Scholars' Mine Scholars' Mine

Bachelors Theses Student Theses and Dissertations

1911

Friction of air in small pipes and fittings Friction of air in small pipes and fittings

Bejamin H. Cody

Ernest J. Allen

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Part of the Mining Engineering Commons

Department: Mining Engineering Department: Mining Engineering

Recommended Citation Recommended Citation Cody, Bejamin H. and Allen, Ernest J., "Friction of air in small pipes and fittings" (1911). Bachelors Theses. 103. https://scholarsmine.mst.edu/bachelors_theses/103

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~. .~ .• .,.!II,. ... " ..... ,,\" •• oft, ~ •.... ~ .. : :: ::.-:...... " • .. • &.... : "',. :

,. ... ", .... .

T2..51

by

Een. H. Cody

.. Ill .........1Io ~ ....... ' .

.. • '" lit ~ '. ...

......... "' ..:'. :": :.~~_\••:,- .0"

.. '" .... ..

)~1·nel3t J. Allen

A

THE SIS

auurni t ted to tile facul tj' 0 f the

in partial ful fillment of tHe work required for tb.e

lJEGHEE OF

Rolla. Mo.

1911 •

Approved by .........----_._-_.........._,-~.~Professor of' Civil Engineert••

... : : .. : ..II., ,. 41

.....~ :: :"". :'::.i....:?,., .Iic.\.l'e

In tro cru.c tiOD - - -- - - - - - _ .. -_ .. :.~ - - -~.:+ ~::;~~~~~~_~F~ ~~ ._.::- :....: .. , .. ~ .....:: -.::-

Description of ApP~"il'n,tus ---·r.-·......... --:"..--·_--o:-- -.·..t-4.,: : =..:: :: ; . :~-" :".:"......::. «

1,,_e tl.UU. 0 f })ro ce eUUl'e i:n tfW'~ ~rJ~ lola 1:~.,:':''':-::'':'.. -~ 4

ForLiulae UbOll in CtHllpUt".I. 1. iOLlS --- ... -------- 5-10

lliscel1r:dleou..s notes ---------------------- 10-11

Tables No B.1 to 20

" Jt C:ind D.

Plates It 1 to 6

Llf3T O:p Il~1JSTHA'!IONS.

Plan of Apparatus ----------------------

Pl:l.Otogrc-q)li of Apph:catus ----------------

Pb.ge2-a

2-b

the

In;]'lIIlIGS.

.' '. h·:H::;::;( ;~..H:.~ ~ ..The wo rk 0 f Park an d I)e t e rso:h-' ·G·tJ":x.'.i Db 1909 10 . .at-:: -.::-... ... ., ".~ :,. . -- ~ : ~ "' .

MissOUI'i Sc:uool of l\,iines revef~1"e'd'-'t:lij"f~:!6~ {{J.\.~~"

r:lore dEt tn are needed con cernin6 t!H~ 10 ss of p reSBure

due to elbows and other fltti.n~s of pl.pes under three

incheo in size. According'~Jwe declded to undurtake

the continu.atio:n of t~J.eir work as a tllesis.

THe appar~.;,tus used v,ras practi.chl1y tlle nhliJe as

u13ed ..Ln the previous thes1.s Ci.nd W<::U:3 ciS follows:

One single sta~e air co~~res60r of 77 cu. ft. per

min. free air capacity and pressure up to 100 pounds,

gage at 110 revolutions per minute.

0 1" ...On e two stat;;;e comp re iJSj4 of lOU 01.4. ft. f;ree air

capacit.y and presBure UIJ to 1fJO pourHis bage at IlG

revaluti OL1 S .!J e:c rninute .

One air rece~ver of about three eu.ft. capacity.

One drum especi~il1;y constructed for Illeasurlng air

by ori fice according to tlle tie thod origin~ted by Prof.

Dudley at 1'lTcGill Un 1versi ty an d pu'b1i.shed in "Compressed

Air" Vol. II, 1906-07, pp. 4181. This drum is supplied

'Nith orifices Ci.lt in copper p1ate~) about 3/J(2, inCH in

tL.l ckneHs and rang~YJb from 1/2 inch to 3-1/2 inclles in

dia.rneter.

All pip~;s H.l1u fittine::;8 uGed VJere tte:'·~(·:ld!6.~J?j.:P~f:)., ~ .. '" " 1; ~. • -.. '"

•• • • ,... 1II • , .......... : : ....

being galvanizeu anl.t tHe 1'1 ttin(;s ··l.::ei-"~ .•cctBt iron Tl~e··::-

}npe s iZffi wer<; 1/2, ::>/4, 1, 1-1/2, ~r;d ; "~H c~~·~. :{~'::"~le fittin~s for each size of pipe:

urdinary ~OO e11)ow s .

Long Bweep 90° u

"RetJrn heltli'ls (open an d c10 sed pat tern)

Globe valves

A number of 12 inch nipples.

The pressure gages used were corrected by

a gage tester.

Tlle d~fferentit.Ll gcJ.~e w:ab t:rle one constructed

expre~sly for tilis work by liolrJes and Wander of clr;'G~

1910.

l?or a r:JOre detailed. description see tne tnesis

by tile se ben tlemen.

Tile indicatinb fluids used were mercury for the

small pipe up to 1-1/2 illcl~US a.mrA-0r tile 1-1/2 a.nd

2 inc}l, water. Tile plan of tHe assemulecl apparatus

;)~':."

0.~

p r •F ~

"I

,~

-,

,CJ1,

~

~r::-:l

I

i,

u~,,

, I'8U 'Jt I II~!- .

II' '.

~~ I:: !eJ i .,

, ,

<;S I ~.,

:

~ ~ 'ID,' mI~ i,.'1]. " ., ~I ~~ ':le'".":'~" : , .=·-1iI ...

""EE"'s'

~,~ i,

I-- ~ ! I I, ,............ 0,l./ :J:::-~--=-.:- 0

,

I

, /~.

--~

•... --,1,~

~ - - -I.e:- I"' I~

./,--

IH'

,

=:1-''S

-3-

is SHown in ::Flc.;.l. S.'1.i.e explhnatlon of ·t.L~·:ltf.t":fjo~r~ng• _"." ~ .,.tI' til ..

SHoO\'J n uelow.WJ:..iC1J. icl~ ..:" : ::: :: ~:" ':; ~ ~:: ~ - -

a :: C01;1P re s so r 0 f 1: .rGel' CHJ1,h~,~tS··.. :('sinr;il" corI~ <-·::-'t •••• .-" '. - "' .

pressor VH::.S ULh:~d cornp(:.l'F.l.tively little ~:e'I;~j Via8:':cri"';:~\~~'ted" • • 'I< • ~ <II. ...

of

in pa.rallel wi til the 1~"i.tge,.).

b = receiver of 3 cu..ft. capcA.cit~y.

C :: preSGlu:e gftge s!l.owiJls ini 1~iCl.l pressure in

air pipes.

d = differentihl gage.

e :: point at which fi ttings v:el'e connected in

the line.

f = throttle valva fO'l' controlling pressure in

the line.

5 = screen in orifice drum.

h = baffle bortrd in orifi ce drum.

i -;: po 8i tion of t~Llermometer.

j = liD" Gage for measuring p reSSUl.'e in drum.

k = position of orifice in drum.

The gages "e u , tid") ana UjU are sJ.lOwn in ct b.ori-

zontal position for the purpose of tetter illustration.

The photograph on page fA.- w~ll also a.id in giving a

clearer idea as to apparatus.

-4-

B.y vr.trying tne speed of tHe c()ltIpressors:::::~~·:i~;f''t~~::"::• a.. : .... : : .,~ ~ •• : .. ~ : :~ .. : : ..... :

a.ir volurne "Vft." We,to controlled. Whlle ·"tl:e.: .cgInpressor ,". -.'.... '..,',: .: .... :: .... : .... ~"" ~.: : ......4_.:,,__ ~ . _

was runn.Lng f .. t ~t urliform b.i.~)(:~"eci tilt) f)I'eSDu..I.'e· il\"~;le-·-~Ys;:·:"·"

'tern was controlled L;y t..iJ.e tli.l'ottle v':i.lve 111'11.

THe orifice '!I'hS var~edLo ~eep tile pressure in

w.licll range \va" covered bJ' :r;u.dle~{ :1.11 .Il.if; l3xperiments.

l~ach si~e of p~pe required, on tlle average, seven

run s. Eigllteen readings V'-ier e tfJ.ken on e[1.ell. run. Tl1i s

makes a total of" tlbout 35 sets of readiI1r;s.

Data for each run "VI'as taken as follows:

Reading on differential gage or ttzU of tables.

Hending on f1D It gabe U ill 0 f ta"bles.

Initial preBuure in pipe--- ttP 2 U of tables.

'l'emperature in drum --- uTe" of tables

Dia.n 1eter lind length of Dipe. hlso number C4nu

kind of fi ttint;.

Dicuneter of orifice --_uDo \n of' tables.

T.Ll.e prebsure ran~e in eaCll rU11 on pipee less

tHan 2 incilcs in diameter' waD from 0 pounds to 150 pounds

gage, or about twelve atmospneres.

-5-

Tile friction fa Dilula, f = C.~5

from "Harr'is t Corlpressed Air Cornputa,t1.ons":;;' ::LicPCt,-t.j.:OJ:·:ttS.. :.:=~~ .. ~~....": ::\:follows:

f = loss of pressure

~ ., ... .."'",.. .,41 i "'~.. :: ,,_,

. ",:'. -- -.- c.~: , ... ~ __,1. .. "

1 = len~th of pipe :in feet.

Va := Yolum e of free a ir pH :=..sing in eu. ft. per sec.

d .. d.iameter of pipe in inches.

r = ratJ.o of compressiun in t-ttJII()Slllieres.

c = experimental coefficient covering all constHnts.

The free a.ir YO lum e (Va) was <.lete~cr.iined i.J.Y tne use

of the orifice drUIn of Dudley's experiIllen'tland l.Xl the

calculationld of wnioh two fmrmulae 'liyere used W.i:liCll were

also taken from tfHarris f Cornpressed Air Computhtions u •

Weignt of air passing = Q. = K 0.1632 d2/f Pa.

The free air volum e = Va

Va = free air volurne in cu.ft per second.

Wa = weight of 1 cu.ft. of free hi!' = .073. pound

approximately at Halla.

-6-

Q, = VHti 6 ht of air phssing the orifice in pounds

per second.

d = d i alII e t e r 0 for i fie e i 11 inc /i.e s •

i = difference in level of water columns in nu"

t;!;fige in inche s.

t == a 1,) 80 1 ute t empera. t u r e (:i!'[Ulr.) 0 :f Hi r in 0 r i f .J.. Ce

drwn.

pa == absolute pressure of atruosphere i.n pounds per

square inch == 14.2 pounds apprOXil~jhtely at Rolla.

k = experimental coefficient deten.;ined "bJ" Dudley.

THe Hfff in tlle fri.ction forl;iula v"o'as COl'iJputed J.,11 the

fa l~owing manner :from the readings on the differential

gaga.

f ( 62. 5 x 13. 6 ) ., . n It d1 if .== 1728 Z, wnere Z == . er.ence lrl

height of tll.e mercur~y coluJlJns in lnches. When water was

the ind-,-cc.ttine; fluid used, the above f'orrllula becomes J

f == (6;'L 5) Z: wllere z' := di fferen ce in He igilt172b

of tl1e water columna in inches.

THe ur u of tHe friction formula was the a.vera.be in

the pipe and. was calculated. as follows:

a- ~U2 f + Par - Pa

-7-

P = gage prestiure at entrance.

THe meaning of tIle various syrnLols used in tile

tables is shown below.,...~~he5lJf

z = ~ifferential gage~inAmercury or water.

f = loss 0 f preoBure i:n pipe in pounds per square

inch.

P2 = gage reading ht entrance.

"2 = ratio of compresion in terms of atmospheres .

.. = avercige rat io of compression i£.l pipe.

i = "un gage reading in incnes of wuter.

To = temperature in dru.m in degrees. Centibraue

(Co:nverted during calculation to au solute degrees ]'allr.)

Do = diwneter of orifice

Va2-rID =~lf eXPlanator~velocity of uir i6 pipe in feet per second.

f ' = n f tt aub j e <.; ted to a corr e c t ion for pipe t eUl-

perature made thus:

ft = t'(.~.3.:.r~.~.\.•...',~~.

ft corrected friction

-b-

f = oriGiYHtl friction

tflX;: abso lu te room ter"peratu.re

t" =. I) ip e t e;.p era.turE~ ." ,

Dur ing t}le e igh.tee.!'! readings on eacl1 run J l'eHtu.ngs

were tal<en on St thermometer strapp ed to tHe pip e niidway

on its lerlgth.

'l'.l1ese read;i.ngs averaged for six different pressures:

ta"c2(.. - - - - .. - - - - - - - -

50

75

100

125

150

b3b

u36

542

54d

b54

560

An effort was made at fl.l'st to keep tile lengtn of

pipe constant but ali tlle only advantC:4.ge of tHis 'WHS tlie

saville;; of a little algebra (witn t.n.e expenditure of

much muscular effort l?1'1d the v.Taste of IL1.Pt?) tl1is VJas soon

abandoned.

-9-

1 Va2In tHe forrtlula f = C,. witn lilfl u,nd ud"

d'~------r;-con stetnt, i file If i G fl.l so can stan t , tl18n It f U H Il d Va 2 wi 11

r

plet to a stTai~ht line. 'Illie we fl.fhl to ve the case

to a verJ reassuring degree, [I.S is eviJ.enceo. in pl1:"~tes

1 to 6.

The object of t.nese experiments vntS to find tile

value "c u ill t.ilC friction forrnulh and coefficients for

loss in the various fittings.

In tables "A" I "BII and I'CIf will Le found ~ulder the

headin6 IILost> of Pressure u a. coeff~cient wHich, 1)Julti-

Va2plied by . will Give loss) ~y frictiun,r

sq. lllCh for one fitting as indicated.

in po un d s :p e r

In table liD" will be found tHe coefficient nc" of

the fo rrnula

1 Y!l.2f = c ~u5 r

Th i 8 tJ C It i s f (j un d as 1'0 110""S :

Wllen 1 := I tlie above formula. uecomes

1f =cr

5

Now from resu.lts worked out froJrl plates and equa-

tiona we have the valiJles fo!' "1'11 for one foot of pipe.

:fa l'

-10-

1 J. ,;':1 C ,:'1, ) i P 1,;:- .t.' -- .U70l'

vVhen ce ,-', Yl f,

.V.Vr

L[" c.t: 01

l/;~ a d ~)/4 il1CJl pipe n,n

VC:,2 in 't: .. e cal ...iLG J

r

fitti ;s.

teet Il •

-11-

The effect of unreawed ends proved to be of inlpor-

tance so tHis was i:ncluded in our investigation. The

resul t S 0 f tlii G ~ .. re n1 SQ shown in tatIe s ItA" ~ '.'!'~~ .:.. ii.i'~d·. ~...~ ..: .. :"'.: ':.;." -

tt en. The effect 0 f recuned ends Vias found t9. :"~~'.~.~~.9~t.::

cally neglie;able. Thiu fact enabled .~~ ...i¢o ;~}:cik:~·:~"i:i.·~· :6·il- ·.~~._.~.' ,;.. . - --

culation of results on the 1-1/2 inch ;i~:J""~~if<?l('~Wi~r~"""":':':'"

to one run being incQrrect (due probntly to some ob-

staole in tile pipe) would otherwise have had to be

omitted or ro-run.

It will be seen tlla t tabl es "1\..", 1113 U J and "C II

give valuable conclusions as to the friction due to

various fi tti.ngG in terms of feet 0 f stra.::;'ght pipe.

Itl calculatillg "Va2 11

rand tiS", of the tables,

logritl.lms were uBed as mUCh ES posoii)le. T.l'.l.is fJirapli-

fied tile work consideJ:'c.'l.LJly a.fter. tIle scheme was syatema.-

tized.

Tae nominal diameters of tHe pipes were found to

be slightly leas th~dl tile ftctual diameter; the actu.al

dimneters of tJle pipes were used in the ca.lculations.

Table of nominal and actual diameters of pipes.

8i z e 0 f pip e in inche s .

( Nominal 1/2 - 3/4 - 1 - 1-1/2 - 2Diameter (

.( Actual .64 .82 1.071.63 2.08

IUCI' / /citUI '-IIUIIICJi.-:,· L··:pl/e. /.,)7' LCi/g,'-17jJ,,'Jf'.

r. ,('rJ3s: ::: eiDowS, ,.] (,"ff,t."·;[L'i/r't':.<.1inCC1 ell,',")

80

I------ . - --

r-~~~-'.- - . - . ~EEilii-

I I 1 i" ,

I Z I " ~2..

;1/0 f P;, r" 1".... L Tc. ,d" 4 S f(Hi)

. -(Ont/c.e) Y"", ~ ,rrc clt.zj

I .5(~~·0. /81 2.2 .::H .z $6 :J /3 0 / S"c , I ¥{,

t·/5 / S5. - ... --,

:'c j./4 ,24 1.74 26Z '12 / 't, 0 " ,'10 J b5 344- --- -:;-

"/77 .25" ,2 7'}.,

f,2 ~ i I j. C .. ,560,

177';I -, A I 76. ,I

L' J, 'i O,b "/ .JZ 1(· ':} 467 /4 / ~ 0 " ,e 7 z 17 (,b"- . · - . · __ I

j j,j ZZ )0 <1 ~ f 4 54 ;.4 I jO " ,124, ,on I, I SI. . .j

..{, S' / 2,' 6 ~I '1 6'1 4. 51 -u 1 j ()

..'261 .:' j

.7:>~

, 2.5 I I 3 7~ G j 3 ~. jO 3," Ij :i ·/34 ;-,.. / , ( :>, •6' J S 0 7+ ~ :,- b j 3 " :, I 20 U.5 "

'1 'I I '3 ( .69., .... « 3 :: / I 7 S fd5 626 5,J 1,/,0 '. ,240 32 , ')6

. -10 D ~ (,j':} 100 ! . r :. S ( '& 1.3 J.5".O .. ,0 '10 /2 ~, 5... ,

II /3 C 93 loe ~,c9 S ( 7 " ' I~: 0 ...e9~

I / S' __0-=,8'1-=- j " ,.; I- · •

IZ }.3 1,62 /00 S,0 '3 '1,04 S,S IS-O ' . ,13.'>

j..24 I 'I ~· ---- -==-

1.1 °7 D ~~ / 2 ~- 98 (, ~,8 4 / j 16.0 " ,021 S 0 !Jr,1 .....

I't I, ~ c 1$" 12 J 9,8b J S5 j,.5 / oJ) ,

" ·085 ;S C·7~+- .I:> Z,j I 1 j /24 :; .8 C' 976 6,,5 17,0 " ,Ib':' ;:/ o ') y.. -=I" o'i 0,5'3 ISo /1 b<f II. G) I. '$ no .. .02g S () ,3 3I -I 7 / 1 0,6 '} 150 1/6'1 II (, I j,O If.tI_1. " 'o,u, ':i o :iI'

--- ~ . j

, ~ 2.~,

1·'13 1.5 0 1/6'1 1/ GI n 6.(, /8,5 n " , 140 /~ n ,3 c,

TABLf 2- I· - ,~ .' a .. a/,','cfcr- o'~c "pcc 107': LerigO? p,pe. . 8o~L~ , ..... , J - -

Fi+-f I 'n9 s : 2,. C-.IJL'''V~, /.3 ·/,·.lc<f'J //eu ena.s) ,I f,t' /....J I f:_

- - - .~ --- -- --="'l_; I I

... - ~ - -------------,- -- · ..

" ",'- ,

No. z f 'f'L T"m I Tc <1. 0 v. S f()-I~)

~ - --r..,

.z 1 /,0' ...~ 0 .z ..,1- .. -It /, s- ,1,0 / jo , 157 43 /03; ~

1--=

Z 56 ,7 3 ;:0 2,'i.l ~2 4,0 10·0 " " 32 72 ~- 7311:1.<: A

3 105 ')'/ i 20 2."1.z .221 ;. g " , Hi 102 S,IB.11,0 ,

,

4 /, ; D, 86 50 -1 :> :J ·/55 23 //,0 " ,125" ";7 0, S.5-

" 3 l 1.6;; 5C "i ;,:> '1 So "f.6 // () " ,;H6 40 I~{,-~ · .- .

b 5,6 Z7~ 5c 155 146 7. 5 I 1.0 .. ·424 SI A- 6.5_

7 . c '] 0·12 7 ~, 6 3;: 6 jO ;,6 ,. 2.0 " ,Db' Ii 0.')

· J_? 2,5 1.20 7.5 (dZ t .d 37 12,~ " ,/'1 S ;:s- I·J 2_'1 3.5 /,5"9 is 662 b ,J. 7 .5.4 I-<,S '. ,'215" 30 1,'1 I'· . ..-- - -, i.~ 0 9 0.<14 100 8 cc) ~ ( 7 /7 1..,,0 " .0 S I /J C 3 9

-

I 1 2/ 105 100 80 'J ~,c 6 '1. 'Z 140 .. ./ Jj .2 1 o 'J J+ · . -

3, IJ I, 'i 7 100 ~ ( ~ 'i.c~) t 8 I .5", J .. .213 29 IbL' L... · ., - .! ; 04 0.1 (j 125 C' ~ 6 ;Jj5 0'7 IS: 0 .. -0 :'-1

.,.C co :3· -=

) I ; C ,6'1 I:: S ') , I .' ~-I ' . If 0 ,os I / ~' c.ss.. ""- - -

".

155 12. j ') ,, ., i 7 2 .6 j .II( 22 I' IS-J J~ 7 ' . .

- t --10 C " OJ 7 .5" 'j 64 /1.63 /,6 ,. 7·'; I , ,D jj '1 (). j /

j .. -

/7 ,, .' LJ, 74 , ~-:,; /1 64 1I. 6~ '1 0 IS, C ,C gs 4 C ~;.• -

/ ~. , /1/ . :-J /64 /I ,: 0 b.S I g C ,us /8 0 '-'5-. '-