M5: Ditribution and Storage Reervoir, and Pu Robert Pitt Univerity of Alabaa and Shirley Clark Penn State - Harriburg Ditribution Reervoir Provide ervice torage to eet widely fluctuating deand ioed on yte. Accoodate fire-fighting and eergency requireent. Equalize oerating reure. Deign Period and Caacitie in Water-Suly Syte (Table. Chin 000) Tye of Ditribution and Service Reervoir Surface Reervoir at ground level large volue Standie cylindrical tank whoe torage volue include an uer ortion (ueful torage) uually le than 50 feet high Elevated Tank ued where there i not ufficient head fro a urface reervoir ut be ued to, but ued to allow gravity ditribution in ain yte
Location of Ditribution Reervoir Provide axiu benefit of head and reure (elevation high enough to develo adequate reure in yte) Near center of ue (decreae friction loe and therefore lo of head by reducing ditance to ue). Great enough elevation to develo adequate reure in yte May require ore than one in large etroolitan area Storage Tank Tye Deterining Required Storage Aount Function of caacity of ditribution network, location of ervice torage, and ue. To coute required equalizing or oerating torage, contruct a diagra of hourly rate of conution. Obtain hydrograh of hourly deand for axiu day (in Alabaa, thi would likely be either late ring or uer, and would include deand for lawn care, filling and/or aintaining wiing ool, outdoor recreation, etc.) Tabulate the hourly deand data for axiu day. Find required oerating torage uing a diagra, hydrograh, or calculated table.
Deterining Required Storage Aount: Exale Tie (hr) 0 Deand (g) 0 Tie (hr) 7 Deand (g),60 Tie (hr) Deand (g) 6,440 Tie (hr) 9 Deand (g) 9,,70 8 5,90 4 6,70 0 8,0,00 9 5,60 5 6,0 5,050,00 0 5,900 6 6,40,570 4,970 6,040 7 6,640,470 5,980 6,0 8 7,0 4,90 6,080 To calculate total volue required for torage Calculate hourly deand in gallon. Calculate cuulative hourly deand in gallon. Divide cuulative deand by 4 hour to get the average hourly uly needed. Calculate the urlu/deficit between the hourly uly and hourly deand for each hour. Su either the urlu or the deficit to deterine the required torage volue. REMEMBER: Thi reult ean that the tank i full when the urlu i greatet and ety when the deficit i greatet! It i filling when the loe of the u curve i greater than the loe of the deand curve and i etying when the loe of the deand curve i greater than the loe of the u curve. There i no exce for eergencie! Deterining Required Storage Aount: Exale Deterining Required Storage Aount: Exale Tie (hr) 0000-000 Deand (g),70 Deand (gal) 0,00 Cuulative Deand (gal) 0,00 Surlu/ Deficit* (gal) 56,008 Deficit (gal) urlu 000-000,00 6,000 56,00 60,08 urlu 000-000,00,00 77,400 65,008 urlu 000-0400,970 8,00 495,600 68,008 urlu 0400-0500,980 8,800 64,400 67,408 urlu 0500-0600,080 4,800 79,00 6,408 urlu * Surlu or deficit average hourly deand (86,08 gal) actual hourly deand
Deterining Required Storage Aount: Exale Tie (hr) 0600-0700 Deand (g),60 Deand (gal) 7,800 Cuulative Deand (gal) 957,000 Surlu/ Deficit (gal) 68,408 Deficit (gal) urlu 0700-0800 5,90,400,68,400-5,9-5,9 0800-0900 5,60 7,00,605,600-50,99-50,99 0900-000 5,900 54,000,959,600-67,79-67,79 000-00 6,040 6,400,,000-76,9-76,9 00-00 6,0 79,00,70,00-9,99-9,99 00-00 6,440 86,400,087,600-00,9-00,9 Tie (hr) 000-00 Deterining Required Storage Aount: Exale Deand (g) 5,050 Deand (gal) 0,000 Cuulative Deand (gal) 6,49,80 Surlu/ Deficit (gal) -6,79 Deficit (gal) -6,79 00-00,570 54,00 6,58,80,008 urlu 00-00,470 48,00 6,7,580 8,008 urlu 00-400,90 7,400 6,868,980 48,808 urlu Average* Storage Required 86,08 gallon,465,75 gallon (u of all deficit) lu additional for eergencie Su of deficit,465,75 * Average cuulative hourly deand / 4 hour 6,868,980 gal/4 hr 86,08 gal/hr Deterining Required Storage Aount: Exale Tie (hr) 00-400 Deand (g) 6,70 Deand (gal) 8,00 Cuulative Deand (gal),469,800 Surlu/ Deficit (gal) -95,99 Deficit (gal) -95,99 400-500 6,0 79,00,849,000-9,99-9,99 500-600 6,40 80,400 4,9,400-94,9-94,9 600-700 6,640 98,400 4,67,800 -,9 -,9 700-800 7,0 49,00 5,067,000-5,99-5,99 800-900 9, 559,980 5,66,980-7,77-7,77 900-000 8,0 499,00 6,6,80 -,99 -,99 Surlu/Deficit Chin 000, Figure.4 4
Exale.8 (Chin 000) A ervice reervoir i to be deigned for a water uly erving 50,000 eole with an average deand of 600 L/day/caita and a fire flow of 7,000 L/in. The required torage i the u of: () volue to uly the deand in exce of the axiu daily deand, () fire torage, and () eergency torage () The volue to uly the eak deand can be taken a 5% of the axiu daily deand. The axiu daily deand factor i.8 tie the average deand. The axiu daily flowrate i therefore: 8 5 ( 600 L / d / caita )( 50,000 eole ).7 x 0 L / day.7 x 0 day.8 / The correonding volue i therefore: 5 ( 0.5)(.7 x 0 / day) 67,500 V eak Exale.9 (Chin 000) A water uly yte deign i for an area where the iniu allowable reure in the ditribution yte i 00 kpa. The head lo between the low reure ervice location (having a ieline elevation of 5.40 ) and the location of the elevated torage tank wa deterined to be 0 during average daily deand condition. Under axiu hourly deand condition, the head lo i increaed to. Deterine the noral oerating range for the water tored in the elevated tank. Under average deand condition, the elevation (z o ) of the hydraulic grade line (HGL) at the reervoir location i: where γ z h in in 9.79 L 0 : 00 5.4 kn kpa / in z 0 z in γ h L Therefore, under average condition: 00kPa z 0 5.4 0 46. 0 9.79kN / () The fire flow of 7,000 L/in (0.6 /ec) ut be aintained for at leat 9 hour. The volue to uly the fire deand i therefore: ( 0.6 /ec)( 9hour)(,600ec/ hr) 0,00 V fire () The eergency torage can be taken a the average daily deand: 6 ( 50,000 eole )( 600L / day / caita ) 50x 0 L 50,000 V eer The required volue of the ervice reervoir i therefore: V V eak V fire V eer 67,500 0,00 50,000 7,600 Mot of the torage for thi exale i aociated with the eergency volue. Of coure, the ecific factor ut be choen in accordance with local regulation and olicy. and under axiu deand condition, the elevation of the HGL at the ervice reervoir, z, i: 00kPa z 5.4 48. 0 9.79kN / Therefore, the oerating range in the torage tank hould be between 46.0 and 48.0. 5
PUMPING Two tye of u coonly ued in water and ewage work: Centrifugal Pu tyical ue i to tranort water and ewage Dilaceent Pu tyical ue i to handle ludge in a treatent facility Scheatic of hydraulic grade line for a ued yte (Walki, et al. 00 figure.6) Pu election guideline (Chin 000 Table.) Pu effect on flow in ieline (Chin 000 Figure.6) 6
Sizing Pu To deterine the ize of the u, ut know the total dynaic head that the u i exected to rovide. Total Dynaic Head (TDH) conit of: the difference between the center line of the u and the height to which water ut be raied the difference between the uction ool elevation and center line of the u friction loe in the u and fitting velocity head Static v. Dynaic Head HGL hydraulic grade line TDH total dynaic head TSH total tatic head DDH dynaic dicharge head SSH tatic uction head DSH dynaic uction head SSL tatic uction lift DSL dynaic uction lift SDH tatic dicharge head Head Added by Pu (Total Dynaic Head) If the u ha been elected, Bernoulli Equation can be rearranged to olve for the head added by a u: P P V V h γ g A Z Z h f where h a head added by u (total dynaic head) P atoheric reure γ ecific weight of fluid V velocity Z elevation h f head lo in attached ie and fitting 7
Intallation of Pu into Water Suly Syte Exale of Head Added by Pu Exale: A u i being ued to deliver 5 g of hot water fro a tank through 50 feet of -inch diaeter ooth ie, exiting through a ½- inch nozzle 0 feet above the level of the tank. The head lo fro friction in the ie i 6.7 feet. The ecific weight of the hot water i 60.6 lb f /ft. Exale for Head Added by Pu Solve: P P V V A Z Z h f h γ g Set reference oint. Let oint be the water level in the tank. Let oint be the outlet of the nozzle. 8
Exale for Head Added by Pu Since both the end of the nozzle and the to of the tank are oen to the atohere, let P P 0 (gage reure). In a tank, the velocity i o all a to be negligible, o V 0. Calculate V. ft / ec 5g 449g V 57.4 A π ( 0.5 in) ft ft 4 44in / ec Calculation of TDH fro Pu Tet Data TDH H L H F H V Where H L total tatic head (difference between elevation of uing ource and oint of delivery) H F friction loe in u, ie and fitting H V velocity head due to uing Exale for Head Added by Pu Subtituting into Bernoulli Equation: h h h A A A P γ 60.6 87.9 P V 0 lbf / ft ft V g Z Z (57.4 ft / ec) (. ft / ec h 0 0 ft 0 ft 6.7 ft ) Calculation of TDH fro Pu Tet Data Subtituting ter fro Bernoulli Equation for Velocity Head: TDH H L H F V g Can lot yte head (total dynaic head) veru dicharge. TDH ay not be contant becaue of difference between elevation during uing (deleting uly and adding to torage). TDH alo ay not be contant becaue dicharge rate will affect friction loe (a well a the velocity head ter). 9 f
Pu efficiency curve (Net Poitive Suction Head) (Walki, et al. 00 figure.8) Effect of a change in deand on a contant-eed u in a cloed yte (Walki, et al. 00 figure 9. and table 9.) Syte oerating oint (Walki, et al. 00 figure.7) Exale. (Chin 000) Water i ued fro a lower reervoir to an uer reervoir through a ieline yte a hown below. The reervoir differ in elevation by 5. and the length of the teel ie (k 0.046) connecting the reervoir i.. The ie i 50 in diaeter and the erforance curve i given by: h 4.4 7.65 where h (the u head) i in eter and i in L/ 0
Oerating oint in ieline yte (Exale.) (Chin 000 Figure.7) In general, f i a function of both the Reynold nuber and the relative roughne. However, if fully turbulent, then the friction factor deend on the relative roughne according to: log ε and the relative roughne i given by: f.7 k relative roughne ε D k equivalent and roughne 0.046 for thi cae ε f f 0.046 50 log 0.09 0.00090 0.00090.7 7. Can alo ue the Moody diagra and read the friction factor by reading traight acro fro the roughne value if auing turbulent flow. Uing thi u, what flow do you exect in the ieline? If the otor on the u rotate at,400 r, calculate the ecific eed of the u in US Cutoary unit and tate the tye of u that hould be ued. Neglecting inor loe, the energy equation for the ieline yte i: fl h z 5. ga D fl ga D Where h i the head added by the u, f i the friction factor, L i the ie length, A i the cro-ectional area of the ie, and D i the diaeter of the ie. π 4 π 4 A D ( 0.05 ) 0.0096 Subtituting thi friction factor into the energy equation: h 5. 5. 5. 08500 0.09 fl ga D in unit 5. of / ; ( 0.09)(. ) ( / )( 0.0096 ) ( 0.05 ) 9.8 for in L / ec Cobining the yte curve and the u characteritic curve lead to: 5. 0.09.09L /ec 4.4 7.65 The next te i to verify if the flow in the ieline wa coletely turbulent
V.09x 0 / 0.556 A 0.0096 / ( 0.556 / )( 0.05 ) VD Re.78x 0 6 ν.00 ( x 0 / ) 4 The friction factor can now be re-calculated uing the Jain equation: f and f log ε.7 0.06 5.74 Re 0.9 log 0.00090.7 5.74 4 (.78x 0 ) 0.9 6.7 Therefore the original aroxiation of the friction factor (0.09) wa in error and the flow calculation need to be reeated, leading to:.09l / Table. Chin 000 Therefore, with a ecific eed of 59 and the low flowrate, the bet tye of u for thee condition i a centrifugal u. ( L / ) 5. h 4.4 7.65 4.4 7.65.09 In U.S. Cutoary unit: h.09l / 7. g 5. 50. ft ω,400r The ecific eed i given by: N ω h 0.75 0.5 ( 400 )( 7. ) 0.75 ( 50. ) 0.5 59 Cavitation If the abolute reure on the uction ide of a u fall below the aturation vaor reure of the fluid, the water will begin to vaorize, thi i called cavitation. Thi caue localized high velocity jet than can caue daage to the u through itting of the etal caing and ieller, reducing u efficiency and cauing exceive vibration. Thi ound like gravel going through a centrifugal u. Exale. (Chin 000) A u with a erforance curve of h -0.0 (h in, in L/) i above a water reervoir and u water at 4.5 L/ through a 0 diaeter ductile iron ie (k 0.6 ). If the length of the ieline i.5, calculate the cavitation araeter of the u. If the ecific eed of the u i 0.94, etiate the critical value of the cavitation araeter and the axiu height above the water urface of the reervoir that the u can be located. The cavitation araeter i defined by: σ Net head Potive added Suction by the Head u h NPSH Where NPSH (net oitive uction head) i: NPSH z h L γ o γ v
where : γ z o v atoheric reure, 0kPa ecific weight uction lift, of water, 9.79kN / aturated vaor reure of water at 0 o C,.4kPa The head lo can be etiated uing the Darcy-Weibach and inor lo coefficient. The flow rate and Reynold nuber are: 0.045 / V.0 / A π ( 0.0 ) 4 ( / )( 0.0 ) 5 VD Re x ν.00x 0 /.06 0 6 The Colebrook equation give a friction factor, f, of 0.057 uing thee value. If the ecific eed of the u i 0.94, then the critical cavitation araeter i etiated to be 0. (uing the to cale for SI unit). Since the calculated cavitation araeter wa.04, cavitation hould not be a roble. Chin 000, Figure.8 The head lo, h L in the ieline between the reervoir and the ection ide of the u i: ( 0.057 )(.5 ) ( 0.0 ) ( ) h fl V.0 0. L D g 9.8 86 ( / ) The NPSH can now be calculated: v 0kPa.4kPa NPSH o z h L 0.86 6. 9.79kN / 9.79kN / γ γ The head added by the u, h, can be calculated fro the u erforance curve and the given flow rate: ( L / ) h 0.0 0.0 4.5 6 The cavitation araeter of the u i therefore: σ NPSH h 6. 6.04 When cavitation i iinent, the cavitation araeter i equal to 0.0 and the reultant NPSH i: NPSH σ h ( 6 ). c 0.0. z h L γ o γ v The head loe between the u and reervoir i etiated a: f D h L ( z 0.5 ) V g ( 0.057)( z 0.5 ) ( ) h 6 0.0 9.8 L 0.57 0. z ( / )
Cobining the equation reult in:. γ o 0kPa 9.79kN / z z h L γ v ( 0.57 0.6z ).4kPa 9.79kN / 9.56.6z and olving for z : z 7. 49 Therefore, the u hould be located no higher than 7.49 (about 5 ft) above the water urface in the reervoir to revent cavitation (thi ut alway be le than at, or about ft). Calculation for Pu Efficiency η P P BHP *00 where η P u efficiency P fluid ower BHP brake horeower actually delivered to the u Calculation of the Theoretical Required Power of a Pu Power (h) γ(tdh)/550 Where dicharge (ft /ec) γ ecific weight of water (at ea level, 6.4 lb f /ft ) TDH total dynaic head (ft) 550 converion factor fro ft-lb f /ec to horeower Each u ha it own characteritic relative to ower requireent, efficient and head develoed a a function of flow rate. Thee are uually given on u curve for each u. In general, the efficient for centrifugal u i between 50 and 85%, with u efficiency generally increaing with the ize and caacity of the u. Pu Power and Efficiency Exale: A u i being ued to deliver 5 g of hot water fro a tank through 50 feet of -inch diaeter ooth ie, exiting through a ½-inch nozzle 0 feet above the level of the tank. The head lo fro friction in the ie i 6.7 feet. The ecific weight of the hot water i 60.6 lb f /ft. What i the ower delivered to the water by the u? If the efficiency i 60%, calculate the ower delivered to the u. 4
Pu Power and Efficiency γ ( TDH ) Power ( h ) 550 Convert the dicharge to cf. 449 g cf 5g 0.078 ft Pu Power and Efficiency Efficiency calculation: BHP BHP BHP P *00 η P (0.755h ) *00 60.6h /ec Pu Power and Efficiency Subtituting back into Power equation: TDH wa calculated to be 87.9 ft. Power Power Power ( ( ( h h h ) ) ) γ ( TDH 550 ) ( 0.078 ft /ec)( 6.4 lb / ft )( 87.9 ft) 550 ft lb 0.755h / h Generating Pu Curve Exale: The characteritic of a centrifugal u oerating at two different eed are lited below. Grah thee curve and connect the bet efficiency oint. Calculate the headdicharge value for an oerating eed of 450 r and lot the curve. Sketch the u oerating enveloe between 60 and 0 ercent of the bet efficiency oint. 5 f f
Generating Pu Curve Dicharge (g) 0 Seed 750 r Head (ft) 0 Efficiency (%) NA Dicharge 0 Seed 50 r Head (ft) 96 Efficiency (%) NA 500 6 6 000 9 65 500 0 8 500 89 77 000 9 85 000 8 8 00 8 86 00 77 84 500 76 85 500 70 8 4500 0 7 000 49 7 Pu in Serie and Parallel For erie oeration at a given caacity/dicharge, the total head equal the u of the head added by each u. For arallel oeration, the total dicharge i ultilied by the nuber of u for a given head. Generating Pu Curve Pu in erie (Chin 000 Figure.9) 6
Pu in arallel (Chin 000 Figure.0) Pu in Parallel: For a yte coniting of three u in arallel, one-third of the total flow,, goe through each u, and the head added by each u i the ae a the total head, H added by the u yte: H 0. and the characteritic curve of the u yte i therefore: H 0.0 Multile Pu Exale.4 (Chin 000) A u erforance curve i: h 0. What i the u erforance curve for a yte having three of thee u in erie and a yte having three of thee u in arallel Pu in Serie: For the u in erie, the ae flow () goe through each u and each u add one-third of the total head, H : H 0. The characteritic curve of the u yte i therefore: H 6 0. Variable Seed Pu Equation for Variable Seed Pu: H H P P N N N N N N where Pu dicharge H head (total dicharge/dynaic head) P ower inut N u eed (revolution/tie tyically in inute) 7 i i
Variable Seed Pu Pu Selection Exale A u tation i to be deigned for an ultiate caacity of 00 g at a total head of 80 ft. The reent requireent are that the tation deliver 750 g at a total head of 60 ft. One u will be required a a tandby. Pu Selection Exale 8
Pu Selection Exale Poibilitie are Pu A and/or Pu B. Pu Selection Exale One u will not uly the needed head at future condition. Pu B i better choice. Therefore, need to look at the three condition ioed on thi deign and ee if B can uly. Two u ut roduce 00 g at 80 ft TDH. One u ut roduce 600 g at 80 ft TDH. One u ut eet reent requireent of 750 g at 60 ft TDH. Pu Selection Exale Puing Station for Sewage Contant-eed u hould not be turned on and off too frequently ince thi can caue the to overheat. In all uing tation there ay be only two u, each of which ut be able to deliver the axiu anticiated flow. Lower flow accuulated in the wet well until a ufficient volue ha accuulated to run the u for hort eriod (the run tie). The wet well ay alo be ized to enure that the u will not tart ore often than a ecified tie eriod (the cycle tie). Exale 5- (McGhee 99) A all ubdiviion roduce an average watewater flow of 0,000 L/day. The iniu flow i etiated to be 5,000 L/day and the axiu 40,000 L/day. Uing a -inute running tie and a 5- inute cycle tie, deterine the deign caacity of each of two u and the required wet well volue. 9
5 in 0.5(40,000 L / day ) x 65L 440 in/ day out V V 0.5out 0.5out A iniu deth need to be aintained over the u uction. With an intake velocity of about 0.6 /ec ( ft/ec), a ubergence of about 00 ( ft) i needed. It i alo coon to rovide additional freeboard (about 600, or ft) above the axiu water level. Thi i a uitable wet well for thi exale: McGhee 99, Figure 5-. The required volue i deterined by the -inute running tie requireent in thi exale and will therefore be larger than 56L. V 5 in The cycle tie will be hortet when in i 0.5 out. Therefore, for a iniu 5 inute cycle tie: in V (40,000 L / day 5,000 L / day ) 56.5L 440 in/ day For a -inute running tie: V out in V in Suberible ewage u intallation: tc tr t f McGhee 99, Figure 5-4 and 5-5 Wet it-dry it ewage uing tation: V V out in in The total cycle tie i therefore: tf The filling tie with the u off i: tr The u running tie i the working volue of the wet well divided by the net dicharge, which i the uing rate inu the inflow: Each u ut be able to deliver the eak flow of 40,000 L/day. 0