PUBLISHED BY THE NATIONAL ENVIRONMENTAL SERVICES CENTER

FundamentalsBy Zane Satterfield, of P.Hydraulics: E., NESC Engineering Scientist

Summary Hydraulics is the branch of engineering that focuses on the practical problems of collecting, storing, measuring, transporting, controlling, and using water and other . This Tech Brief is the first of two that will discuss some fundamental hydraulic problems and will focus primarily on pressure. The second will discuss flow.

Why is understanding hydraulics important? cubic (62.4 lb/ft3); so, one (1ft x 1ft x 1ft) of water weighs 62.4 lbs. There are 7.48 in The science of hydraulics is as old as civilization itself. a cubic foot, with each weighing approximately For centuries, engineers have succeeded in making water 8.34 pounds, so 7.48 gal x 8.34 lbs/gal = 62.4 pounds. flow from one place to another with as few hitches as possible. When problems do occur, they are usually In the metric system, the term for weight (force due related to the hydraulics involved in pipe flow. to gravity) is called a (N), and the unit weight of water is 9,800 Newtons per cubic meter (9,800 Liquids in motion produce forces and pressure whenever N/m3). More appropriately, this is expressed as 9.8 the velocity, flow direction, or elevation changes. kilonewtons per cubic meter (9.8 kN/m3), where the Knowing pipe pressure and flow at certain points along prefix kilo stands for 1,000. the pipe’s path can help determine pipe size and capac- ity. It also can help in determining what pipe material Other important design information: would work best in given situations. Further, having an One per square (lbs/in2 or psi) is approx- understanding of hydraulics can help system managers imately equal to 2.31 feet of water height (column of decide if pressure reducers or pumps are necessary to water) no matter how big around or square the transport water in an efficient manner. Most small water column is. One foot of water height is approximately and wastewater systems do not have an engineer on equal to 0.434 psi. staff, or even one they can consult, who might be able to answer simple or basic questions about hydraulics. And the cost of engineering advice can quickly add up. Pressure Because many small systems are on tight budgets, Water or wastewater exerts force and pressure understanding hydraulics can save money. against the walls of its container, whether it is stored in a tank or flowing in a pipe. But there is a differ- Units and Variables ence between force and pressure, although they are closely related. Specifically, pressure is defined as First of all, understanding that water has a unit weight force per unit area. In U.S. units, pressure is usually is important. System designers need this information to expressed in pounds per square inch (lb/in2 or psi). calculate other variables. The physical and hydraulic In SI metric units, pressure is expressed in Newtons behavior of wastewater is so similar to that of clean per square meter (N/m2). For convenience, the unit water that there is generally no difference in the design N/m2 is called a (Pa). Since a pressure of 1 Pa or analysis of systems involving these two liquids. For is a relatively small pressure (1 Pa = 0.000145 psi), the practical purposes, water and wastewater are considered term kilopascal (kPa) will be used in most practical to be incompressible liquids because their volume does hydraulics applications. 1 kPa = 1000 Pa = 0.145 psi. not change significantly with changing pressure. Water or wastewater has a unit weight of 62.4 pounds per In this equation, pressure can be expressed as: P = F/A Where P = pressure Download all of our F = force at A = area over which the force is distributed wwwTech.nesc.wvu.edu/techbrief Briefs .cfm DWFSOM147 two hydrostatic pressureatpointsB, C, Dareequivalent. Likewise, the these pointsareatthesamedepthinwater. The pressureatpointAequalstheE,since Figure 1 PAGE OF FOUR W fr at thesameelevations— thatpressure expresses lar upgrade andfindthatthe oldertankmaybe whentheyneedto this circumstance tered height. Manywatersystems mayhaveencoun- thesame volumesbutare that havedifferent 1showstwostoragetankssideby Figure asopposed toabsolutepressure. pressure pressure point. Thisapplicationisr orstarting reference tobeazero is considered sur cal applications,however, atmosphericpres- 14.7psior101kPa.Inpracti- approximately atsealevelis Atmosphericpressure sure. pres- iscalledatmosphericorbarometric sure because oftheweightairabove.Thispres- Pr equalszero. atthewater’ssurface Pressure atthesame elevation. faces inbothtanksare zontal pipeshowninFigur Consider thetwotanksconnectedbyahori- hydr The pressure waterexertsiscalled The pressure Hydrostatic Pressure AK1TANK2 TANK 1 ater Surface om alar essure also exists at the free surface alsoexistsatthefree essure ger thanthenewerone.This figur B A B AE 4. Pressure atanypointinthewateracts Pressure 4. 3. to proportion indirect increases Pressure 2. dependsonlyonthedepthof Pressure 1. e isnotusedforhydrauliccalculationsand ostatic pr all directions atthesamemagnitude. all directions same depthorelevation. atthe is thesameatallpointsthatare Pr the depthofwater area). the watersurface water abovethepointinquestion(noton essur . Theseprinciplesalwaysapplyto ger diameter (mor e inacontinuousvolumeofwater essure: Z ero GagePressure Connecting Pipe C C . eferr e water storage) to a e waterstorage) to e 1.Thewatersur ed toasgauge T D E D e hydrostatic c h e

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• Fundamentals ofHydraulics: Pressure - and and D C B points BandD. as aboveit,itstillhasthesamepressure water directly though pointCintheconnectingpipedoesnothave ofthewater. area not onthevolumeorsurface Even depends onlyontheheightofwaterabovepointsand pressure 1.Hydrostatic thanTank 2isnarrower Tank that atpointA.Notethatitmakesnodifference sure atpointEisthesameaspres- point A,thepressure as point Eisatthesamedepthbelowwatersurface 2.Since 1,considerpointEinTank Again, inFigure tothedepth. proportion variesindirect because pressure atpointA at pointBwouldbeexactlytwicethepressure exactlytwiceasdeeppointA,thegaugepressure were atpointA.Inapplication,ifB than thepressure atpointBnearthebottomoftankisgreater pressure smaller diameterstoragetank—isstillthesame.The meter (m)depthofwateronanar Wher P =0.43xh ally writtenas: So a1-ftdepthofwateronanar in atthebottomwouldbeP=62.4lbs/144 the pressure In customaryU.S.units,1ft Calculating Pressure the tank overflow for maximumwaterheight. the tankoverflow of maybe topographicmaps withsomemeasurements as-builtdrawingsor the elevationscanbeobtained from the operatorhasworked on thispipeinthepast.Usually For theaboveexample, diameterisknownbecause Solution and D. Calculate thehydr classifiedandsavemoneyinthelongrun. that iscorrectly system willaidinselectingpipematerial,suchasPVC, atthispointinthedistribution Knowing thepressure isnownecessary. something otherthanductileiron with pipe the of two or joint an entire option and replacing Patching thepipewithbandclampsmaynolonger bean leak atpointD,thelowestelevation. be arecurrent A typicalsituationforasmallwatersystemoperatormight 2. pipelineasshowninFigure and connectingductileiron A smallwatersystemhasanelevatedstoragetank Example 1 inkPaorkN/m pressure P=hydrostatic Where P =9.8xh This canbewrittenas: In SI-metricunits,1m a pressure of9.8kN/m a pressure 2 = 0.43psiperfootofwater(lbs/in e P =hydr 9.8 kPaor(kN/m inmeters(m) surface h =waterdepthfrom 0.43 psi/ftor(lbs/in h =waterdepthfr ostatic pr ostatic pr 3 2 2 essur of waterweighs9.8kN.Soa1 , Winter 2010,Vol., Winter 9,Issue4 om sur )/m or usuallywrittenas9.8kPa. 2 essur )/ft 3 e inpsi(lbs/in of waterweighs62.4lbs. face inft ea of1ft es atpointsA,B,C, ea of1m 2 )/ft). Thisisusu- 2 , or144in 2 2 would have ) 2 2 , Point A: The depth of water above point A in the tank is In this example, a 6-inch main provides the equal to the difference in elevation between the maximum service line. The pressure at the water meter water surface and the tank bottom, or 2000 ft – 1,950 ft well or pit is 48 psi. The house sets on a hill, = 50 ft. using the above U. S. equation for calculating and, according to the topographic maps, the pressure we get: meter is at elevation 350 feet, and the house is set at elevation of 430 feet. The elevation dif- P = 0.43 x h ference is the problem—not the service line P = 0.43 psi/ft x 50 ft that winds back and forth up the hill, despite 2 P = 21.5 psi or lbs/in the pressure losses due to friction in small Point B: the total depth of water above point B is diameter service lines (minimal for our con- 2,000 ft – 1,900 ft = 100 ft. The pressure at point B is: cerns in this case). P = 0.43 x h Calculate the pressure drop from the meter to P = 0.43 psi/ft x 100 ft the house location: 2 P = 43 psi or lbs/in Meter elevation is 350 feet and house Point C: The pressure at point C is equal to the pressure elevation is 430 feet at point B because these points are at the same elevation. 350 ft – 430 ft = h Pressure at C = Pressure at B = 43 psi –80 ft = h Point D: The total depth of water above point D is Using the pressure equation: 2,000 ft – 1,600 ft = 400 ft. The pressure is: P = 0.43 x h P = 0.43 x h P = 0.43 x –80 ft P = 0.43 psi/ft x 400 ft P = –34.4 psi of pressure drop 2 P = 172 psi or lbs/in In this problem, the house has a bathroom on The pressure is 172 psi (this would be the maximum work- the second floor. Estimate another 10 feet of ing pressure at Point D) so the pipe class or pressure rating elevation to the second floor of the house 430 would have to be able to handle a pressure of 172 psi. ft (elevation at first floor) – 440 ft (elevation at second floor) = –10 ft. Figure 2 So there is an added pressure drop to the Illustration for Example 1. second floor of: Elevation 2000 ft — max water height P = 0.43 x –10 ft P = –4.3 psi additional pressure drop A Elevation 1,950 ft — bottom of water in elevated tank Total pressure drop of –34.4 psi + –4.3 psi = –38.7 psi. Water Storage Tower So the pressure at the second floor of the house is: Ground Surface 48 psi at the meter – 38.7 psi pressure drop = 9.3 psi Closed Valve Water Main B Elevation Whether required or not, it may be good cus- C 1,900 ft tomer relations to tell customers that they will Elevation have low-water pressure on the second floor. A 1,900 ft low-pressure waiver agreement or a long-serv- ice line agreement is an option. Also explain to customers that they can install small booster Elevation 1,600 ft D pumps that they own and maintain—not the water system—to increase pressure. P Example 2 A Example 3 G E

Another example an operator might encounter is provid-

An inverse of the situation in example 2 might

ing a water-tap for a customer with a house at the top of be a customer with a house in the valley with O three F a hill. The tap and meter are at the bottom of the hill. F an elevation below 139 feet from the connect- O U

Most state regulatory agencies or public service commis- ing point at the main at the property line. The R sions require a minimum pressure of approximately 30 pressure reading at the meter reads 106 psi. psi at the meter at the property line.

NATIONAL ENVIRONMENTAL SERVICES CENTER four

PAGE OF FOUR hr h=theheightofwaterinmeters where h =P/9.8 Or theequationcanbesimplifiedto: In someinstances,thepr of waterinstead172psi. headatpointDwouldbe400ft the pressure For example,inthefirstexample(example1) in question. or equivalentheightofwaterabovethepoint head,andistheactual This iscalledpressure ofpsiorkPa. meters orfeet,insteadofterms oftheheightacolumnwater,terms in in pressure It isoftenconvenienttoexpress Pressure Head maybenecessary. agreement waiver Ahigh-pressure tomers responsibility). aswellatthehouse(cus- responsibility) installed at/withthemeter(watersystems needstobe regulator house. Apressure plumbing andeventheservicelineinto forthehouse This istoomuchpressure = 165.77psi of106psi+59.77 Giving atotalpressure Neglect thefrictionlossesinserviceline. beatthehouse? What wouldthepressure hr h=heightofwaterinfeet where equation,weget: the pressure a hillinelevation.Rearrangingtheter willpushthewaterup how highthepressure uating waterdistributionsystemstodetermine instead. Thisisdone,forexample,wheneval- head touseunitsofpressure would prefer psi orkPamaybeknownbutthesystem Or theequationcanbesimplified to: Published byThe National Envir The 0.1 comes from 1dividedby9.8 The 0.1comesfrom h =0.1xP For theSIunits dividing1by0.43 the 2.3comesfrom h =2.3xP P = 59.77 psi increase in pressure inpressure P =59.77psiincrease P =0.43x139ft P =0.43xh equation: Using thepressure h =P/0.43 For U.S.units P = hydrostatic pressure inkPaorkN/m pressure P =hydrostatic 9.8 kPaor(kN/m P = hydrostatic pressure inpsi(lbs/in pressure P =hydrostatic 2 )/m essur onmental Services CenteratW e inter T e c h

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• Fundamentals ofHydraulics: Pressure 2 2 ) est V Simon, Andrew L.1986. Simon, Andrew users getthemostoutoftheseprograms. input. Knowingthefundamentalsofhydraulicscanhelp thatis they generateisonlyasgoodtheinformation assist inthehydraulicsofsystemdesign.However, thedata availableto are programs andspreadsheet Several software allkeyingettingwatertosystemcustomers. tion are functioningsystem.Pipesize,tankstorage,andloca- properly isthefirststepinhavinga orpressure las tocalculateforces formu- collection ordistributionsystems.Knowingthecorrect Hydraulics canbecomplexwhendesigningoranalyzingentire Closing due tofrictionlossesinthesmallerdiameterpipe. drops diameter pipetoasmallerthepressure alarger anything, whenthewaterisflowing(inmotion)from goesfaster. thewaterorfluidmerely the pipesizedecreases If theflowrateofwater—meaningthatas ity, butwillreduce theveloc- pipediameterwillincrease Decreasing everywhere. ofpipediameter,that, regardless isfelt watersystempressure system.Thismeans theentire isfeltthroughout system atrest appliedtoafluid Pascal's Principlestatesthatapressure withchangingpipediameter. doesnotincrease Pressure the pipesizedecreases. when increases A commonmisconceptionisthatpressure Hwang, NedH.C.andRobertJ.Houghtalen.1996. References: Nathanson, JerryA.1997. Lindeburg, MichaelR.1999. and emailto for anominalcostbycalling(800)624-8301or sending T For acompletelistof at Second Edition.NewJersey:Prentice-Hall. W Publications. John Wiley andSons. Fundamentals ofHydraulicEngineeringSystems for thePEExam Edition. NewJersey:Pr ir ech Briefs ginia University,P ater Supply,W www.nesc.wvu.edu/techbrief.cfm NESC Engineer professional engineerand water operator whopreviously for fr worked forworked the West Bureau ofPublicVirginia Health, [email protected]. .O. Box 6064, Morgantown, WV 26506-6064 .O. Box6064,Morgantown, Environmental Division. Engineering . SeventhEdition.Belmont,CA:Professional aste ManagementandPollutionContr ee fr ing Scien om thesiteoryoumay T Hydraulics entice-Hall. , Winter 2010,Vol., Winter 9,Issue4 ech Briefs Basic Environmental Technology, Civil EngineeringReference Manual An EqualOpportunity/AffirmativeActionInstitution tist Z ane S . Third edition.NewYork:. Third , visittheNESCwebsite . You maydownload atterfield is alic , Third der them ensed ol .