r AD-7eO 776
IhL COMHUIATIOtl OF THE BULK HÜDULl OF A
SYfiMTIC HYDROCARBON HYDRAULIC FLUID
AIR FORCE KATLRIALS LABORATORY
APRIL 1^75
Distributed By:
Natioiial Tickiicai liftnHtiM Sirvici U. S. DEPARTMENT OF COMMERCE
i
AFMl-TR-73-81
THE COMPUTATION OF THE BULK MODULI OF A SYNTHETIC HYDROCARBON HYDRAULIC FLUID
CO
o <
h C BROOKS 1 :; , . 7 1375
JUUv-
TECHNICAL RFPORT AFMl. TR 73 81
APRIL 1973
Approved (or public release dutribubon unlimited
•,,■ ... .,
NATIONAL TFCHNICAL INFORMATION SERVlCF
AIR FORCE MATERIALS LABORATORY AIR FORCE SYSTEMS COMMAND
WRIGHT-PATTERSON AIR FORCE BASE. OHIO
NOTICE
When Government drawings, specifications, or other data are used for any purpose
other than in connection with a definitely related Government procurement operation,
the United State« Government thereby incurs no responsibility nor any obligation
whatsoever; and the fact that the government may have formulated, furnished, or in
any way supplied the said drawings, specifications, or other data, is not to bo regarded
by implicatton or otherwise as in any manner licensing the holder or any other person
or corporation, or conveying any rights or permission to manufacture, use, or sell any
patented invention that may In any way be related thereto.
'IT W m we t fv mvmrax MStolUIUI
■ 'in.. ~ i «;L u * •' -'u
A
Copies of this report should not be returned wiles« return is required by security
considerations, contractual obligations, or notice on a specific document.
IR FORCE/ S67«0/4 Jun« 197. - 350
mmam
UNCLASSIFIED Sccutity CU««ificotion
DOCUMENT CONTROL DATA • R&D fSm€unlr cimmmili€mtian at lirl«. b»»rfy of mbtifct mnt indmamg annolmi'oti muti 6* wilsrW MAMI tt*9 ontmll rmpott ■• cJ*««ifi*d;
Air Fore* Materials Laboratory Wright-Patterson Air Fore* Baa«, Ohio 45433
|l* «C»0"' »t Co« '• C t.**>IF<C*'IO*
UMCUSSIFIED Ik ••Ou»
I mtPomi TiTLt
The Computation of ehe Bulk Moduli of a Synthetic Hydrocarbon Hydraulic Fluid
( OltCOI^Tlvt MO*CI (Trprn al mm"
T«ctulcai hei-ort m*4 mckfiw 4mtmmt
F. C. BROOKS
« ■C^OKT 0*TI
Apt 11 1^73
1 Tt NO 0' ••>•
28 I« CONTHACT Om t«*MT NO
• vaojICT MO 7340
' TASK m 734008
tmit
AFML 111-73-81
»>• npMtJ
10 * VA Ik «aiLlTT LIMITSTIOM HOtlCIS
Approved for public raleaae, distribution unlimited.
II l*OMIOMme Wi-ITAM* «CTlvtTV
AIR FORCE MATERIALS LABORATORY (MIT) AIR FORCE SYSTEMS COHMAKD JWRIGHT-FATTERSOH AIR FORCE BASE, OHIO
II «atTMACI
The bulk noduli of a aynthetic hydrocarbon are calculated and appropriate equations are preaented. Methods of datemlnlnt and predicting bulk aodull are reviewed. A conservative low value of isothermal secant bulk modulus of the aynthetic hydrocarbon candidate was selected from determinations produced with the .aaua apparatus. This selected value served aa the primary datum point for calculating Isothermal aecant and tangent bulk moduli and adiabatlc eecant and tangent bulk moduli.
The results of thsee calculations are preaented in tabular and graphical form for temperatures of 100, 200. 275, 300, 400 nd 500 F and pressures between 0 and 5000 pslg.
DD '^ 1473 UNCLASSIFIFD Security Classifirabon
UNCUS SIFTED Secur:t Classtfication
•• l<I:Y WOI'OS
SYNTHETIC HYDROCARBON
BULK MODULUS
ADIABATIC
ISOTHERMAL
TANGENT
SECANT
INSTilUCTIONS
I. ORIGINA'nNG ACTIVt'l'Y~ Ent~ the- and ..Wrns of th* controoctor, aoabcOfttrector, 11'-t••• Oeput-t of D• fenae ectavity or otll« orcanlnUoa (COIJ'OI'MO ..,,loot) -~the '*PO"· 2a. REPORT SECU'IIITY CLA .. P'ICATIOM. Enter tloe ov all aecuttty cloaaifkMioa of the "POrt• la4koto -..~~er "Restrtct*<l Data" ss iftChsdK lledtiJII lo to be Ia oocccw• ance 11111th appropriate oocllllty roclllatloe ..
2b. ROUP: Autolllatic: dowacradl .. i.e .. ctflod Ia DoD D,. rec:tlve 5200.10 and~ P'otc: .. llllduotrllll ...... Ill. Ent• be r<>up null!ber. Alao, wl\ltn opplic:oblo , a how thet "4'tloMI
111ark1 • havr b.,en sod for Group 3 atod Graue> 4 •• •uthor· t&ed
3. REPORT TITLE: Enter the o..,lato ~It title lA aU ' u&l Iotter&. TlUea 111 all caaoa otlould be ua.c:loaaifl ... If a --u•cflll till* c annot be M locted th<>ut claa .. fac• Uol\. aho"' tatle clau•f c:at1011 a 1111 copi.lola Ill p-lllhnla 1 -d1ately rollow•nc the utle.
4. 0 R PTIVE NOTES: If liPPf ..... oatet the t~ of '' · e. , a!lt H JIII, P'"ll'" • · au-•• . aaiiQIII , or final .
Ulc:luaave d•t•a •h- • -c>•c:•hc: reportl,. penod Ia
E er the na.-( s) of ..,t I( a) aa tthoWII oa In th report. !.ntet l ost .._, tint - · lll.ld4a all al.
If •1\ t • , ahow ••'* ""'" twa.eh of • ...,ic: The - of tonc•pol · ·•thor 1 on abo lute •illllftu• raqt&i•-"'-
"'PORT DATto .nteJ tbe dete of t report •• day, rt '· yeer; l'llt>nt ~~~u. U m«e • on o~ ltat• ..,.... a
n 1 ' " t*Port, "' d te of publ at 10 7 • TOT At. UIIIUER OF PAGES: The totlll POC* count
uld follow nof'll'\111 i llatlot\ procM~~rea, 1. •· , a ntH tho er or p• "' cl'lllailllftC lnfot1110tlo11.
Ea OF Jt£FEJUt E;a Eater tlw tO(el ....-.. of 01 Cit ed .. the r 011.
• CO AC OR GRANT NU tbe opphc a le 11111111.ber I th<t onlr t Ita report woa -111en.
: It .,,.pr iate, ""'..,. t or cr• ll "'"'-
lb, ld. PROJECT UIIIS tar the ..,opnata mlhtor 1101-nt ident•hcation, ..,c •• roJec:l .......,, au I'OJI?<'I nutllb•r. aystem --.. teak n~. etc.
9e. ORIGINATOR'. Rf:J>ORT NU at( : Eat• tbe offi· cu•l r rt numbof t- which: tho doc:aa- ••11 IK i:detlliiiM •nd controtled by th:a OfJ&Inatillc Ktl¥1ty. T'hio ........, -•t be uNque to tlua report.
b OTHER REPORT NUIIBER(S): If the ropott h• ..... 1 l'led any oth~ repott nulllb.,, ( e,ber by tlte orilin-r
or by ti>Jt apon.a<>r:l. elao .. t.., tluo -ber(•)•
10. AVAlLABlLfTY IMITATIO NOTICE &alar any U.. 1tet fllrlhoJ' d1 •••inataon of the fOIIM , o r tile• t .....
"'U.S. Gwernment ""'nt1r9 Office: 1913- 751-• 94/ 532
~~
i81pooo4 by IOC\11' ty c le .. iflc:otloll, uoi"C etondard otatementa ouch eo:
(1) "QII&llfl ,.quaataro _,. obtain copies of tbla report from DOC."
( l)
(3)
( 4)
"Foralp annolltiC-enl allld dlooOllllaotlon of thle report by DOC I not authorized."
"U, S. Govemment .. oncln IIIOY obtain coplaa of thla ropr rt directly f10• DOC. Oth• qullllfled DOC uaeta 4 all rOCNoat throaach
.... .,; .. r
($) "All dt tribut on of thie report •• controlle<l. Qual· 1fied DOC 110 .. shell raqu .. t thru~~&h
---------------------------------------- .·· If the report hao beer~ furnloh<td to the OWce of Tech11l al s-tc••· Deport-.nt of eo-erce, for .... to tho pllblic, indl· cat a thle feel o..t •"'• dla pn o, Jf known. lL IUPPLDUUfTARY NOTU: Uoa for edduaOfl.lll uplo11• .. , ... , ... l:t. IP()Jflu, ,..a MILITARY ACTIVITY: ENar the nama o f the d•ort-ntol project office or loborMory aponeorona (P • Y" lrtf lor) the tltac uc:h oad ...,cloplllltllt. lnelude oddru
l3 A TRACT• llnter •n abotroct 1ivln1 a brief and ractual , __ ,. f tho docu-.t i.lldlcotlve of tho report, even lhouah 1t ••Y oleo appear eloawhere ill lila body of the tochn• a l ,.... port. It addlu-1 apace Ia required, • contlaaaauon sheet aha II be attached .
It •• II clll)' daauable the l ho abstract of cl•ntf• II " ' po1 t.. -clna•fiod. £a pare roph of the • tract shall l'nd with aa Indication of the aulltory sacaanty clau1hcolioft of 111 Ill· fOI"'IIatiCifl an the perecrapjt . repreaonted •• (TS) (•). (C J, ' " (U)
There IS ftO hrailotion oe the loftCth of the abstract How· .... , , the •"uestetl lenwth ia froa ISO ,., 225 •otda.
14 . K£ • no . Kt!y " .. , .... tec:llnlcall)' IIIOOftlllfi{UI ten!lo or • "'" phra n..at cl- 1 "terlze a report and may be aased •• •nda• f'llmea 1 , •tah>ll'"l the ,.port. Key words •uat oolocted • ·• u .... ,., aecaanty clooalflc:otlon Ia reqllired. ldenll • flora , such •• equ•P-1 ...S•I doalpation, trade Mae, lllilltary PfOJec:t cocle na•e, poa,.,.Uc: location, ,..,. be used •• kay wordo WI will loe fol -ad 111r • ladkation of technic:• I con· teat. 11M ooal...-ttt of li.alta . rt~laa , and wolpto Is optJonol.
UIICLA!»SIFIED Security Cluaific:atlon
THE COMPUTATION OF THE BULK MODULI OF A SYNTHETIC HYDROCARBON HYDRAULIC FLUID
F C BROOKS
Approved (or public release; distribution unlimited.
Ih
*m
FOREWORD
This report was prepared by the Lubricants and iribology Branch of
the Nonmetallic Materials Division, Air "^orce Materials Laboratory. Air
Force Systems Coraraard. Wright-Patterson Air Foice Base, Ohio. This -»ffort
was conducted under Project No. 7340, "Nonmetallic and Composite Materials."
Task No. 7 54008, "Energy Transfer Fluids," with F. C. Brooks acting as
Project Engineer.
This report presents the purpose and results of an effort expended
between November 1972 and January 1973.
This technical report has been reviewed and is approved.
a*«*' (&CKeJ' KENNETH A. DAVIS, MAJOR, USAF Chief Lubricants and Tribology Branch Air Force Materials Laboratory
ii
iMMiAHMMM
ABSTRACT
The bulk moduli of a synthetic hydroca-'^on are calculated and appro-
priate equations are presented. Methods of determinirg and predicting
bulk moduli are reviewed. A conservative low value of isothermal secant
bulk modulus of the synthetic hydrocarbon candidate was selected from
determinations produced with the Klaus apparatus. This selected value
served as the primary datum point for calcolating isothermal secant and
tangent bulk moduli and adiabatic secant and tangent bulk moduli.
The results of these calculations are presented in tabular and graph-
ical form for temperatures of 100, 200, 275, !00, 400 and 500 F and pres-
sures between Ü and 5000 psig.
in
I^M*
I
CONTENTS
ction Page
I Introduction 1
II Isothermal Secant Bulk Modulus of Mil-H-83282
5
III Isothermal Tangent etc 9
IV Adiabatic Tangent etc. 12
V Adiabatic Secant etc. 15
VI Reference 20
IV
ILLUSTRATIONS
FIGURE PAGE
1 A COMPARISON OF BULK MODULUS RESULTS FROM THREE INVESTIGATORS 4
2 THE ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282 8
3 THE ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282 II
4 THE ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282 14
5 THt ADIABATIC SECANT BULK MODULUS OF MIL-H-83282 17
6 BETA AS A FUNCTION OF PRESSURE 18
7 GAMMA AS A FUNCTION OF TEMPERATURE FOR MIL-H-5606A 19
HYDRAULIC FLUID
TABLES
TABLF
I
II
III
IV
V
THE BULK MODULUS OF MIL-H-5606A HYDRAULIC FLUID
ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282
ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282
ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282
ADIABATIC SBCANI BULK MODULUS OF MIL-H-83282
Page
3
7
10
13
16
VI
mm
Wljmmmm—m^^m
SECTION I
INTRODUCTION
Bulk modulus is one of the important engineering properties of a hydra-
ulic fluid. Therefore it is advantageous that accurate, reliable bulk
modulus values be distributed. It is the purpose of this effort to provide
reliable values, of isothermal and adiabatic secant and isotherma. and
adiabatic tangent bulk moduli of MIL-H-83282 hydraulic fluid for engineering
ant research applications.
Bulk modulus is the volumetric modulus of elasticity of a liquid, or
simply, a measure of a liquid s spring rate. It is, therefore, the recip-
rocal of liquid compressibility.
Hydraulic fluid bulk moduli are used in hydraulic system and component
design calculations to determine such factors as static and dynamic stiffness,
resonant frequencies and pump characteristics. The kind of bulk modulus
values which are used depends upon the factors which are being studied.
There are two common methods of determining bulk modulus. One is the
pressure-volume-temperature (P-V-T) method which measures the isothermal
secant bulk modulus of the test liquid. Klaus and associates (references
1, 2) have reported on the development of a direct reading apparatus which
utilizes calibrated pycnometers housed in a high pressure glass windowed
cell. Liquid densities aay be determined to ^ 0.2 percent of a pressure
range of 0 to 10,000 psig. These measurements result in a precision of
+0.5 percent when translated to bulk modulus.
The second common method of determining bulk modulus is the sonic method,
which measures the velocity of sound in the liquid and determines the adia-
batic tangent bulk modulus. Peeler and Green (Reference 3) , and Noonan
(Reference 4) have studied several hydraulic fluids using the sonic method
of bulk modulus dgtermination.
1
Wright (Reference 5) made a comprehensive study of bulk modulus deter-
minations and proposed a method of predicting the bulk modulus of petroleum
oils from their density. Wright notes that the bulk modulus determinations
made by Klaus are in agreement with his findings.
The results of bulk modulus determinations of MIL-H-5606A hydraulic
fluid, conducted by three investigators, are shown in Table I. The iso-
the.-mal secant data, reported by investigator B, cannot be directly com-
pared to the adiabatic tangent data reported by investigators A and C. By
calculating ^iabatic tangent bulk modulus from the isothermal secant
values, the results of the three investigators, as shown in Figure 1, became
comparahTe. The results of investigators A and B are in excellent agree-
ment over the pressure range of 2000 to 5000 p -g. The results reported by
investigator C are approximately 21,000 psi less than investigator B's
results, over the entire pressure range.
Klaus, Fteference 6, presented a method for predicting the isothermal
secant and isothermal tangent bulk moduli of several hydraulic fluid species.
Over the 0 to 10,000 psig pressure range, the predicted values agree with
experimental bulk modulus determinations within + 2.'0 percent. Predicted
values of isothermal secant bulk modulus were related to ASME "Pressure-
Viscosity Report" density results with an accuracy of +_ 4.0 percent over a
temperature range of 32 to 425 F and a pressure range of 0 to 150,000 psig.
The bulk moduli values computed during this program were obtained by
reviewing the isothermal secant bulk modulus of four different samples of
MIL-H-83282, which were measured with the Klaus apparatus, and selecting a
conservative value as a starting point. From this starting point, isother-
mal secant and isothermal tangent bulk moduli values were calculated using
the Klaus equations. These values wert then used to calculate adiabatic
tangent and secant bulk moduli values.
TABLE I
THE BULK MODULUS OF MIL-H-5606A HYDRAULIC FLUID
Temperature: 100 F
Investigator A Investigator B | Investigator C j Pressure Adiabatic Tangent Isothermal Secant Adiabatic Tangent
psiq psi psi psi
1,000 235,000 191,000 220,300
2,000 254,000 196,600 233,800
1 3,000 268,000 202,000 245,400
4,000 279,000 207,500 258,400
5,000 291,000 i 213,000 270,200
10,000 240,500 i
A COMPARISON OF BULK MODULUS
DETERMINATIONS BY THREE INVESTIGATORS
FLUID: MIL-H-5606A TEMPERATURE: 100 F
300
i o
Q Ö
§
250
200
PRESS^P, PS IG x 10 -3
FIGURE 1
SECTION II
ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282
The isothermal secant bulk modulus of qualification samples of MIL-H-
83282, as determined in the Klaus apparatus, were compared and a conserva-
tive low value was selected for the starting point of this effort. The
value selected was 202.500 psi at 100 F and 2000 psig.
Using this datura point and equation (1), the isothermal secant bulk
modulus at 100 F and 0 psig was calculated.
|^B = Bo + 5.30 PJ i (1)
where:
B = isothermal secant bulk modulus at pressure P
and temperature T, expressed in pounds/square inch.
B0 B isothermal secant bulk modulus at 0 psig and
temperature T, expressed in pounds/square inch.
F = pressure, in psig.
Using this calculated value B0 ad BT, at 0 psig and equation (2),
values B0 were calculated for temperatures of 200, 275, 300, 400 and 500 F.
1r. log
3 (T2 - T1) (2)
—j p
where:
B_ = isothermal secant bulk modulus at pressuie P and 1
temperature T^, ''F, and
BT = isothermal secant bulk modulus at pressure P and 2
temperature T0, F.
Values of (3 , a generalized relationship of the slope as a function of
pressure, are presented in Figure 6.
Using the calculated values of B0, at temperatures of 100, 200, 275,
I
300, 400 and 500 F, and equation (1), a complete set of values of B were
calculated for pressures of 1000, 2000, 3000, 4000, 5000, 6000, 8000, and
10,000 psig. The results of these calculations are shown in Table II, and,
for easy access of intermediate pressure values, is presented graphically
to 5000 psig in Figure 2.
*—mt
00 (M
00
X I
OQ
o o o o o o o o o lr. o o o o o o 0 o c
a (N m oo r-< ■t N CO o ! O
o M 00 en 00 t a ^r in in 1 in m in vO o N N 00 a o
r-l |
o o o o o o o o o 1 i ^ o s o o o o o O o !
o vO a 0» in 00 t '0 1 o n oo m oo t <?> Tt in ■c
1 ^ i^ r- ao oo a> a o rH
I-I
r-l
o o o o o o o O c i
o o o
o s s o o s O rH
O 1
o o r-l m H t^ (N CO w o o rH r-l CM CJ CO 'd1 in l-l rH H r-l r-l i-i r-l iH 1-1 !
o o O O O O o O o 1 lb o o O O o o 2 o o
00 iH t t^ o ri CNJ oo
N m oo CO o» 3 a o 9 VI o i-( rH (M (N co m <o
iH H r-l r-l r-l i-i r-l i-i iH !
o O o o o o o o lb o o o Q o o Ü o 2 0 o
o ro o o w m oo ■<t
a •<* o> ■« 8 m o r-l N 1 M C1 Tf ■* m «o N 00 0»
H r-l r-l r-t r-l H 1-1 1-1 H
U. o o o o O O o o o o o s o o O o o 2 o N oo rH ■<* t^ CO a 1 1-1 N CM h< M co CO •* "* Ov a o 8 H rH <M CO ' H r-l CM (N rg (M M N
1 31 M 0> o 8 o o o 8 O o o 3'H o o o 8 o o vi in o o o Ü o o o o (X •> * • •> •• " 1
1 01 iH M CO ■>* in <o ao o ^ I-I 1
Bu
•H in
I/I tfl (U
VI 01 J
rH «
in 3 i-l 3 •o 0 B
3
ISOTHERMAL SECANT BULK MODULUS OF MIL-H-83282
300
i o
IT D-
tf)
Q
i
250
200
150
100
50
P%ASSURE, PSIG x 10"
FIGURE 2 8
mm
SECTION III
THE ISOTHERMAL TANGENT BULK MODULUS OF MIL-H-83282
The isothermal tangent bulk modulus of MIL-H-83282 was calculated for
temperatures of 100, 200, 275, 300, 400 and 500 F at pressures of 1000,
2000, 3000, 4000 and 5000 psig using the previously calculated values of
B and equation (3).
(BR)p = 8^ (3)
where:
(BR)p = isothermal tangent bulk modulus at tempera-
ture T and pressure P, and
Bp- = isothermal secant bulk modulus at temperature
T and twice pressure P.
The results of these calculations are shown in Table III and are pre-
sented graphically in Figure 3.
00
CO oo
X I
tu
O o o o o o u. O o o o Ü o
O in r-l r- n ON
o o (N ro t t m m m in X> N oo a O
o o o o o o (b o 0 o o o o
o v.0 M 00 t o o o
m,
-o ro ■t TT in NO
I1 I-- oo ON o r-l r-l r-l
o O o o O o u. o s o o O o
N a m iH N o o o t-l rH w cn m en o H N ro T» m
i-H H r-l rH i-j iH
o O O o O u. o o Q O o o
oo ■t Q o M oo IT) » »V m r- *■ f»
f-. t^ 00 ON O o o N o 1-1 O) n m NO
H iH 1-1 r-l iH r-l
o o o O o O (I. o o o O o o
o o
o ■c f\) oo ■<* o
a a o o iH CN)
N m -«t >o ^ OO ON H H iH iH i-H 1-1
o o o o o o fb o o o o o O
ON m iH N en ON
o o H N m n 3 ■«*
H Ov o rH (N T*
H (M (N N CV) CNJ
a M 0 3 -H O O o Q o o (A 1/1 O o Q O o (fl 0
N
O o o o o i-( CV) ro ^t m
0.
•rl ID a
'S w m 41 u
e- (H
v. 01 3 H n > in 3 r-l 3 •0 0 e
3
10
ISOTHERfliU. TANGENT BULK MODULUS OF MIL-H-83282
JOO
n i o
a.
i
250
200
150
100
1 2 3
PRESSURE, PSIG x 10"3
FIGURE 3 11
SECTION IV
THE ADIAB.ATIC TANGENT BULK MODULUS OF MIL-H-83282
The relationship between adiabatic and isothermal tangent bulk modulus
may be expressed by equation (4).
fs= Y =fp BR Cy
(4)
where:
and pressure P,
and pressure P,
Bg = adiabatic tangent bulk modulus at temperature T
BR = isothermal tangent bulk modulus at temperature T
Cp = specific heat at constant pressure,
Cv = specific heat at constant volume,
Y = ratio of specific heats or bulk moduli.
The adiabatic tangent bulk modulus of MIL-H-83282 was calculated by
using the previously calculated values of isothermal tangent bulk modulus
and equation (4). Values of Y, which are presented in Figure 4, were deter-
mined for hydraulic fluid MIL-H-5606A. However, these data are considered
applicable to calculations for typical mineral oil base fluids (references
3 and 6).
The results of these calculations are shown in Table IV and are pre-
sented graphically in Figure 4.
12
MMa rfk
CQ
o c o o o o u. o o o c c o
i Q
>0 0> n >o o 1^ 1
■o s o- c <M r^ 1 m m 'O r- a c rH 1
rH j
o o o o o u. o o c o o o o 00 ^0 fl f-H a o * ► i
•^ f-l rg t ■a » a> Tt oo a- c —I O) n
f-H f-* ^H rH 1
;
o o o o o o U. o c o o Ü o
o CO o n t «o ao in 00 o (M t vO
fO r-t rj <* in >o t^ i—i FH f-i i-i r-( rH 1
o O o o o 0 u. o s o o o Q o o a M in in ^ fc » * I t^ in t~- a rH ^t vC (M
PH r-4 r-( rH CO rH 1
o o o O o o 1 ^ o o 2 O o o
^r o m a m o *■ » • • '' 1 o m GO c m m 00 1
1 M «0 r^ a O rH N 1 »-» r-* r-l N <N (N
u. o 8 8 o o O
o s s r- 1-1 <N C) (N 1
o •> » • » 1
o <c a (N m ao ^H 1 r-t c^ •<» 'O h- ou Q 1
<N (\ (M CJ (N en 1
Oi v^CJ o c g C c 3-H rt o c o 1 m i/i O o Q o 1 '/i a ■> - • * 1 « r-t rj m f if\ [ u a.
in
in in 0)
IT i> 3
rH I« >
3 rH 3
3
i
13
vwpi
ADIABATIC TANGENT BULK MODULUS OF MIL-H-83282
300
n i o
in
I
250
200
150
100
1 2 T
PRESSURE, PSIG x 10"3
FIGURE 4
14
SECTION V
ADIABATIC SECANT BLLK MODULUS OF MIL-H-83282
The adiabatic secant bulk modulus of MIL-H-83282 was calculated by
using the previously calculated adiabatic tangent bulk modulus values and
equation (5).
BB - BR + BR (5)
where:
and pressure P,
B = adiabatic secant bulk modulus at temperature T
Bp = adiabatic tangent bulk modulus at temperature T o
anH 0 psig, and
B = adiabatic tangent bulk modulus at temperature T
and pressure P.
The results of these calculations are shown in Table V and are pre-
sented graphically in Figure 5.
15
tM jtm
>
<
o O O o o o ^ o O o o o o
NO cn o >o en o o »< »■ V »■ •> r-
o vO CM oo cri (Jv m | ID vO o t- t^ oo
o o o O o 0 i u. o o o o o o o a oo N vO m 1 o •. »« •*
0 rH vO CM oo Tt o ^ oa oo <* & o
r-l rH rH
o o O o o o fc o o O o o o
co a O rH CM en
m H oo •* O «o i ! cr iH M CM CO •<* T*
rH r-l rH rH rH '-,
O O o O O o i u. O O o O o o o (N CO m ^o oo 1^ ^ »1 »- »* *• 1
<■" in 1-1 f- en a in (\ N m f) •t •<t m
H i-i rH rH rH rH
O o o o O o i (X. o o o o O o
•t N o •<* r- o c * ^ r. •* •« * 1 c m rH oo ■<f o ^ i K o N r^ 00 a <^
rH r-l rH rH rH i-H
O O o O O o (i. o o o o O Q o o rH o rH <5
1 c * t\ •> r- «• c « (N a in CM 00 r- ro ■* rt m >o KO
CM CM CM (N CM CM
<D n a O O O o O 0 a-H O o o O 8 V, V) O o o O « ft "« •^ 1 a M
tH N en ■<t 10 ^
Ou
•rl W a c
•H
^ V) V) 0) M
&
w OJ 3 l-H (0 :> in 3 H 3
3
16
ADIABATIC SECANT BULK MODULUS OF MIL-H-83282
30(
en i o
X
M
a- to i
250
200
150
100
PRESSURE, PSIG x 10"
FIGURE 5 17
Mi
^
tu a
m a Qu
o z o
o o
o ON
O CO
O
en o o vO H
X
0 NO -H W w
o Cu a in
n B w M a tt. D W (0 w
o a ^ 0.
o CO
o c\)
OT x visa
18
■la
w
O
O
c/) <
e 3 tu
U
o o in
i Ä
i j H
ö o
S o CM
o o
AD/4D 'VWWVO
19
SECTION VI
REFERENCES
2.
3.
1. Klaus, E.E., Fenske, M,R., and Tewksbury, E.J., "Fluids, Lubricants,
Fuels, and Related Materials," WADD TR 60-898, Parts TI and III,
1962 and 1963.
O'Brien, J.A., M.S. Thesis, "Precision Measurement of Liquid Bulk
Modulus," The Pennsylvania State University, 1962.
Peeler, R.L., and Green, J., "Measurement of Bulk Modulus of Hydraulic
Fluids," American Society of Testing Materials, Bulletin 235, p. 51,
January 1959.
4. Noonan, J. , "The Ultrasonic Determination of the Bulk Modulus of Hydrau-
lic Fluids at Elevated Temperatures and Pressures," National Research
Council of Canada, Report NX: No. 8455, March 1, 1965.
5. Wright, W.A., "Prediction of Bulk Moduli and Pressure-Volume-Temperature
Data for Petroleum Oils," Transactions, American Society of Lubri-
cation Engineers, Vol 10, p. 349, 1967.
6. Klaus, E. E. , and O'Brien, J.A. , "Precise Measurement and Prediction of
Bulk Modulus Values of Fluids and Lubricants," presented at the
American Society of Mechanical Engineers Lubrication Symposium,
Boston, Mass., June, 1963.
20