A Brief Study of Economic Penstock Design Citation Makosky, Frank Charles and Morrison, Lloyd Elverton (1921) A Brief Study of Economic Penstock Design. Bachelor's thesis, California Institute of Technology. doi:10.7907/62GY-YH58. https://resolver.caltech.edu/CaltechTHESIS:10022015-143246360 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: Civil Engineering Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: None, None Defense Date: 10 June 1921 Additional Information: Supplementary to Course 800, Department of Civil Engineering Record Number: CaltechTHESIS:10022015-143246360 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10022015-143246360 DOI: 10.7907/62GY-YH58 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9193 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 12 Jan 2016 23:25 Last Modified: 16 Aug 2023 22:08 Thesis Files Preview PDF - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

l. B~I 2? STlJDY OF ECON011.~I C PENSTOCK DESIGN Supplimentary to course Aco Department of Civil Engineering CA!.;lrFORNIA INSTI':'.'UT:S n;::i T::CHWHi)GY Pasadena California June 10, 1021 BY Fran..?.{ C. Makosky Lloyd ?: • !forris ·Jn 1. __ ....... .,.. ;.J1r :corm:.uc ·- .! - ,. -- By ~ ' Fr~n.lf C • Mako sl-:y Lloyd E. ~orrison I n order to eli rnin.. te cert; .:. in :A r e ·""'-: J..,.• - co m~-·l i ::: :.'. tl 'J:'.l~' -.Li. '";" ine..dvi sabl e 'bo iltvo"iv=e the following a ssumptions a nd b5<.s i s of l::ltucly were used. { l) The plant is to g per.::t te con.tinou;;,ly ·J./'..u.8.2 ~ ::''.lll lo <.:.d of 600 second feet brought in thru two penstocks. ( 2) The ve.i.lue of power is taken a s th.-.. t Th io b~sed v~ lue v~. luc o;.. t is estimated as .Scents per kilowatt hour. on value given by rnr. ·Heywoocl of Professor Sorenson. th E~ tb.: 0<. i t c~·.~'TJ .::.' u. Thi ~ v~luH iB :: .;c.i b:J n Co. ind advi se of Expressed ~s the ea.nnu-.1 v-.lue of a hor se-::i') v;er ths is ~ 654, assuming capit:l..liz.ation ??.t 8% • ( 3) The cost · of pipe is Pcents per pot»ad, rivetB and. ov erl •,ps bein5 o:ni tted. The formul a for the econorn i c d. i Ln0t 0; 1" of n. ::ienstock v;a s t he one derived by W.L.Butcher, in the 'I!r ~nsac tions of the A.S.C.Z . . Vo l.LI X The forrnu l ;;. 1 s b<::.D8d upon the fund-.mente:.l a ssurnption tha t of the pi pe line p lus the annuii?.l '-· ·1i nJ. l U.l!l . ~ . 1 c D.i ;;~ . ..::.conor11 v~lue of the po vwr lo..:J the cost ~,l--:..<:1 ; ·J.~ h . r. ----:.~4n 2? d '-' .,. _ ~ 3 4'l. b - fb er. == 11eG?,d 1 11 feet on sccti.or1 -:..1:~.c~,=-.:r C·o r~ Qi ~~ l l~~ t i../ . :. doll a r s per pound d =va lue or· of one cu.ft.per sec . with h e ~ d of one foot f == tota l lo ps - b y fr1 ct.ion 1~1 tl: :: e-.. 'bov c; l:}'3 C ::.t ·.)'1. Q qaantity flowin g in s ecmnd f e et. 100 00 = t ensi l e stres o in s t ee l i n po unds n0r ~ ~ . l ~ . 4 00 = ~.- ·i z ht of· 0n <: . cT . f'':.. in pounds. b -.. C ' ) ;;,t. D f' '1l.'');; ln ener~y -., . This 2.ssuraes 2 t. ·3 noil ~ stess ::i.llo wP.ble of 1..0,CC'C'i;:l/in ': or ~~ n ' efficiency 0f riveted joints l0 :::5.;. 5;~ lR L1. o ni.(;:::C th~. t o ur C:i : ·.:1 .::- ~3::-J as obt~, ine d. by the for:m.J.1 <j 1Jc co:aprable with the p ipe thickness in which vre thous~;t t.0 'J ;_, P 7t;;~ o:::~:"Jet·:n c y') which is in accordance with : ·'.~ vl.~:_ -,, , .~; 1t practic~ s oodA w ev:or ~~ed us1n9 Butcher's forJiula thru~1 ::;coo instead of lC'OC0 for t h,~ .. .:,. i.:;.,.,,,.. u,.., .:u.L Th0 on ly change, of ~ course ,being the cons~ant. t ~:::~.::.11...: :tr. The .,, /". \ "'".',.. new constant obt~ined is .05R7 This for.:nulet t;ives Q.'~- di<:u'l eter ouch th~.t t '10 V'<.lue of the energ y lost in frictional resistance equals .4 the cost of th e ~')l ne, . v:hi ch Oi.cc~rdin:.:; to the original Oilssumption is the most economic diameter. No account is taken of the fact that steel :i l<:.tH i:; usu-..lly rolled to th r' nc:tr ·3 St 1/16" or that a factor for corrosion must be added. The corrosion factor is const-.nt the nearest 1/16'' v:ill not vary much. ~ncl the ch e n :::,1: t n However in order to m-.ke the cost C-) mparison equR.1 2/5 the exact di<:Jueter <' nd r.:~;;i.ct t'licknec s of pipe. for that d1.wneter and pressure must be used. The pens tock w&s di vitled into four eq.-.1 pa.rte .such that the h~~ ~rst was C'-2CO feet , the second 2nc-4o0 feet , etc. ·. ;c.r' tJ i:) _c1Jlr.: tee~ for t h e .1 e sections. ~i r: , ; 10 i t ~. r.., ·For comparison a "cut-•md -try" ,aethod w.,.s used !im the firs L. tv;o s e ctions. Curv·c B \':ere: nlott..f d i ::.w1eter of pipe as :;ibsciss9!, and the sum of the cost of the r t;1.ctual thickness of pipe was used <md a minL:iurn of 1/'.)':?" was ed for corrosion . The di w11et0rs RP. those obtained by the formla · v:i thin of the y>ipe. ·. ::i_ -:,11 ~J'!.0e <illlo~r - inc' i c>r t(?C. h y t ,h 0 '''1.r v::;s check '1. re;asonRbl e 1i. r:i1 t. Th~ :.:,1).'1dc~ n 3. DZ3 IGN OF AN :SCONO!.U C P::NSTOC ?: For KR-3 "2dfson Pl ant. AOO:?t. Hc;..d 6PP Sec. Ft . Two Pipes ~a xi~um Tet.bu la ted _results com:pu t e<.l by forn:m l ;;.. based upon the criterion that the cost of the pi~e plus the a nnual value of the energy lost must be .._ :11iruJ.um Section Diameter 9.4'=113" Thickness Cost of pipe ·of She ll in Without cori n che s ros~on f a ctor 75'.lb ~ ff . :~ 9100 '7/16 0-200 Cost of pipe with corrosion f .. ctor Ve lo c ity Fri e. in Ft/Se c .tion he-.d c == lOO 4.32 .15 9 $ 15290 5. 28 . 262 ~ 2 0 200 5 . -9 3 .3 3 5 ~ 6.45 . 4l 0 Diameter 8.5'=102" 20 0-·4 00 j 1 ·4 500 3/4 Diameter 8 - ~ 03 '=96" 400-6 0C l ~ l/16 $19850 Diameter '7.7':::Q3" 6 00-800 1-3/8 ,ll . 63560 Totals Total value of the enersy ~3500 + 63560= .4 CO 25600 $7o78c ·l .166 lost~ Which a8rees with the accept ed condition. 4. ;:._ = The head in feet on se ction under consider• tion = The cost of the pipe in dollars per pound d = The of the energy of one c11. ft. ]er sec. with ~ heaJ of one f oot f ~he total loss of friction in the above section > Q =The· qu«.ntity fl0wing in secon feet 1200 = The tensile stress in the st e e l in _!)o un U.;:, ~J e;> sq. in. This considers 75~ efficiency at the joint. 490 The weight of one cu.ft, of steel in pounds b = = Samp l e computation -4'/ir-~~~~--~~ Di a. = .0587Y3oo 3 x654 200Y.08-1.2 ~ .08 ~ Q.405 Ft.=l13I n. Thic¥_ness ::::: 113 x 63.4 x 200 2 ~ 16000 x .75 x 144 () Velocity = 300 + 9.4~ Y. 3.a416 4 Friction head from table = .409 = 7/16 Inches = 4.32 ft./sec. = .069/lOOft. Va lme of enersy lost .069 x 3.31 x .1134 ~ 654 x 300 = •ii 3540 ~ Cost of pipe line 113.44 x 3.14 ~ .438 144 ~ 490 Y. 231 x .98 - . ~ -- 97130 5. Soluttpn by c·1t and Try ~·.1 ethod. For comparison with results obtained by formul-. Head-- 0-200 Feet Di a . Thi c~-cn es s Co s t Vel. inchesCa l c. Ac t ua l of Jipe 110 113 114 116 1' 5 .375 •.409 .41£ .419 .4 al 6 .4375 t"' 9560 .4375 9820 .4375 9900 .500 11500 11400 .500 Friction Value of loss Energy lost 4.55 4.32 4.23 4.09 4.17 . .l8 .169.155 .143 .148 Cost of pi pe + Vlue of eneri;y loS:.. J 4020 3540 3430 3190 3300 ~ 1358'0 133 6 <; 1233 0 J_ 4 5 g , l4?00 Head---a c o-400 Feet gg 101 96 100 .717 .731 .694 .?24 • '7 5 ~14750 .813 16250 .75 14300 .75 14800 5.62 5.39 5.97 5 ';1 51 .2ge .271 .345 .284 $ 6600 6040 7 700 6330 "' 21350 2 3290 '°J 2 ~ 000 2 1130 The --.bove data has been plotted in curve form M-nd the i:lin ' 1rrnm points compar.ed with that obtained .by formula. Economic Di.uneters Comp:;,red Sec ti on By -Ii'ormui a 0-2 " 0 113" 114tt 200-400 102 11 1 0 0 11 By "Cut and T_ry" Curve Note: The apo foot sections were arbi-trarily chosen as representing an averae;e for -the cond itions of the probl8n. In 9!. more complete study the 800 foot head should be varini ng lene; thc of .Jection - nd compari s on mad e .