FIRE PROTECTION HYDRAULICS

Transcription

1 GAP A Puliction of Glol Asset Protection Services LLC FIRE PROTECTION HYDRAULICS INTRODUCTION Fluid mechnics is concerned with the forces nd motions ssocited with gses nd liquids. Hydrulics, distinct rnch of fluid mechnics, concerns itself with the study of the flow of wter. Mny of the prticulrs tht re essentil to ccurte fluid mechnics mesurements re unnecessry for the ccurcy of fire protection mesuring devices. There re mny equtions tht del with pressure loss in piping systems. This section will concentrte the theories nd methods from the work of Bernoulli nd Hzen/Willims. Equtions derived or used, will contin vriles tht cn esily e red from tles, or mesured with conventionl, portle, wter testing equipment such s pressure guges nd pitot tues. Sprinkler system hydrulic clcultions re covered in GAP This guide will: Discuss sic hydrulic theory. Derive pertinent equtions. Present pplicle chrts nd tles. Physicl Properties Of Wter The properties of wter re often used s the sis for compring other liquids. Density of wter ( ρ ) is defined s mss per unit volume. ρ = Mss Volume At tmospheric conditions the density of wter is 6.4 ls mss/ft 3 (1000 kg/m 3 ) nd is considered constnt for fire hydrulics purposes. Specific grvity (s) is the rtio of the density of liquid to the density of wter t specific temperture nd pressure, usully 60 F (16 C) t one tmosphere pressure (1 r). ρ s = ρ Specific grvity vries with temperture; however, for liquids this chnge is only slight. liquid wter Viscosity is mesure of resistnce to flow. The viscosity of wter decreses with n increse in temperture, however, the chnges experienced in fire protection systems re so slight they re ignored in fire protection hydrulics. The specific weight ( ω ) is defined s weight per unit volume. (1) () 100 Constitution Plz, Hrtford, Connecticut Copyright 015, Glol Asset Protection Services LLC Glol Asset Protection Services LLC nd its ffilited orgniztions provide loss prevention surveys nd other risk mngement, usiness continuity nd fcility sset mngement services. Unless otherwise stted in writing, our personnel, pulictions, services, nd surveys do not ddress life sfety or third prty liility issues. The provision of ny service is not ment to imply tht every possile hzrd hs een identified t fcility or tht no other hzrds exist. Glol Asset Protection Services LLC nd its ffilited orgniztions do not ssume, nd shll hve no liility for the control, correction, continution or modifiction of ny existing conditions or opertions. We specificlly disclim ny wrrnty or representtion tht complince with ny dvice or recommendtion in ny document or other communiction will mke fcility or opertion sfe or helthful, or put it in complince with ny lw, rule or regultion. If there re ny questions concerning ny recommendtions, or if you hve lterntive solutions, plese contct us.

2 GAP Since force is expressed s: Weight ω = Volume F = m (4) (3) Then: m = l mss (lm) = ccelertion = 3. ft/s 1 lf = (1 lm) (3. ft/s ) Eqution (1) (3) nd (4) cn e used to derive the following: ω = 6.4 lf/ft 3 (9810 N/m 3 ) ω = ρ g (5) Pressure, expressed in terms of column of liquid, is the force per unit re t the se of the column. Asolute pressure is usully expressed with reference to locl tmospheric pressure. Guge pressure is the difference etween vlue nd locl tmospheric pressure. P = P + P (6) Asolute Gge Atmospheric t gge Unless otherwise indicted, ll pressures discussed will e guge pressure. A conversion fctor cn e derived from the density, which is quite useful in determining pressure chnges tht re due to corresponding differences in elevtion, such s pressures developed y grvity fed wter sources. P = Pressure ω = Specific weight s = Specific grvity (1.0 for wter) Z = Elevtion P = ω s Z (7) The pressure developed per unit of elevtion of wter cn e expressed s follows: English Units: P = Z (7E) Where P is expressed in psi nd Z is expressed in feet. SI Units: P = 9810 Z (P) or P = Z (7S) Where P is expressed in r nd Z is expressed in meters. A Puliction of Glol Asset Protection Services LLC

3 GAP Flow In Pipes The flow of wter in fire protection piping system cn normlly e chrcterized s stedy, one-dimensionl, nd incompressile. This mkes the ppliction of the sic physicl principles of conservtion of energy nd conservtion of mss esier to pply to flow conditions long pipe. The effects of vrious ostructions to flow cn then e determined. If wter ws not confined y pipes nd ws elevted ove n estlished dtum, the mximum potentil energy stored would depend on the weight of the wter nd the height to which it ws elevted. If llowed to fll freely, the potentil energy relesed would e converted to kinetic energy nd would depend on the velocity ttined y the wter, which is function of the height. However, if pipe ws used to convey the wter, some of the stored energy would pper s friction in the piping system. The lw of conservtion of mss sttes tht mtter cn neither e creted nor destroyed. In single entrnce single exit system, the mss tht enters t one point should e the sme s the mss tht exits t the other. Flow is mss per unit time, which cn e expressed in terms of three vriles: the density of the liquid, cross sectionl re of the conduit, nd the velocity of the liquid. Referring to Figure 1, the conservtion of mss cn e expressed mthemticlly s constnt flow t two points long the sme pipe segment. Q = ρ A V = ρ A V (8) Becuse of incompressiility, the density of wter does not chnge pprecily; therefore, density cn e cncelled out of ech side of the eqution. As result, t ny point in wter system the flow cn e expressed in terms of its cross sectionl re nd its velocity: Q = A V (9) Q = flow (usully ft 3 /s [m 3 /s]) V = velocity (usully ft/s [m/s]) A = flow re (usully ft [m ]) Figure 1. Typicl Pipe Between Two Points. For the ske of simplicity, most of the remining equtions will e shown without units until reduced to usle form. The lw of conservtion of energy sttes tht energy cn neither e creted nor destroyed. Therefore, the totl energy t one point in system is equl to tht of nother. 3 A Puliction of Glol Asset Protection Services LLC

4 GAP In 1738, Bernoulli formulted his theorem of conservtion of energy. It cn e pplied to simple pipe system y tking into ccount the vrious forms of energy tht exist in n idel frictionless model. Applying Bernoulli s Theorem to the piping system shown in Figure 1 results in the following: V g + P V + Z = ω g + P + Z ω (10) V = Velocity g = Grvittionl ccelertion P = Pressure ω = Specific weight Z = Elevtion Rerrnging nd comining like terms: V V g P P + + ω [ Z Z ] = 0 Ech term of this eqution is expressed s n elevtion. Multiplying ech term y ω results in ech term eing expressed s pressure: V ω V g + [ P P ] + [ ω ( Z Z) ] = 0 The first term of the eqution is the chnge in kinetic energy, which is due to the chnge in velocity tht results from the chnge in the cross sectionl re. This term is referred to s the chnge in Velocity Hed or Ρ. υ In uniform dimeter pipe with stedy flow, there is no chnge in the velocity etween entrnce nd exit points, so the Ρ υ term reduces to zero. Velocity pressure is usully not considered, since: The effect of one pipe size difference in dimeter is usully negligile. The procedure dds significnt mount of complexity to hydrulic clcultions. The overll effect of velocity pressure reduces the nticipted hydrulic demnd nd, therefore, is less conservtive. The second term of the eqution is the chnge in potentil energy. This is the norml pressure exerted ginst the side of the confining vessel with or without wter movement. This term is referred to s the chnge in Pressure Hed or Ρ. n The third term of the eqution is the potentil energy tht is due to chnge in elevtion. This term is referred to s the chnge in Elevtion Hed or P. Since the rel world is not frictionless, the friction is dded to the lgeric sum of the other energy terms: v n e e P + P + P + P = P (11) f t 4 A Puliction of Glol Asset Protection Services LLC

5 GAP Pf P t = Pressure due to friction losses. = The totl pressure chnge. In most discussions nd writings on hydrulics, the system losses in piping system re referred to s either mjor losses or minor losses. The mjor losses involve friction loss long pipe system. The minor losses include the losses through fittings tht re due to chnges in direction, nd losses which re due to sudden enlrgement nd contrctions, usully found t dischrge devices. These losses re ddressed lter in the section on friction loss. Flow Through An Orifice The eqution for flow through n orifice cn lso e determined y pplying Bernoulli s Theorem, eqution (10). Refer to Figure showing n open top continer with hole locted t the dtum tht psses through reference point. Figure. Flow From An Orifice. V g + P w + Z V = g + P w = Z Since the velocity t is pproximtely zero nd since there is no externl pressure other thn tmospheric cting on, the first two terms on the left side of the eqution cn e eliminted. There is no externl pressure other thn tmospheric cting on nd, since Z is zero, the second nd third terms on the right side of the eqution cn e eliminted. There is no piping nd, thus, no friction losses etween reference point nd reference point. The eqution cn e simplified to: Z V = g Solving for V : V = g Z Velocity t the orifice is shown in terms of elevtion nd the grvittionl constnt. See eqution (7). The elevtion cn e converted to pressure y dividing y w. Resulting in: V g P = w 0.5 (1) 5 A Puliction of Glol Asset Protection Services LLC

6 GAP By pplying conservtion of mss, modified eqution (9) cn e used which expresses the flow in terms of velocity. The modifiction consists of pplying dischrge coefficient C d to compenste for non-idel flow conditions t the orifice: Q = C AV (13) d The cross-sectionl re of the orifice cn e expressed s: D = internl orifice dimeter π D A = 4 Sustituting ll of the vriles in eqution (13): D Q = Cd π g P w All of the constnts cn e replced with single dimeter dependent constnt K: (14) (15) D g K = Cd π 4 w 0.5 Sustituting with the new constnt results in simplified eqution sed on pressure nd known K-fctor: Q = flow P = pressure K = orifice coefficient flow/pressure 0.5 Q = K P (16) This eqution is vlid for flow through n orifice such s hose nozzle, hydrnt, or sprinkler hed. It is lso vlid for n equivlent orifice t ny point in pipe system where the flow (Q) is ssumed to e flowing out of n orifice nd where the pressure (P) is the totl pressure of ll sources of energy pplied t the ssumed orifice. This could pply for portion of the system such s rnch line, the entire sprinkler system t the se of riser, or n entire wter supply eing dischrged from reservoir. A piping rrngement with single flow outlet cn lso e nlyzed using fictitious nozzle hving n orifice K-fctor sed on the ctul flow nd pressure. Identicl piping configurtions will result in the sme K-fctor, therefore, given K-fctor cn e used to represent piping configurtions with similr flow chrcteristics. If two or more flows re comined or split, then the K-fctor will chnge downstrem of the rnch point. 6 A Puliction of Glol Asset Protection Services LLC

7 GAP Description C d C c C v A Shrp edge B Round edge C Very short tue D Short tue E Short tue (rounded) F Reentrnt tue (thin) G Reentrnt tue H Underwriter s ply pipe Figure 3.Typicl Nozzle Coefficients The K-fctor for prticulr flow device, such s sprinkler hed or nozzle, cn e determined y tking pressure nd flow mesurements t the device in question. A sprinkler hed must e held in pipe fitting; thus, its specified K-fctor includes nominl 1 in. (5 mm) tee y convention. Another version of eqution (15) tht is useful when performing wter tests is shown elow. By knowing the dischrge coefficient of the dischrge device (see Figure 3), the center of strem pressure (pitot tue pressure reding), nd the dimeter of the flow opening, the resulting flow cn esily e determined. English Units: Q = 9.85 C D P (17E) d Q = flow (gpm) D = internl orifice dimeter (in.) P = pitot pressure (psi) SI Units: Q = C D P (17S) d Q = flow (L/min) D = internl orifice dimeter (mm) P = pitot pressure (r) When conducting wter mesurement tests, the pitot pressure reding is tken t the center of the strem where mximum velocity is present. By using nozzle with known dischrge coefficient, the mximum pressure reding t the center of the strem, nd eqution (17) (flow from n orifice), the dischrged flow cn e firly ccurtely determined. Flow results of this type re occsionlly put into tles where the flow cn e red s function of pressure redings. The Glol Asset Protection Services (GAPS) Hydrulic Clcultor is n exmple 7 A Puliction of Glol Asset Protection Services LLC

8 GAP of such device. The eqution is helpful in determining flow t pressures not included on the GAPS Hydrulic Clcultor. The dischrge coefficient C d is pplied to ccount for minor losses t the dischrge device. The significnce of this fctor increses s the disruption to the flow condition increses. The coefficient is normlly etween 0.54 nd Idel flow conditions re chieved if the coefficient reches unity. The dischrge coefficient is result of two minor losses cting on the flow. C c is the coefficient of contrction which corrects for the reduction in flow dimeter which occurs when wter psses through the orifice. C v is the coefficient of velocity nd is cused when wter flows through free dischrge opening. The coefficient of dischrge is the product or result of oth of these coefficients cting on the flow. The vlues of these necessry coefficients cn e found in Figure 3. Velocity Pressure C = C C (18) d c As stted erlier, velocity pressure is usully omitted from most sprinkler clcultions ecuse of loss of conservtism nd the complexity of clcultion method. However, when very ccurte results re required, such s fire pump cceptnce testing or performing hydrulic grdients, it is necessry to determine these quntities. Equtions for flow velocity nd velocity pressure cn e determined from previously derived equtions. Using eqution (1), the velocity pressure P v cn e solved for y rerrnging the eqution s follows: wv P v = g v English Units: Pv = V (19E) V = Velocity (ft/s) P = Pressure (psi) SI Units: Pv = V (19S) V = Velocity (m/s) P = Pressure (r) Using eqution (10) nd sustituting for flow re in term of pipe dimeter, it is lso possile to solve for velocity in terms of flow nd dimeter. English Units: V = Velocity (ft/s) Q = Flow (gpm) D = Internl pipe dimeter (in.) Q V = D (0E) 8 A Puliction of Glol Asset Protection Services LLC

9 GAP SI Units: V = Velocity (m/sec) Q = Flow (L/min) D = Internl pipe dimeter (mm) V 1. 1 Q = D (0S) Tking this one step further, the velocity pressure P v cn e shown in terms of flow nd internl pipe dimeter using equtions (19) nd (0): English Units: P v = Velocity pressure (psi) Q = Flow (gpm) D = Dimeter (in.) Q P v = 4 D (1E) SI Units: Pv= Q= Velocity pressure (r) Flow (L/min) D = Dimeter (mm). 5 Q P v = 4 D (1E) Friction Loss Losses which re due to friction re result of sher forces cting on the individul wter molecules within the pipe. At the pipe wll, sher forces lso ct etween the wter molecules nd the wll of the pipe. There is more resistnce ner the wll thn ner the center of the strem. This results in fster moving prticles of wter t the center of the strem s shown in Figure 4. The rougher the pipe surfce the more resistnce to flow. When very slow flow in piping segment or wter chnnel occurs, it is termed lminr flow. As velocity increses, rief trnsition stge occurs efore reching turulent flow. Most fire protection flow occurs in the turulent rnge. The pressure loss ( P f ), contins the losses cused y friction in pipe, vlves, fittings nd enlrgement or contrction devices. The gretest prt of this loss is ttriuted to friction in the pipe. The Drcy-Weisch friction loss eqution is commonly used in hydrulics. It is suitle for ll liquids where the viscosity is constnt. It is rther difficult to use in tht it involves complex set of vriles tht must e known or estimted. 9 A Puliction of Glol Asset Protection Services LLC

10 GAP Figure 4. Typicl Pipe Velocity Profile. The most commonly used friction loss eqution in fire protection hydrulics is tht empiriclly derived y Allen Hzen nd Grdner S. Willims in It is sed on dt collected over mny yers of wter mesurement. It involves vriles tht cn esily e mesured or estimted. The Hzen-Willims eqution is rrnged s follows: English Units: Fp = friction loss fctor (psi/ft) Q = flow (gpm) SI Units: D = internl dimeter (in.) C = roughness coefficient F p = friction loss (r/m) Q = flow (L/min) D = internl dimeter (mm) C = roughness coefficient 4. 5 Q F p = C D Q F p = C D (E) (S) It cn e seen from the previous equtions tht the mount of friction loss in segment of pipe depends on: The inside dimeter of the pipe. The length of the pipe. The mount of flow through the pipe. The roughness coefficient, C. The numer nd type of fittings. 10 A Puliction of Glol Asset Protection Services LLC

11 GAP The inside dimeter of the pipe is the externl dimeter minus twice the wll thickness. The lrger the internl dimeter, the less resistnce to flow nd, thus, less friction loss. Pipe lengths re usully mesured from the center of one fitting to the center of the next. The longer the pipe the greter the friction loss. The C-fctor or coefficient of friction is dependent on the condition of the pipe. If the pipe s internl surfce is rough when mnufctured or if it ecomes rough with ge, there is incresed resistnce to flow t the wll. C-fctors ecome smller s the flow condition worsens. Tle 1 shows the verge C-fctor for different pipe types nd ges. These fctors cn e used to correct friction loss tle figures from C-fctor of 100 to the C-fctor in question (refer to Tle 3). The correction fctors in Tle 1 re simply the rtio: C Fctor C for Friction Loss Tle Fctor Actul The losses in piping system lso depend on the numer nd type of pipe fittings used in the system. The fittings nd other devices in the pipe system cn e expressed in terms of n equivlent length of pipe of the sme dimeter, even though most of the pressure drop cross fitting is ttriuted to the turulence cused y chnge in the direction of the flowing wter. This is very simplistic pproch ut hs gined much support over the yers nd is now ingrined s the ccepted norm. The verge equivlent length of fittings is estlished y lortory testing. The totl equivlent length in segment of piping is the ctul length plus the sum of the equivlent lengths of the fittings. The loss due to friction cn e expressed y multiplying the equivlent length of pipe ( L eq ) etween two points y the friction loss fctor per foot of pipe ( ) F p p ( L eq) Tle shows equivlent length fctors for vrious size fittings. f 1.85 (3) P = F (4) TABLE 1 Typicl C-fctors Pipe type C-fctor Correction Fctor New steel pipe unlined 10 yers old unlined 15 yers old unlined 0 yers old unlined 30 yers old unlined 50 yers old unlined 75 yers old unlined Riveted steel Enmel-lined Brss copper Cement-lined Cement sestos Ruer lined hose Unlined linen hose A Puliction of Glol Asset Protection Services LLC

12 GAP TABLE Equivlent Lengths in Feet Bsed on C = 10 FITTING / SIZE Elow Long Turn Elow Side Tee Gte Vlve Swing Check Alrm Vlve Dry Pipe Vlve SI Units: 1 ft = m The loss through fitting is independent of C-fctor nd pipe schedule. Therefore, it is necessry to lter the figures in Tle so tht when the friction loss per foot is pplied to the fitting equivlent length, the net loss through the fitting does not chnge. The Fitting Length Correction Fctor cn e clculted y the following rtios: nd C (5) FctorTle 1.85 C Fctor Actul D (6) TleSchedule 4.87 D ActulPipeSchedule A convenient wy to use friction loss fctors is y selecting them from tles sed on flow, pipe size nd C-fctor. There re mny such pulished tles. They re nothing more thn the result of friction loss/ft s clculted using the Hzen/Willims eqution. An exmple of clculted results is shown in Tle 3. Tle 4 shows ctul inside pipe dimeters in inches for common pipe types used in sprinkler systems. Tle 5 shows ctul inside pipe dimeter for common pipe types mde in Frnce, Germny, nd Englnd. Exmining the Hzen-Willims eqution, we cn see tht friction loss cn e simplified to three vrile eqution: P f = Constnt Q 1.85 The constnt my s well e expressed in terms of K. Rerrnging the eqution to solve for Q results in the following: 0.54 Q = (7) K P f This eqution is vlid when the resulting pressure is dependent on friction loss rther thn flow through n orifice. It is importnt to emphsize tht the K-fctors in equtions (16) nd (7) re not equivlent. 1 A Puliction of Glol Asset Protection Services LLC

13 GAP TABLE 3 Friction Loss Tles in psi/ft Bsed on C = 100 Size gpm SI Units: 1 psi/ft = 0.61 r/m;1 gpm = 3.74 L/min 13 A Puliction of Glol Asset Protection Services LLC

14 GAP TABLE 4 Internl Dimeter In in. For Nominl Pipe Sizes In in. Size Cu L Steel Thin Cu K Cu M XL Berger CTS IPS Poly-B SI Units: 1 in. = 5.4 mm TABLE 5 Internl Dimeter in mm for Nominl Metric Pipe Sizes in mm Size Frnce Germny Englnd SI Units: 1 in. = 5.4 mm Use Of Semi-Log Grph Pper Since pressure loss ecuse of friction vries directly with flow rised to the 1.85 power, flow nd pressure cn esily e plotted on specil grph pper where the verticl xis is pressure nd the horizontl xis is flow rised to the exponent The unique thing out the otined curves is tht the plotted results re stright lines llowing for results to e extrpolted eyond the vlues exmined. In order to chieve the est ccurcy in line drwing, the flow cpcity should e s fr out on the horizontl xis s prcticle. Generlly the higher the flow cpcity the more ccurte the results. Semi-log grph pper is quite useful for plotting wter supply results, showing friction loss curves for prticulr sized pipe, plotting sprinkler system demnd curves, nd plotting the hed pressure t the most remote sprinkler hed in the system. Wter supply curves cn e plotted from wter test dt y knowing two points. The sttic pressure is the pressure ville with no wter flowing. The residul pressure is the resulting pressure with 14 A Puliction of Glol Asset Protection Services LLC

15 GAP known quntity of wter flowing. These two points re plotted; then they re connected to form stright line. This line is clled the supply curve for the prticulr wter supply. Friction loss curves re determined y first ssuming flow nd clculting the friction loss for given length of pipe. Then the friction loss curve is drwn y plotting the pressure which is due to friction t zero flow nd zero pressure, nd the clculted pressure which is due to friction t the ssumed flow. For ny flow long the horizontl xis, the corresponding pressure loss cn e found from the curve. Friction loss curves cn lso e drwn for complex looped piping systems. See GAP Sprinkler system demnd curves for specific re of ppliction cn e plotted in the sme mnner. First, the demnd t the se of the sprinkler riser is clculted. At zero flow, certin mount of pressure is required ecuse of the elevtion of the most remote re. The totl elevtion chnge from the most remote sprinkler to the se of the riser is determined nd multiplied y psi/ft. The resulting pressure is plotted t zero flow to form one point nd the system demnd pressure nd flow is plotted to form the other point. The points re then connected to form stright line clled the demnd curve. This curve represents chnges in demnd for vriety of densities long the curve for specific re of ppliction. SUMMARY The two min equtions used in fire protection hydrulics re the orifice eqution (16) nd the Hzen/Willims eqution (7). Hydrulics is further simplified y putting these equtions into ccessile tles nd grphs. By using equtions with vriles tht cn e mesured y simple devices, such s pressure guges nd pitot tues, fire protection hydrulics hve een reduced to simple procedures. These procedures cn e used to predict the cceptility of wter sed fire protection, nlyze present nd future wter demnds, nlyze wter tests, confirm the design of sprinklers, nd multitude of other functions. This suject is further expnded in other. Section 1 dels with wter-sed protection. In prticulr, GAP dels exclusively with sprinkler system hydrulic clcultions. Section 14 involves wter supplies. The entire GAP grouping is concerned with the hydrulic nlysis of fire protection wter supplies. 15 A Puliction of Glol Asset Protection Services LLC