons per minute, to or from aplumbing fixture during actual operation.

Q=the total volume of water in gallons thatflows to or is discharged by a fixtureat each use.t=the average duration of flow in seconds

for a given kind of fixture for one use.T=the average time in seconds betweensuccessive operations of any givenfixture of a particular kind.r=a time interval in seconds such that theevent in question (for example, exactly r fixtures will be found operating) will occur for an aggregate of 1second.

C~=the number of combinations of n thingstaken r at a time.p;'=the probability of exactly r fixtures outof a total of n fixtures being found inoperation at an arbitrary instant ofobservation.

r=n

:8p;=the probability that some number ofr=m fixtures between r=m and r=n, in-

clusive, will Iw found operating at anarbitrary instant of observation.

IV. BASIS OF SELECTION OF PIPE SIZESIn order to select from a series of available or

stock sizes the minimum size of pipe adequateto convey a given flow of a liquid, it is necessaryto know accurately the capacities of the different sizes of pipe for the conditions under whichthe pipe is to be used and to know accuratelythe load the pipe will be called upon to carry,capacity and load being expressed in the sameunits or in convertible units.Pipe formulas, given in terms of the velocityof flow and factors on which the velocity de

pends, are the usual means employed in estimating capacities of pipes. It is an easy stepto convert a formula giving the velocity of flowin a pipe into one giving the volume rate of flow.As previously indicated, the applicability ofpipe formulas to the conditions existing inplumbing systems in service will be treated inother papers. However, since it is necessary toexpress capacity and load in the same units inselecting the proper size of pipe for a given use,it becomes necessary to consider the units inwhich both the expected load and the capacityof the pipes involved can be expressed beforechoosing the units in which load estimatesshould be expressed. A pipe-flow formula ismerely an equation of dynamic equilibrium and,as such, applies only to the particular conditions-namely, the condition of uniform continuous flow in the pipe. Hence the conventional pipe formulas apply to the irregular andintermittent flows that occur in plumbing systems only during that time (usually very short)and in that section of pipe in which the variablefactors involved (velocity or volume rate offlow, pressure or hydraulic gradient, and hydraulic radius) arc constant.

V. CHARACTEI~ OF FLOW INPLUMBING SYSTEMS

Probably the best conception of the limitations of the applicability of a pipe formula foradequately estimating the capacities of plumbing pipes, and the best indication of the logicalunits to apply in expressing capacity and loadin selecting the proper size of pipe to use inparticular parts of the system, will be givenby considering the changing character of flow

[ 3 ]


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as the water passes through the system fromthe source of supply to the building sewer.Water closets with flush-valve control of thesupply are chosen for this illustration of varying flow characteristics, partly because criticalloading conditions in the various parts of theplumbing system are usually produced bythese fixtures and partly because the factorsthat determine the load for an individualfixture are more nearly constant and can bemore readily evaluated than for other fixtures.Assume that each water closet demands foreach flush Q=4 gallons in the average timet=9 seconds, giving an average rate of supplyto the closet of approximatcly q=27 gpm, andthat each of these demands will occur on theaverage of once in T=5 minutes=300 seconds.Since the water-supply pipes are flowing fullunder pressure, there will be continuity of flowin both time and quantity in any part of thesupply system through which water flows tothe water closet or to a group of closets; andtherefore the peak load at any time will be thesum of the separate demands, r, occurring atthat time, or rq gpm, where q is the averageflow per fixture. In this case a pipe formulais applicable for computing limiting capacitieson the basis of diameters, lengths, roughness,and available head. The difficult part of theproblem is to estimate the maximum r out of atotal of n water closets supplied by the systemfor which provision should be made.In the drainage system the flow from thewater closet through the fixture drain (closetbend) into a horizontal branch will be at aboutthe average rate of 27 gpm for a period of from8 to 10 seconds. However, the flow will beless nearly uniform than the flow into the bowl,rising to a rate offrom 30 to 40 gpm temporarily,as siphon or jet action comes into play in thebowl, and dropping immediately following thepeak siphon action to a rate approximatelyequal to that of the supply at the time.In the horizontal branch the temporary peakflow will flatten out, and the stream will tendto assume the terminal velocity (see definition)for the diameter and slope of the drain and theexisting volume rate of flow. As the streamenters the vertical stack, the sudden change indirection pilcs the water up, tending to form aslug of water at the entrance. In fact, the

surge from a single water closet entering a 3or 4-inch vertical stack through a short llOl'izontal branch of the same diameter will almostfill the stack at this point. Immediate acceleration tnJ~es place in the vertical stack and continues throughout the length of the stack oruntil the terminal velocity of the stack isreached for the volume rate of flow.From the stack the stream will enter thesloping primary branch at a velocity muchgreater than the terminal velocity for thatbranch (shooting flow) 2 and will be decelerated until the terminal velocity for that volumerate of flow is approximately reached. If thevolume rate of flow, the entrance velocity, andthe slope, diameter, and roughness of the primary branch are in the proper relation, thl'transition from shooting flow at the entrancpto gravity flow will occur in a hydraulic jump,a phenomenon which frequently occurs in theprimary branches of building drains.Throughout the drainage system in the direction of flow there is a continuous decl"pasein the volume rate of flow from a single closetor a group of closets flushing at the same time,a corresponding increase in the time of flow,and a continuous decrease in the peaks produced by siphon or jet action in the bowl orby the overlapping of the flows from differentclosets.

The conception of flow in plumbing drains asdescribed has been verified by numerous experiments in the laboratory and by numerousobservations and depth measurements made onthe building drains of large systems in actualservice. In plumbing drains the peak rate offlow from a water closet at the point of entranceto the horizontal branch is usually reduced toabout one-half that rate at the point of transition from shooting flow to gravity flow in aprimary branch, and the volume rate of flowcontinues to decrease from that point on.If a single water closet flushes on the averageat intervals of 5 minutes and delivers 4 gallonsfor each flush, the stream in the drain tendstoward a continuous flow of Q/T=4/5=0.8 gpmas the distance from the water closet increases.Likewise for a very large number of water

2 Shooting flow h('r(~rdt'rs to the high-yelocity constantly ctect'leratingflow that occurs in the primary branch of a building drain betwecn itsjuncture with the soil stack and the hydrauIic jump in the primarybranch.

[4 ]


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closets, n, eneh used nt thnt average rate, 1Ulda very long building drain, the flow tendstoward a uniform value 0.8 n gpm. If n isgreater than Tit, it is obvious that flow in themain building drain will be continuous for thegreater part of the time that each of the closetsis being used at the average rate of once in Tseconds, and that the tendency towat'd uniformcontinuous flow will increase as the size of theplumbing system increases-that is, as n 1tndthe length of the drains increase. Hence in avery large system in which all n closets are incontinuous use, the outflow will be continuousand the rate will fluetuate around 0.8 n gpm.Since the stream in the main building drainand building sewer of large buildings approachesunifot'm flow, and since these drains are ordinarily laid with a uniform slope, load andcapacity can be most adequately expressed involume rate of flow and a pipe formula foruniform flow may be used in estimating limitsof capacity for building drains. However, itshould be kept in mind that the volume rate offlow in any particular section of the drainagesystem is not an additive function of the separate volume t'ates of flow into the system.There is another consideration that has adirect beat'ing on the method chosen for estimating the loads to be provided for in a building drn.inage system and on the choice of unitssuch that load and capacity may be expressed inthe same units. The horizontal branches, theentrance fittings to soil and waste stacks, andprimary branches arc paTts of the drainagesystem in which critical loading or possible overloading arc most likely to occur. In horizontalbranches which lie near the fixtures, and to alesser degree in the stack fittings and horizonta.l branches, the determinate factors in theselection of adequate drain pipes are the charging load and the receiving capacity. In estimating the charging load to he provided for,the problem is again to obtain a reasonableest,imate of the value of r to be provided for inrelation to n. The details of the method relating to l"Cceiving capacity will be comph,tedin the papers dealing with capacities.

1. CASES OJ


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to explain more fully the suggested method ofemploying the function in making the estimatesin question, and to point out certain limitationsin its practical application. The problemmay be stated as follows: Assuming that thereare n fixtures in a system, each operated oncein T seconds on the average, and that eachoperation is of t seconds' average duration,what is the probability that r fixtures will befound operating simultaneously at any arbitrarily chosen instant of observation?It is necessary to define the expression,"operating simultaneously," in order to completely define a particular even t of "r fixturE'Soperating simultaneously." In the followingdevelopment of the theory, this event will beconsidered as occurring when r, and only r.fixtures are found flowing at tIlE' instant ofobservation; and hence the r fixtures foundflowing will include all those, and only those,which began their opera.tion during the t-secondinterval immediately preceding the instant ofobservation.

VII. DEVELOYtdENT OF THE PROBABILITY FUNCTIONBy the gem'rally accepted concept of probability, the probability that a particular fixture out of a number, n, will be found operating

at any arbitrarily chosen instant of observationis tiT, where t has been defined as the durationof each operation and T as the time betweenoperations of each fixture. In the same manner, the probability that the particular fixturewill not be in operation at the instant of obsE'rvation is I-tiT 01' (T-t)IT.A law of combinations that applies to tllE'composite event of which the probability issought in this problem may be stated as follows: The number of ways in which two ormore independent events can occur together isthe product of the ways each can occur separately. A similar law of probability may bestated as follows: The probability of two ormore independent events occurring together, inthis case at the same instant, is the product of[,he probabilities of their separate occurrence.By the law of combinations, the probabilitythat none of the remaining n-l fixtures willbe operating at the instant of observation is

(T-t)"-l. The probability that a particularone of nfi~tures and none of the remaining n-lfixturcs will be operating at the' instant is

But since there an' 11 fixtun's, there an' n waysin which the event, am' and only one fixturefound flowing, can occur, and hence the probability of this event l)('ing found occurring atthe instant of observation is

(1)This can be generalized for any group of r,and I' only, constituting the particular eventfor which the probnhlity is sought, by againapplying the definitions and laws.In any group of I' fixtures the probabilitythat any particular OIll' will begin to operatewithin a given t seconds is tiT, and sinee there

are r cases in thp group, the probability, thatall r fixtures will begin opC'ration within thesame t seconds is (tiT)'. Also, of the n fixtures, anyone of

n(n-l) (n-2) to r factors_ lIJ __ a:-r!------. -"!(n-r)!- rdifferent groups is equally likely, and hence bythe law of combinations the probability thatsome one of the equally likely groups of r fixtureswill be in operation at tIll' instant of observa-tion will be O{~r. As l)('fore. the probability thnt tlH' remaining 11 -I' flmn will fall

(T-t)"-rutside' this particular t s('conds is -r .Therefore, the probability that exactly r fixtures will be operating at n particlllnr instantof observation in the mann('r defined is

This is the general term of a series, expressingthe probability that r out of n fixtures will 1)('found flowing at any a.rbitl'Hr'y instant ofobservation. This spries may 1)(' representedas

[6 ]


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or

Kquation :3 is ('quivalent to the binomial

(6)n-I' t=r+1XT-(

IX. PROPOSED USES OF THE Pl{OB-ABILITY FUNCTION FOR MAKINGLOAD ESTIMATES

There are certain characteristics of tll';= 1/7 ...r=m+l

'fj]J"= ,O"tr (T- t) n--r = 1r=O r r=O r 1'n

time of r fixtures operatingtotal time

3 Equations 2 and 3 may he developed by other rncthods and in different. forms. However , the results wil l be identical or may be reducedto an identity, as cyidenced by the function denlopcd by Fry [2] for theanalogolls prohlcm or husy lines in telephone fiysteIl1s (see eq 156, p. :~:{; \of thc referencc), which differs from eq 2 only in the form to which it isreduced and in the notation employed,

is also the probability of the occurrence.Hence for any given values of nand r, if theprob!lbility function as developed is multipliedby a time 7 in seconds such that

(t)'(T-t)p';=70'; l' -----rr' ,,-r=l second, ... (4)

VIII. INTERPRETATION OF THE PROB-ABILITY FUNCTION

. f (t + 1'-t)" 1\XpanSlOn 0 l' -1' - =.

As previously stated, the probability funetion,p;', eq 2, gives the probability that exactly rfixtures out of a total of n will be found operat-ing at an arbitrary instant of observation, pro-videel that all n fixtures are in continuous usea t the assumed rate. The pro babili ty, p~,may also be interpreted as the percentage orfrnction of the time in the long l'tm that r flowswill occur in the manner defined, since thefraction

('onven tional ('xpn'ssion for certainty, smceeither no fixtun~s, 1'=0, or some number offixtures from 1'= 1 to r=/1 must be operatingat, the instant of observation.3

(lIe N]uat,ion sign i(ie" Lilat /' fixtures will he in"illlult.alwo\ls operation for an aggregate or Isecond out qf every 7 seconds that all n fixturesare in usc at the assumed rate. Likewise, thecondition that a chosen design factor, r=m,will not be exceeded more than a given fractionof the time 1/7, is expressed by

[7 ]


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value or values and then decreases. Also, theratio of any term to the preceding term of tht>series decreases continuously as I' increasesfrom 1'=1 to r=n. These characteristics makeit possible to determine the value m that willnot be exceeded more than the fraction l/T ofthe time without completing the entire summation from the m+ 1 to nth term.If p~, /') ..1'+ 1 T-t 1 -, summatlOJI IS necessary

in order to determine a value of r=m that willnot be exceeded more than l/T of the time, butit is unnecessary to carry the summation beyomln-r tthe term when' 1'+1XT_t


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246TIME - SECONDS

FIGURE ] .-Typical lime-supply curves for lOater-closclbowls.

flush valve or flush tank: it rises to a maximumat or near the beginning and gradually decreases as the valve closes or as the tankempties. The characteristics of an effectiveflush may be summarized as follows:A quick priming of the siphon; a continuoussiphon action for sufficient time to clear the

bowl of its contents and carry them throughthe trapway; and a breaking of the siphonaction before the flow ceases, in order to refillthe trap. Whether by design or chance, thecharacteristic operation of conventional supplydevices (flush valves and flush tanks), if properly adjusted for volume and time, controlsthe rate of supply in a manner that meetsthese flushing requirements admirably. Infigure 1, curve 1 is the reproduction fromCamp's report of a typical rate curve for itflush valve, representing it flow of 3.8 gallonsin 8.5 seconds giving it peak rate at the end oftwo seconds of approximately 37 gpm and anaverage rate of 26.9 gpm over the time thevalve is in operation. Curve 2 is the ratecurve for a flush tank plotted from Golden'sdata for a flow of 4 gallons in 9.1 seconds givingit peak rate about 31.5 gpm at the end of 1second and an average rate of 26.4 gpm. Inboth cases the flow reaches a rate within thefirst second amply sufficient to prime the siphonof any standard type of closet bowl and thereafter is maintained for 6 or 7 seconds withinthe range required to produce continuous

which thc bowl will be effectively emptied ofits contents with an average rate of supplyanywhere within the smaller range referred to.From the evidence of experiments reportedin the earlier paper [1], the Subcommittee onPlumbing of the United States Department ofCommerce Building Code Committee agreedupon an average rate of 30 gpm for 10 secondsas a reasonable and safe basis for estimatingloads to be expected in building drainagesystems. The experiments referred to weredesigned to obtain the maximum loads percloset that could be delivered to the drainswithin the operational range of water closets,and no attempt was made to determine eitherthe most effective rate of supply for a particulartype of bowl or an average rate that would produce a satisfactory flush in all types of closetbowls. It is to be expected, as has been thecase, that overestimates would result when themaximum values of all load fa(~tors involvedare employed in estimating. More recent experiments [3] by Camp give rates of supply forsafe and economical flushes ranging from 20gpm to 29 gpm for different types of closetbowls and times of flush ranging from 7.5 to 9seconds, omitting data for one bowl with spiralflow action. The averages for six differentbowls are 25.9 gpm and 8.2 seconds. Unpublished data from still more recent experiments[4] at the National Bureau of Standards indicate that the most effective removal of thecontents of a closet bowl occurs with rates ofsupply ranging from about 20 to 24 gpm andthat the complete contents of the bowl areremoved, if removable by any rate of flow, intimes ranging from about 6 to about 10 secondsfor different types of bowls.In both cases the data were obtained withapproximately uniform flow through the bowl,and that average rate of flow which maintainedcontinuous siphon action through the bowl wastaken as the criterion for the most effectiveflushing rate. Considering the wide ranges inrate and time of supply within which a closetbowl will operate effectively, Camp's andGolden's data may be regarded as in substantial agreement. However, none of theexperiments cited closely simulates serviceconditions, for the rate of supply in actualservice is not uniform, whether supplied by

r 9]

40

~& 30,wC)a:


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- ._-- ---- ------------ARLE l.--Vallles of tiT, q. and Q

to the overflow. Ordinarily only a fraction,possible ~,to ~~,of these volumes will be used fora bath. The time, T, between uses will includethe time required to draw the water, the timetaken for bathing, the time required to emptythe tub, and any additional time consumed inthe complete bathing operation. This totnltime, T, between operations of the fixture seemslikely to range from about 15 minutes for hurried baths to about 30 minutes for ba,ths takenmore leisurely. It also seems likely thatsmaller quantities of water will be used underthe former than under the latter conditions.Now, assume that 8 gpm is an ample averagprate of supply for a bathtub. This is GO percenthigher than some [5] and 20 percent lower thanother [6] estimates of a satisfa,ctory average ratpof supply for a bathtub. An average rate ofsupply of 8 gpm, an assumed average time offilling of t=60 seconds, and an assumed timebetween operations of 1'=900 seconds (15minutes) would provide for an average of 8gallons per bath. For an average volume of 16gallons per bath and the same rate of supply. 8gpm, 120 seconds (t) will he required to drawthe bath. If the rate of operation (averagptime taken per bath) is once in ~o minutes, giving 1'= 1,800 seconds, the ratio of tj T is thesame in both cases; 60j900= 120j1.800= 1j1.5.Since for a given value of n the value of p; forany value of r is determined by the ratio tjT, theprobability of a selected design load mq beingexceeded will be exactly the same for the twocases cited or for a,ny other case in which thetime l' is proportional to the volume used andthe same basic rate q is employed. From theseconsiderations, a design load mq, for bathtubsin congested scrvice, based on an average rateof supply of 8 gpm, and a ratio tjT= 1/15 appears to insure fairly satisfactory service and isused as the basis of the development, and comparisons following.'1'11(' values selected for the three fixtlJreS discussed are given in table 1.

siphon action. The total volume, the averagerate of flow, and the duration of the flush inthese examples are all greater than necessaryfor an effective flush in the types of bowls mostcommonly used-washdown, reverse trap, andsiphon-jet bowls. It is impractical to attemptto estimate individual variations either inrates of supply or in rates of use of fixtures.Hence, it is advisable to set the factors chosenfor making estimates high enough to allowsome leeway in adjusting down to the volumeand rate of supply needed for satisfactoryservice in particular cases, since it is impossibleto adjust for greater rates of supply than thesupply pipes are capable of delivering.Considering the problem of estimates fromall angles, an average rate of supply of 27 gpmfor a duration of 9 seconds, giving a volume ofapproximately 4 gallons per flush, appears tomeet requirements generally as nearly as canbe done in l'Ound numbers and will be employedfor flush valves for water closets in evaluatingthe probability function in the further development of the methods of estimating demandloads.

The rate of supply to flush tanks for wa1


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Equations 4 and 5 arc not satisfied in generalby integral values of rand n and a given valueof l/T; that is, for occurrence exactly a givenpercentage of the time. However, by trial anderrol', a value of t for each given value of ncan be computed for which the probability ofoccurrence is in excess of a given perccntage,for example 1 percent of the time, by the smallest possible fraction. From this probability,71;, a particular value m of r, for which theprobability of occurrence of any numberg'renter than m is not greater than a givenpef'(~(mtagc of the time, may be rcadily deter-t=nmined by an approximation of 'i:.p~.t=m+1If P,::+l < (1/2)p;:', no further computation ISnecessary as pointed out on page 8. If71;;,+1 > (1/2)p;':, it will ordinarily be necessaryto carry the summation to a few terms only todetermine the value of m required.

Probability data for flush valves for waterclosets, flush tanks for water closets, and bath

.,v. PHESEN'l'A'l'ION OF PROBABILITY DATA tubs are given in table 2, in which t is thegreatest number of fixtures out of n that willbe in operation 1 percent of the time and mis the number of fixtures that will not be exceeded more than 1 percent of the time.TARJ,E 2.-Probability data for three types of fixturcs

Flush valves, for Flush tanks, forathtubs, forI/T~9/3OO~3/100 I/T~ f.o/3 00~ 1/ 5/T=I/15n

r V;mV;mV;III-- --------------6 2.0119 2.0960 2.0124 2Hi 3010230512 30118 :J30 401010281 454012ti 447 5010450165 5250107 566 601066570138 7160118 G85 701007500118000112 7107 801050401154901049129 901049400112013401024151 10010103260104772901039199 120102240GO0101721301023299 1G0101t10574010280!)001001

It will be observed that for flush valves tiTis small, and r=m for all values of n in therange given, and that the greater tiT the smaller is the range in which r=m.Figure 2 shows the curves obtained by plotting m and n for the three fixtures, curve 1 being

100

I. FLUSHVALV ES, y/'f =o.0 I

2. BATH TUBS, yI'f= 0.01. FLUSH TANKS, V1=0.01.//.././

././

,/V .../..//.,/',. /V/' --- ..--- ~ I.---'..--- - - -75

E 50

25

o o 50 100 150n 200 250 300FIGUUE 2.-Probable relation of In to n from table 1.

[ 11 ]


14/26

500

I. FLUSH VALVES /'",V'"./S

VLUSH TANKS VATH TUBS/'"V'" .//' V........-V1/ ........-V /'::::::::/'L.--::: /"' V.--:;::::;:....-- /'.....--~-/.- /'"--......... ..--3' V................-V ---'"2'..............--.-V --""" ---.....--4.....-/ ---.....--

//~............- ---I-- ~' .-/5-V ---..-.-/........- ---

-:P........-

vc.---~

?-..--400

300

200

100

o o 50 100 150n 200 250 300FIGURE 3.-Probable flow in relation ton.

for flush valves, curve 2 for bathtubs, andcurve 3 for flush tanks. A value of m for flushvalves that would not be exceeded for morethan one-millionth of the time was also computed, and the results are represented in figure2 by curve 4.Estimates of pipe capacities will ordinarilybe obtained in flow units, for example in gallonspel' minute. Hence it will be more convenientin practice to have the demand load expressedin the same units. This may be obtained byplotting mq and n as shown by figure 3, in whichq is taken as 27 gpm for flush valves, 4 gpm forfiush tanks, and 8 gpm for bathtubs. Theaverage flow, nQ/T, during the time the fixturesare being used at the rate of once in the time Tis also represented in figure 3, for flush valvesand flush tanks by line 4 and for bathtubs byline 5.

Curves 1. 2, and 3, in figure 3, show the I'ela-

tion of demand loads to number of fixtures.based on estimated time factors representingcongested conditions of service-that is, themaximum practical rate at which fixtures canbe used continuously in actual service. Assuming the COITectness of the factors employed inevaluating the probability functions, the curvesmay be used for estimating the demand loadsfor any particular number of fixtures of onegiven kind. However, the design load for allkinds of fixtures installed in one system shouldnot be the sum of the design loads computedseparately for each kind of fixture, even thoughthe individual curves may be correct. Simultaneous operation of different killds of fixturesis a chance occurrence which would have to beevaluated by another probability function.Although such an evaluation is possible all thebasis of the assumed average time factors, theprocess is too complicated for convenient appli-

[ 12 ]


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3.353.904.304.423.99

TABLE 3.-Relative demand weights of fixtures

N either the possible accuracy in estimatingthe demand to be expected in a plumbing system nor in estimating the capacity of pipesselected for supplying the estimated demandjustifies the assignment of weights in the scale1 to 10 closer than to the nearest integer.Accordingly, on the basis of average values, therelative weights of the three fixtures become 10for flush valves for water closets, 4 for bathtubs(total hot- and cold-water supply), and 5 forflush tanks.It will be observed that these fixture weights

have the same significance as the fixture unitratings assigned to the different kinds of fixtures in Recommended :Minimum Requirements for Plumbing [1]. This unit in the weightscale is not a definite unit of flow but is simplya load factor to be applied through a relationbetween m and n such as developed in figures2 and 3. However, since the termjixture unitin this significance has become fairly well established by usage during the past 15 years, theterm will be retained here to designate loadweights of fixtures.A further comparison and an illustration ofthe results of applying the average weights ofdifferent kinds of fixtures to a single basicprobability curve may be made by reducing thenumber of fixtures to fixture units (n timesweight) and replotting, as in figure 4. It willbe observed that the curves for flush tanks andbathtubs (total supply) lie very close together,indicating that the relative weights, 5 to 4, areapproximately correct throughout the rangeillustrated for the individual volumes and ratesallowed. It will also be observed that the twocurves both intersect the flush-valve curve between 193 gpm 880 fixture units and 210 gpm1,040 fixture units, indicating again that therelative weights 10:5:4 are approximately correct in that range. For 300 flush tanks, 1,500

cation in thc field or office and, because thetime factors for faucet-supplied fixtures onwhich the probability of simultaneous operationdepends cannot be determined in general,would in the end lead to doubtful results. Forthese reasons it is believed that reasonablysatisfactory results, whieh are much simpler toapply, may be obtained by weighting eachkind of fixture and applying the weighted sumof the total nmIlbel's of fixtures of all kinds to aload curve for flush valv{~so r a load curve forfhlsh tanks, according to which type of supplyis to be used.4. DERIVATION OF FIXTURE WEIGHTS (FIXTURE

UNITS)In I~ecommended 1'vIinimum Requirements

for Plumbing [1], fixtures were weighted in thescale from 1 to 6, this scale being selected. largely because, of the fixtures installed in thegreatest numbers, the smallest load (lavatory)was estimated to be about one-sixth of thelargest load (water closet). The scale chosenis purely arbitrary, and it is now suggestedthat a decimal scale, 1 to 10, would give a muchmore flexible system of estimating.A comparison of the relative loading effectsof the three kinds of fixtures may be made bymeans of the curves in figure 3. Obviouslythere is no eommon exact ratio of the loadingeffects of any two different kinds of fixtures,each kind using water at different volumes, Q,volume rates, q, and different time intervals, T,over any eonsiderable range in number offixtures, n. For example, for a demand of.'50 gpm, the number of fixtures from whieh thisload would be oecurring not more than 1percentof the time is approximately (fig. 3) as 5: 34: 33,respectively, for flush .valves for water closets,flush tanks for water closets, and bathtubsupply (total). The load-producing weightsare inversely as the number of fixtures produeing a given load; hence, on the basis of10 for flush valves, the weights for a demandof 50 gpm are 10: 1.47: 1.52. Table 3 givesthe relative weights computed in this mannerfrom a comparison of the three curves fordemand loads at increments of 50 gpm from150 to 300 gpm, the range in which the proposed method of estimates will have its greatest application and usefulness.

[ 13 ]

Flush valveslush tanksathtnhsDemand.

~---'----------.---------gpm Number NnmherRelativeNUInberRelalf fixture~ Weightf fixturesweight

of fixtureswei~ n n----- ---------------------150. __. 56033.2067200 93085.0338250. 133038.5912300... __.. 176092.0398--- -----~----Average weighL_ 10--------- 5.21----------IVPht


16/26

-

./2. FLUSH TANKS

./,/ .//',/

./V

I")/ ,/'

./,/

/.// /3.// ~~ ;;.-'~~' ~/I~ {//' #/j'// ~'I;500

400

300

200

100

o o 500 1000 1500FIXTURE UNITS

2000 2500 3000

FIGURE 4.-Relation of demand tofixture units.fixture units, referred separately to the flushvalve curve for an estimate, the demand estimate would be about 15 percent lower than thecorresponding estimate made directly from thefiush-tank curve. The corresponding error inthe estimate for 300 bathtubs made in the sameIwumer would be about 3}~percent. Theseerrorsare immaterial, for the only result, in case thedesign load was exceeded in service by thatamount, would be an increase in the time required to refill the fixtures by 15 percent and3}~percent, respectively, or, in case the sametime is occupied in refilling, a reduction by thesepercentages in the volume of water used. Below the point of intersection, referring flushtanks and bathtubs separately to the flushvalve curve would result in overestimating thedemand by amounts varying from very smallpercentages for 880 to 1,040 fixture units to

about 94 and 23 percent, respectively, for 100fixture units. However, the error in an estimate made from curve 1 fol' the total demandload for flush valves for water closets and forbathtubs will be less than the error indicatedby an estimate made separately for the bathtubs from the same eurve in all cases in whiehthe flush valves predominate, 011 the basis oftotal fixture units of the two kinds of fixtures.In cases where flush tanks for water closets arcused exelusively or predominantly in the system, a closer estimate could be made on thebasis of total weights, by using curve 2 and thetotal fixture units for all kinds of fixtures involved. Obviously the error made by usingcurve 2 for both flush tanks and bathtubs forany number of either up to 300 would be small.Also, the demand load relative to the numberof fixture units may be approximately repre-

[ 14]


17/26

500

/"/",

././

.//",v./ .//"/ ./V/ .///' -::?./' ;/IV /V2 VV /V /fj I

100

200

400

~ 300a.


18/26

TABLE 4.-])i~trib/ltio1l of lIIo/"n1'ng calls in hotels

It will be observed that the time of risingin the two hotels is distributed in approximatelythe same manner, the greatest Humber of callsin any 15-minute perioo being for that following 7:30 11. m., and that slightly more than

two classes of supply should be added to obtainLlle esLimnLe for LoLn1demand on any supplypipe common to both services. If the two typesof demand do not come at the same time of day,the greater demand of the two may be tflken asthe peak demand, or design estimate.A bathroom group of fixtures can probably bemore closely weighted to the selected scale of 1to 10 by taking the three common bathroomfixtures-water closet, lavatory, and bathtub orshower-as a unit than by weighting eflchfixture separately. In hotels and apartmenthouses the bathrooms arc not all in use at onetime, and the loading weight of any fixture ofthe group-for example, a water closet-willbe much lower than for the same fixture incongested service, for which it has been assumedthat all fixtures will be in continuous use ouringthe period of congestion. One peak perioooccurs in hotels and apartments in the morningduring the rising hour and another in the afternoon during the preparations for dinner.Probably the best indication of the distributionof the use of the bathrooms in hotels and apartmen t buildings obtainable will be given byrecords of the activity during the hours whenthe peak use of the plumbing fixtures occurs.Table 4 is a summary of reconled morning(rising) calls from the switchboard for two largehotels in New York Ci ty for 7 consecu tive daysi]] one case and 9 days in the other. Hotel] isa large hotel in which the guests were principallytransient. Hotel 2 is a large apartment hotelin which the greater part of tl](' guests wereresident but which also received and accommodated transients.

Till1f' of ('all

4 810[141 01 700[ 18o[ '1I::3[ :382 1 2,81 021)99 I jf) j"RO 1il) 142 ;{41 3, Ofii,ORO[ :J2211,4ROj :3011 OO,oj n31,o .HlO

1

--Be

fore 6::30\:4,\ '5:~O -- -----]74 2288198 212113~m4AO[2311Hotel L_u _Hotol2 __u _

Total cal1su_

Place

5. RELATIVE LOAD VVEIGHTS FOR DIFFERENTCONDITIONS OF SER VICE

flush tanks for water closets, bath tubs. andlavntorics, rcspectively.

Up to this point the discussion has been confined to four kinds of fixtures under congestedconditions of service. There are several considerations that should be taken into account indetermining load ratings for other fixtures andfor other conditions of service, among whichthe following are especially important:(1) Fixtures that are relatively few in numberand unlikely to be used when the predominantkinds are being used most frequently will addvery little to the demand or to the peak sewageload and hence may be ignored, except in regardto the branch supply lines and branch drainpipes of these fixtures. Slop or service sinks inoffice buildings, which are in use to any considerable extent only before or after office hours,add a negligible load to the peak loads of theday. Kitchen sinks and laundry trays indwellings and residential apartments may alsobe placed in this category.(2) Fixtures so installed that they cannot ingeneral be subject to congested conditiolls ofservice in the same sense as fixtures installed inpublic comfort stations, general toilet rooms inoffice buildings, and other buildings in whicheach fixture is open and accessible for use ft t, alltimes, should be given a rating in accordancewith the possible extent or frequency of theiruse. Bathrooms in private dwellings, residential apartments, and private bathrooms inhotels may be considered in this class, and canbe rated advantageously as a group.(3) 'Vater services that demand a cont inuousflow, such as lawn sprinklers, air-conditioningequipment, gang showers in factories, andathletic dressing rooms, present no element ofchance in regard to overlapping and arc notsusceptible of a logical weighting in relation towater closets and other fixtures that use wflterat high rates for comparatively short periods oftime. Hence the demand for this type ofsupply should be considered separately and estimated separately. If the use of these continuous water supplies is such that they ov('rlflp therush period of the day for the weighted fixturesin the system, the separate estimates for the

[ 16]


19/26

TABLE 6.-Distribution of morning exits in apartmentsfor 2 days

TABLE 5.-Distribution of morning calls in apartmentsfor .9 days

one-half of all calls fall within the hour from7: 00 to 8: 00 a. m. This is significant, andit may be assumed that the time of rising ofguests leaving no morning call will be similarlydistributed in time.

Time of callTota]Aftercallg6:30:45:00:15:30:45:00 8:00------- 31317 82229 62328 42314 32211 51211 8331413 4141230 4020318----- 458.\0660621311

tensive use of plumbing fixtures in any singleapartment or in any group of apartments inwhich the occupants rise at the same hour willlast for about an hour. The maximum numberof calls within any single hour ranges from 69to 75 percent for different days. The corresponding percentages for the hotels range from47 to 62. It therefore seems reasonable toassume that not more than 75 percent of thebathrooms in an apartment house or in anyhotel will be occupied and in use at one time.There may be exceptional apartment houses inwhich the occupants are all engaged in thesame occupation that would show a higher concentration in rising time. However, it will bethe exception rather than the rule andshould be treated as an exception in estimatingwater-supply demands and sewage loads.There is another consideration that is important in estimates of loads for bathrooms. In aleisurely use of a bathroom, the fixtures willordinarily be used one at a time. In cases ofhurry or congestion, two fixtures may be inuse at the same time in a bathroom, in the sensethat water is being drawn for or is being discharged from both at the same time. Henceit seems reasonable to assume that, on theaverage, not more than two-thirds of the totalnumber of fixtures in all occupied bathroomswill be in use at the same time. The totalnumber in use at one time on this basis, will notexceed two-thirds of 75 percent, or 50 percent,of the total number of fixtures in bathrooms inthe building. Accordingly, it is suggested thata bathroom group in a residence or apartment,or a private bathroom in a hotel be given onehalf the total weight for the same fixtures inpublic or congested service in estimating supplydemands.

The term "bathroom group" is here definedas consisting of a water closet, a lavatory, anda bathtub with or without a shower head, or ofa water closet, a lavatory, and a shower stall.These suggested weights become (10+4+2)-+2=8, and (5+4+2)-+-2=5.5, respectively, forinstallations using flush valves and flush tanks.Again, in accordance with the convention previously used in selecting fixture weights, thenearest higher integral value will be assigned,giving for a bathroom group using a flush tankthe weight of 6.

47 I 70 I 41 I 31 I 26 I 2799 59 .54 23 21 26296 I 129 1 95 1 54 I 47 1 541

Tota17:4518:00 1 8:1518 :3 0 18 :45 1 exitsto to to to to8:00 8: 1.\ 8:30 8:45 9:00

Interva] of time4.\ 7:00 7: 15:30

0totoo007: 15 7:30:45-- ----I 4816 857-- ---7 123381,7:

Period

1st daY n 1 12d daYnnnnnTota] exi ts. __.I 1

Table 5 gives the summarized record ofmorning calls for a large apartment house inWashington, D.O., for 9 different days otherthan Sundays during a period of 22 days. Table6 gives the summarized record of morningexits from the same apartment house. Oomparing tables 4 and 5, it will be observed thatthe number of morning calls in 15-minuteperiods in hotels and apartments fluctuates inabout the same manner, the principal differencebeing that the peak number of calls in any 15minute period is about 10 to 15 percent of thetotal number higher for the apartment housethan for either the transient or apartmenthotel. Also comparing tables 5 and 6, it willbe observed that the peak of exits from theapartment house, indicating the beginning ofthe business or social activity of the day, occursapproximately 1 hour later than the peak ofthe rising activity. This indicates that ex-

[ 17]


20/26

~See discussion of negligible fixtures on page 16.

TABLE 7.-Demand weights of plumbing fixtures

6. ApPLICA'rION OF LOAD CHART AND WEIGHTTABLE

In estimating the demand load for a supplypipe in any building, the total number of eachkind of weighted fixtures or weighted groups offixtures will be multiplied by the weight of thatfixture or group (table 7) and the products addedto obtain the total number of fixture units.The demand load is given by the correspondingordinate of the appropriate curve in figure 5.For example, assume that an apartment houseor a hotel has 100 bathrooms with flush-tanksupply for all water closets and that any otherfixtures in the building are negligible 4 in relation to peak demand. The total number offixture units will be 100X6, or 600. The ordinate on curve 2 of figure 5 corresponding to thisabscissa is 147 gpm. This estimate, of course,applies only to the main supply or service pipefor the building and does not include any continuous demand, such as that for lawn sprinklersor air conditioning, etc. Again, assume thatan office building has 100 water closets withflush-valve supply, 25 stall urinals with flushvalve supply, and 100 lavatories, and that thedemand of other plumbing fixtures is negligiblein relation to these, but that the building hasan air-cooling system which demands a maximum rate of 225 gpm. By referring to table

105105321.54343866431.5

Wcir,htpcr fixture orgronp infixtureunitsType of supply

Flush valve (total) n_Flush valve (cold only)_Flush tank (total)_ . ..Flush tank (cold only) n~3~wf~erc~~;:spon(linggroup above for total.2; for cold or hot

Occupancyixture or group

Bathromn group un Private00_" 0000__0000 do.__ .._Do _nun_n. ___ 00.


21/26

560

5 it is found that the total number of fixtureunits is 100XIJ+25X5+100X2, or 1,325.The corresponding estimated demand load is 247gpm, to which 225 gpm must be added, giving472 gpm for the total estimated demand on theservice pipe of the building. The method ofestimating for branch risers and other distributing pipes is similar, the estimate beingbased on the' number of fixtures or groupssupplied through the branch, and the weightsbeing selected a.c(~ordingto whether the branchsupply pipe carried the total supply, the coldwater only, or the hot water only.

X. ADEQUACY OF THE IvIETHODThe proof of the adequacy of the proposedmethod of estimating the demand loads to beexpected in building-water-supply systems will,in the end, depend on its success in actual trial

over a period of years. Fortunately, in thiscase we have a means of comparison with asimilar method that has been given a trial.Table 8 is an abridgement of a table from theconstruction manual [5] used by the mechanical

engineering section of one of the Federal departments, based on the method of estimate bymeans of the probability function as originallyproposed [1] in 1923. This table has been usedfor a number of years by that office with reasonably successful results. The only complaintagainst the results of using this table and methodthat has come to the author's attention is thatit tends to give larger estimates than havebeen found necessary for satisfactory service.The principal reason for this tendency to oversize supply pipes does not lie in any inherentfault in the probability function, but in theapplication of the method by means of a tablewhich does not provide for the probability,or rather the improbability, of overlapping between or among two or more groups of differentkinds.TABLE S.-Demand estimates in gallons per minutefrom li'ederal table

Number of f ixtures

The inherent fault of applying the probability function by means of a table is illustrated in the comparisons which follow. Table9 gives estimated demand loads for flush valvesfor water closets, flush valves for urinals, flushtanks, and lavatory faucets, taken from thecurves of figure 4 over the range in number offixtures included in table 8. The values forflush valves for urinals were taken from thecurve for flush valves for water closets on thebasis of five fixture units per fixture, and thevalues for lavatories from the curve for bathtubs on the basis of two fixture units per fixture(table 7).TABLE g.-Demand estimates in gallons per minute frO/iifigure 4

)


22/26

The regularly d


23/26

of the method of estimating sewage load willbe treated in the paper dealing with capacitiesof building drains. Also, before the methodcan be successfully applied in practice, theabbreviated table of fixtme weights for demandloads will have to be expandpd and modifipd.Thesp modifications will also be developpd inthe lakr paper.

XII. DISCUSSIONThe principal purpose of this paper is to

present the fundamental principles and data onwhich the proposed method of estimatingloads to be provided for in plumbing systemsis bascd. It, has been pointed out that thedetails of application of any method in practicemust be guided to a large extent by engineeringjudgment in order that it may lead to satis-factory results. The choice of values employedin evahmting the probability function and inconverting estimates in number of fixturesflowing to estimates in gallons per minute rep-resents the author's judgment.It, has also been pointed out that it is impos-sible to determine or to estimate closely eitherthe maximum demand load or the maximulllsewage loael that will occur in service. It isonly possible to estimate the loads having acertain probability of being exceeded in a givensystem. In this respect, it is believed thattable 7 and figure 5 will enable the engineer toobtai n t,hat, estimate as closel~Tas the vnr~Tingo

conditions encountered in plumbing systemspermit, and that the results of applying thedata presented in that form will in general leadto the selection of adequate sizes of supplypipes and as economical sizes as are consistentwith safety and satisfactory operation, pro-vided the proper judgment is exercised inestima ting the capacity of the pipes under theparticular conditions of installation.

XIII. REFERENCES[1] Recommendcd Minimum Requirements for Plumb-ing, Departmcnt of Commercc Building and

Housing Series, BH13, 1924. Revised by addi-tion of a supplement, 1932.[2] Probability and Its Engineering Uses, by ThorntonC. Fry, (D. Van Nostrand and Co., Inc., 1928).[3] The Hydraulics of Water Closet Bowl.~ and Flushing

Devices, by Thomas R. Camp. associate professorof Sanitary Engineering, Massachusetts Instituteof Technology. Published in mimeographedform in 1936 by the Massachusetts State Asso-ciatiou of Nlaster Plumbers.[4J G. E. Golden, Research Associate at the National

Bureau of Standards for the Plumbing Manu-facturers Research Associateship. (Data un-published.)[5] Manual of Procedure for the Mechanical Section,Public Works Branch, Procuremcnt Division,Treasury Department (Sept. 1935).[6] Interior Water Supply Piping for ResidcntialBuildings, Bulletin of the University of Wiscon-sin, Engineering Expcriment Station Series, No.77.WASHINGTON, August 30, 1940.

[21 ]


24/26

BUILDING MATERIALS AND STRUCTURES REPORTSOn request, the Superintendent of Documents, U. S. Government Printing Office, Washington,D. C., will place your name on a special mailing list to receive notices of new reports in thisseries as soon as they are issued. There will be no charge for receiving such notices.An alternative method is to deposit with the Superintendent of Doouments the sum of $5.00,with the request that the reports be sent to you as soon as issued, an d that the cost thereof becharged against your deposit. This will provide for the mailing of the publications, withoutdelay. You will be notified when the amount of yotir deposit has become exhausted.I f 100 copies or more of any paper are ordered at one time, a discount of 25 percent is allowed.Send all orders and remittances to the Superintendent of Documents, U. S. Government PrintingOffice, Washington, D. C.

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,BMS32 Struotural Properties of Two Briok-Conor'ete-Blook'Wall Constructions and a Concrete , . Block Wall Construction S p o n s o r ~ d by the Nation8J. Concrete Masonry Association_ IO ,BMS33 P I ~ ~ i c C a l k i n g Materiale -- --- -- _ _-- _-- _-- _ -- _---- __ -- - r - - - IOBMS34 Performance Test of Floor Coverings for Use In Low-Cost Rousing;PartL L._ IOBMS35 Stabilityof'Sheathing Papers as Determined byAccelerated .i\.ging "__ " 1O. BMS36" StrlicturllJProperties of Wood-Frame Wall, Partition,Floor, anci:R6bi Gonstruotions

/ ' 'with "Red Stripe" Lath Sponsored by the Western Paper and Mfi:riufaoturing Co __ 1O:)'BMS37 Structural Properties of "Palisade Romes" Constrtictiops J>r Walls, Partitions,' and

, Floorif Sponsbred by Palisade Roines._ - - -- --'- -- -- - --.:.. _- -='== : . ' : ' ~ ' "___ lOtaMS38 ,StructUral Pr()perties of Two "Dunstone" W a l l C 6 n s ~ r u c t l o i l $ _ S p o D . s O i e d by tpe W. E.. Du:t1ll Manufacturing - - __ - - ~ . : _ - ..,_ " _ ~ _ ~ __ ~ ' : ' ~ _ ~ _ _ _ ___ __ 1OBMS39 Structural Properties 'Of 'a Wall ConstrUction of "Pfeifer Units" Sponeored by the Wis1_,.- '. . consin Units co . - .: _.---'.:.=---'..,-L IOBMS40; Structural P r b p e r t i e s ~ ( ) f a '!all Construction o!-"Kilap Concrete 'YaUUnlts""Sponsored. by Knap America Inc - __ - .- - - -. __ - -. -,- ._,--- _,- IO

BMS41 EffeetofHeating and Cooling on the Permeability ofMasonryW&lls __ _-=-.:.. _______ 1O. aMS42 Structural Properties f'fWood_Frltme WaIl.ll.nd Partition Constructiorls with"'Celotex", ." In,sulating Boards Sponsored by the Celotex Corporatiollc':".:.,: - - -' _-= _, ________ lOtBMS43' Perfortnance Test of'Floor Covenilgsfor Use in Low-Cost HOUsing:Paft2 = _ ~ , IO'BMS44 Suiface T r e a t m e n ~ of Steel Prior,to p a i n t i n g _ T ~ ~ ' ' : ~ _ ' ' : S - ' ~ - ' ~ ~ ~ _ : : _ . c __ . - ~ ' - - lOtBMS45 Air Infiltratio,n Through-WindOlvs. " -,, c-'- __ __ ".,,_-_ " ' " _ , ; " ' ; ~ - ' : r ~ ~ __ __ IO" BMS46 S t i l u c ~ u r a J . Properties of. S c o t - B j 1 t ; ' P r e f i d ) r i c a . t e d $ h e e t - ' S ~ k e Q ~ t W t i p I l s ' 'fO'r. ~ l l s ,

_ F I ( ) o r s " a ~ d Roofs ~ ~ o n $ o r e d b y the. 1 o b e - W e r n i c k e , q q ~ ~ . - : : ~ ' . , , ~ : ; ~ : ; , ,,_,{... __ .- __ = IOBMS47 .Structural Properties of P r e ~ 1 > i i c a t e d W 0 6 d ' - F r a m e , G o p a t i ' U C : t i o : r u ( f 9 r "Wltlli!'Pa;rti. . tiona' n ~ F l o Q r s S t > o n s o r ~ d by A m e r i c a n I - I o u s e s , ) I ' r i c : " ; f , - , ~ ~ : : : " 2 ~ > ~ ' - ; ~ \ _ ~ ~ ' ~ : ' '- 1O ,BMS48Strnct\lral Properties of "PreciSion-Built" FrameVlirtitiohConstfuctioi::ui .;..~ . ~ .. : , . = ~ ~ ! ; i l ; g ; t = : ~ i ~ c i ~ ~ ~ ; ~ ~ : E ; : : : : : : : . : ~

B ~ $ 5 1 S t r , u c t ~ r " ' l P r ~ e t t i e B ? f . ':Tilecre'te Type A" 'Floor o n s t 1 ' U ~ ~ i Q I i g ~ l l O r e d by the'BMS52" E f f e c ; 1 ~ r b : : t ; g O i : ~ ~ = ~ ~ ~ 6 ~ " ' S ; J ; ; ; ; e ~ ~ C d ~ 6 ~ ~ ~ 1 = = = = = = t = = = ; = = : : ~ ' : = , = ~ C ~ = = ~ = = = = = BMS53 " Struc tural PrOPerties of a Masonry J\tali ,Construction of,"'M!iniock\[)ry.W'all Brick", ., ..' . ' . '.' S p 9 ~ o r e d by the Mlinlock E n g i n e e r i n F t 9 o ~ - . ... - , - ~ - ' - : : ' - i ~ " ' : : ' ; : ' : ~ ' ~ ' ~ : ' ; ~ - - ~ " ' - w _ . . , - = - _ 1OBMS5'4, Ef(ect of Soot on the Ra.tiJ:igofan,Oil-Fired Re atingBo iler _... ... w_,:... ; _ , . : . ~ = ~ ~ lc-'_ _ _ _ _ 1O. :.BMS55, Effect o f W e t i t i n g , ~ n d Drying On the :Permeability O ( M 8 S o n r Y W ~ n . s ~ ~ . : , , ; ~ _ , ~ ~ : , , _ = _ ~ " ~ = iO

j . c ! ~ m f I ~ g ~ t ~ I ~ ; ~ i 1 j l ~ ~ ~ ~ ~ ~ . B M ~ 6 1 S t i ' l i . e t . u r i I P r 6 p ~ r t i e ! l 0 f . Two Nonreiil1orceCl: M o n o l i t h i c c 6 I l ( J j : ~ t e W i t i i ' Q g n s t r i l e t i o n s c _ : 1 0

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