+ LEVEL.'0

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~~NUSC Teebnl" Report 6115

0S

The Effects of Hydrostatic Pressureo On Synthetic-Rope Buoyancyget In Fresh and Salt Water

Gary T. GriffinWilliam A. Watidns, LT. USN

Special Projects Department

Fg'~~ DDC.-,+

F8. 8 WD 16 November 1979

2C Naval Underwater Systems Center[ Newport, Rhode Island 6 New London, Connecticut

i"iAproved for ub m m I ; db t an-- .

+!+/..80 2 6 021

Prefae

This report was prepared under the Ocean Measurements and Array Technology(OMAT) portion of the SEAGUARD Project sponsored by the Defense AdvancedResearch Projects Agency (ARPA Order No. 2976), Program Manager, R, Cook.Tactical Technology Office; NUSC Project No. A-6%-0. Program Manager, B.Cole.

The Technical Reviewer for this report was B. Cole, Code 3104.

REVIEWED AND APPROVED: 16 November 1979

Heatt Specia Pr~t Depotmt

The authors of' this report are located at the New LondonLaboratory, Naval Underwater Systems Center,

New London, Connecticut 06320.

REPORT DOCUMENTATION PAGE DFR OPEIGFR

LHEJ.FFECTS OF JWROSTATICJJPESSURE ON SYNTHETIC.

William A atkins LT. USN 6/ -o2 7 /9. PERFORMING ORGANIZATION NAMIE ANO AOORESS 10. PROGRAM ELEMENT. PROJECT, TASK

Naval Underwater Systems Center V, AREA 6 WORK UNIT'NUMVIIRS

New London Laboratory A660New London, CT 06320

11. CONTROLLING OFFICE MAMIE ANO ADDRESS____________

14. MONITORING AGENCY NAMIE G ADORESS(if dil lfeom Con~toIlng Office) IS. SECURITY CLASS. (of this report)

(A~ UNCLASSIFIEDso. OEC ASSIFrICATION/OOWNGRAOING

J SCi ULE

t4. OISTRIUUTION STATEMENT fol this Report)

Approved for public release; distribution unlimited.

I7. OlSIRIGUTION STATEMENT (of the abstrt en tered In Block 20. It differmnt from, Report)

14. SUPPLEMENTARY NOTES3

19. KE9Y WOROS (Continueo reverse od*e it nocoeay OW Iientlt' br block rnmbe)

Project SEAGUARD Bulk ModulusSynthetic Ropes Compressibility EffectsHydrostatic PressureBuoyancy

20. *04&FACT (Continue on revees side It necesar usW Identify by bleck mumber)ATests were conducted to determine the effect of hydrostatic pressure on

the buoyancy of a large diameter synthetic rope. This report presents theresults of those tests and discusses their meaning in terms of the compress-ibility effects of the rope material and the deep ocean environment.

00 'J*N"7 1473 am-not, air Nov Goisl OUGOLE0.1TES/111 0102-014-661 - .WO

TR 6115

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS.................. . . ..... . .... .. .. .. . . ..

INTRODUCTION..................... . .. ..... . . .. . .. .. .. .. .. 1

DESCRIPTION OF THEROPE SAMPLE........ ..... . .. . .. .. .. .. ...

TEST APPARATUS. ..... .......... .......... .... 3

TEST RESULTS. ..... .......... .......... ...... 3

DISCUSSION OF RESULTS. .. ......... .......... ...... 3

CONCLUSIONS .. .... .......... .......... ....... 7

REFERENCES .. ......... .......... ............ 10

APPENDIX -COMPUTATIONS. .. ......... .......... .... A-1

WCESSION forNTIS White SectionDDC Buff Section 0UNANOUNCED 0JUSTIFICATION

Tkst. AVAILado PC1

IM 6115

LIST OF ILLUSTRATIONS

Figure Page

1 Rope Sample Under Test .... ..................... . 2

2 Nodified Commercial Force Transducer ........ ......... 4

3 Physical Arraent for Testing .... ................... S

4 Buoyant Force Versus Pressure, No-Load Condition,Water Temperature at 18C, Force Transducer Alone ...... S

S Buoyant Force Versus Pressure, Pure Fresh WateratTemperature of 18"C ...... ... .. ... ... .. 6

6 Specific Gravity Versus Pressure, From Millero's Drta ...... 8

7 Buoyant Force in Sea Water Versus Pressure, DataCorrected Using Millero's Data for Salt and Fresh Water . . . 8

8 Buoyancy ?er Unit Length Versus Pressure in Sea Water(3S /oo at l C . . . . . . . . . . . . . . . . . . . . . . 9

A-I Graph Showing Compressibility of Water Greater ThanCompressibility of Rope With Increasing Pressure ....... .. A-4

ii

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THE EFFECTS OF HYDROSTATIC PRESSURE ON SYNTHETIC-ROPEBUOYANCY IN FRESH AND SALT WATER

I NTRODUCTION

In some deep-ocean applications, the use of buoyant rope to suspend arti-cles above the ocean bottom may be less expensive than the use of attachedbuoyancy modules (e.g., syntactic foams, glass balls, etc.).

To ascertain the feasibility of buoyant rope use, tests were conducted atthe David Taylor Naval Ship Research and Development Center (DTNSRDC), Annap-olis Laboratory. The tests were designed to determine the effect of hydro-static pressure on the buoyancy of a large-diameter synthetic-rope sampleunder no tensile load.

DESCRIPTION OF THE ROPE SAMPLE

The characteristics of the rope sample tested are shown in figure I andtabulated in table 1.

Table 1. Characteristics of the Rope Sample

Construction Multilayered braid

Material Multifilament polypropylene of specificgravity 0.91

Circumference 27 ca (1O.S in.) measured at a tensile load of200 x dia.2 (in in.) lbf

Buoyancy Calculated positive buoyancy of 0.477 newtons/u[0.447 newtons/m (0.3 lbf/ft) + 0.045 newtons/u(0.03 lbf/ft) - 0.01S newtons/u (0.01 lbf/ft)]in sea water over a temperature range of 0 to200C and under a tensile loadof 200 x dia.

2

(in in.) lbf

Minimum breaking strangth 564.89 x 103 newtons (217 x 103 lbf)

Sample length 13.675 m (44.9 ft) under a tensile load of

200 x dia.2 (in in.) lbf

Sample weight in air 49.02 kg (108.1 lb).

. , JL- ... ... . -: ;-- -.m ,it II J1

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TEST APPARATUS

To measure the buoyancy of the rope in water under pressure, a commercialforce transducer was modified by immersing the unit in mineral oil, as shownin figure 2. This arrangement maintained the electrical integrity of the unitin water at high hydrostatic pressures. Characteristics of the force trans-ducer are listed in table 2.

Table 2. Characteristics of the Force Transducer

Model Transducer incorporating an unencapsul atedlinear variable differential transformer(LVDT)

Range ±10 kg (±22.05 lb)

Sensitivity ±0.1 percent

The force transducer was supplied with a remote readout unit that pro-vided for excitation and readout display of ac-operated LVDT-type transducers.The readout displayed force in kg to the nearest tenth of a kg. The entiresystem was calibrated in air using known weights.

The vessel in which tests were conducted was the "B" pressure tank locatedat the DTNSRDC Deep Ocean Pressure Facility, Annapolis, Maryland. The ropesample and force transducer were housed in the pressure vessel, as shown infigure 3. To account for the effects of pressure associated with the forcetransducer itself, it was necessary to calibrate the unit. The force trans-ducer alone was placed in the pressure vessel and pressurized incrementally,going both up and down in pressure at 5-min intervals. This calibration, or"zero-shift" curve, shown in figure 4, was then used to correct the forcereadings obtained when the rope sample was tested under pressure.

TEST RESULTS

Following calibration of the force transducer, the rope sample and trans-ducer were placed in the pressure vessel in the configuration shown in figure3. The pressure vessel was flooded with water and the pressure was increasedat 5-min intervals. The measured force, pressure, and water temperature weremonitored over the entire pressure range. The measured force (buoyancy)versus pressure is plotted in figure 5 (the points labeled DATA).

DISCUSSION OF RESULTS

At zero pressure there is a large value of buoyant force, as shown infigure 5. At 100 lbf/in. 2 , the buoyant force drops significantly. This

3

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PRESSURE TANK

7-PINPENETRATOR

1I 5VREADOUT

INTERNAL ATTACHMENT TO UIDECK OF PRESSURE VESSEL

Figure 3. Physical Arrangement for Testing

5.04

IN PRESSURESGOING DOWN

IN PRESSURE

I~OWOO3600 4000 5000b 6000 7000 80 0 9040GAGE PRESSURE (Ibf/in.2)

Figure 4. Buoyant Force Versus Pressure, No-Load Condition, WaterToerature at 180C. force Transducer Alone

S

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'5.

14

13,

10. 0 COMPUTED

9

3 4 5 "7 8 9 1oPRESSURE (Ibf/in2 x I0 3 )

Figure 5. Buoyant Force Versus Pressure, Pure FreshWater at Tenperature of 180C.

initially high value is attributed to air trapped in the void spaces withinthe braided rope. On pressurization to 100 lbf/in.2, the trapped air isforced out of the voids and the buoyant force due to the material itself isrealized.

With increasing pressure the measured buoyant force increases. Thisresult can be explained by the fact that if the buoyant force is expressed bythe relationship

B = (r ) ' (1)

whore

B is the buoyant force in kilogram,

W is the rope air-weight in kilogram,

4w is the specific gravity of the water, and

r is the specific gravity of the rope,

6

TR 6115

then the only variables within the pressure vessel are the specific gravityof the water and the polypropylene rope.

The equation of state for fresh water based on sound-speed measurementsis given by Wang and Villero.1 Tabulated values of the specific volume ofsea water (35 e/..) as a function of pressure and temperature, determinedexperimentally, are given by Chen and Millero.2 Using these equations andtabulated data, the increases in specific gravity due to hydrostatic pressurefor fresh and salt water were computed. The results are shown plotted infigure 6 for 180C pure water and 180C 3S /.. sea water.

If the specific gravity of polypropylene is assumed constant, we can com-pute the buoyancy of the rope sample using equation (1) and figure 6. Theresults are plotted in figure 5 with the measured values. Although the valuesdo not agree exactly, the general increase in buoyant force with increasingpressure can be seen for both measured and computed values. At pressuresgreater than 3000 lbf/in.2, the trend of both values is in good agreement.

The measured and computed buoyant force values corrected for sea water(of specific gravity as shown in figure 6) are plotted in figure 7 versuspressure. In the computed case, the specific gravity of polypropylene againwas assumed to be constant. In both cases there is an approximate increaseof 20 percent in the buoyant force over the 100 to 9000 lbf/in. 2 pressureinterval. The measured and computed buoyant force values corrected to buoyancyper unit length in sea water as a function of pressure are shown in figure 8.Here, length is based on a tension value in pounds equal to 200 times thenominal rope diameter in inches squared.

CONCLUSIONS

The results presented in this report indicate that buoyant rope of con-struction similar to that tested would exhibit certain characteristics notreadily apparent if measured at 1 atm. Air entrapment wit;zin the rope willgive artificially high buoyant-force values if measured at 1 atm.

The compressibility effects of water and the rope material appear to besignificant. If the isothermal compressibility

B t(2)

where BT is the isothermal compressibility,

V is the specific volume, and

P is pressure,

of the water (fresh or salt) changes more rapidly than that of the polypro-pylene, one can expect increasing buoyancy at higher ambient pressures. This

7

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1.06

L0-

144

CL

V) 101 t0 SALT WATER1.004 AT 180C

0 PURE FRESH WATERAT 186C

8 9 10PRESSURE (Ibf/in. x 103)

Figure 6. Specific Gravity Versus Pressure, From tIillero's Data1

e DATAIs 0 COMPUTED USING

171 ~M IL L ERO'S DATA'

0 I5 8 9 1PRESSURE (Ibf/In. x 103)

Figure 7. Buoyant Force in Sea Water Versus Pressure, Data CorrectedUsing N~illero's Data1 for Salt and Fresh Water

Th6115

REFERENCES

1. D. P. Wang and F. J. M4Ilero, "Precise Representation of the P-V-T Proper-ties of Water and Sea Water Determined from Sound Speeds," Journal ofGeophysical Research 78, no. 30, 1973.

2. C. T. Chen and F. J. Millero, 'Me Specific Volume of Sea Water at HighPressures," Deep-Sea Research 23, no. 7, 1976.

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Appendix

CO0PUTATIONS

The definition of isothermal compressibility of a material is given by

BT !BVC )T (A-1)

where

BT is the isothermal compressibility,

V is specific volume,

P is pressure, and

T is temperature.

As an approximation, at constant temperature

B a IV - ) , (A-2)

where

V is the specific volume at pressure P0, and

V is the specific volume at pressure P.

The specific volume at some pressure, P, is given by

V a V0 - (BVO(P - Po) . (A-3)

The specific gravity of a material is given by

SG a 8 a - ina M/v (A-4)

where

p is the mass density of the material,

Pw is the mass density of an equivalent volume of water,

m is the mass of the material,

A-1

Th 6115

im is the Mass of the water, and

v is some unit volume.

Since specific volume, V, is given by

V.- (A-5)m

equation (A-4) becomes

1/vT7w

or

6 WV/V. (A-6)

The buoyancy, B, of a rope sample in water (fresh or salt) can be expres-sed as the difference between the weight of the rope and the weight of thewater displaced by the rope. Both weights must be measured in some commonmedium under identical conditions of temperature and pressure. Then,

B - weight of rope - weight of water displaced

a6 P V, - p V , (A-7)r wr www,

where VI is the volume of the rope and VI is the volume of the displaced water.r w

Since V' VI at a given temperature and pressure, thenr w

B = PwVI(6r- 6)

or

B 0 6 P ( 16r -6w) (A-8)

Lettifig the rope weight be given as

W a a V , (A-9)

r r wr

equation (A-$) becomes

*- (, -6w)1B Vr~ (ar~ * ~( 66w. & aw /6r) (A-10)

The force, F, sensed by the load cell is upward, in response to the upwardbuoyant force of the rope, throughout all pressures measured. Then

A-2

TR 611S

aF - B a W r - (A-i)

From equation (A-6),

V /V/8 " /V w • (A-12)

w wTr r

Substituting values from equation (A-12) into equation (A-li) gives

F a W(l - Vr/V) .(A-13)

Substituting in equation (A-13) values for the specific volumes from equa-tions (A-3) and (A-4) gives

Fu 1 i - / :I~j I- B~rj.. -P 0)]or

F Wr [ (m w/) I (- BT (P-P (A-14)

Let A * mw/m and

1 - BT (P - P0)

in equation (A-14). Then,

if A x C - 1, F a 0, and the rope is neutrally buoyant;

if A x C > 1, F < 0, and the rope is negatively buoyant; and

if A x C < 1, F > 0, and the rope is positively buoyant.

For all pressures tested the rope exhibited positive buoyancy. Thus,when P a P0 C - 1. Therefore, A - aw/ar > 1. Since N, and mr are constants,A > 1 for all pressures.

Consider FI, which is the force at P - P1 , and F2 , which is the force atP - P2" For all data, increasing pressure resulted in an increase in force.Therefore, for 14.7 lbf/in.2 < pl, P2

< 9000 lbf/in. 2 and P2 > P1 9 F2 > F1 > 0.Then, from equations (A-14) and (A-IS), F1 - Wr(l - AICI) and

A-3

Th 6115

F2 *Wr4l -A 2C2); but A, AV, thus Wr -W 1,AC2 Wr, W1.ACi, and C2 C1.

From equation (A-is),

1l-BTr(P2 -PO) 'l1B ( I -PO)(A16

1 - B (P2 PO) - TP1 - PO) *(-6

Since P2 > P1, then - o) > BT (P1 - Poand 1 - B(P 2 -O

2 Tr(2r Tr(B T, (P1 - P ).

If %<~ BT wand BT r, B w 0, then 1 - BT ("2 - PO) < 1 -BT(P1 - P)

and the inequality in equation (A-16) is true.

Therefore, the increasing force levels measured, indicating increasingbuoyancK with pressure (all trapped air considered negligible above 100lbf/in. ), imply that the compressibility of the water is greater than that ofthe rope with increasing pressure. Graphically this condition appears asshown in figure A-i.

hiT

U,00 00 T

hi0

PRESSURE

Figure A-1. Graph Showing Compressibility of Water Greater Than~Compressibility of Rope With Increasing Pressure

A-4

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