Ice Requirements for Chilled Seawater Systems

E. KOLBE, C. CRAPO, and K. HILDERBRAND

Introduction

Chilled Seawater (CSW) is becomingincreasingly popular in the United Statesfor the preservation of fish aboard cer­tain fishing vessels. Also called "slushice" and "the champagne system," CSWhas found recent application in severalfisheries, many of which make use ofportable tanks (200-2,000 I) aboardsmall inshore vessels (Dagbjartsson etaI., 1982; Hansen, 1982; Eddie andHopper, 1974). Larger-tanked CSW sys­tems aboard seiners and transportvessels may be even more common(Kelman, Undated).

Canadian researchers and fishermenhave done much to demonstrate anddevelop CSW on the North AmericanPacific coast. Flooded hold systemshave, for several years, been used onPacific salmon, Oncorhynchus spp.,

E. Kolbe is Associate Professor of AgriculturalEngineering, Department of Agricultural En­gineering, Oregon State University, Corvallis, OR97331. C. Crapo is Assistant Professor of SeafoodTechnology, Fishery Industrial Technology Center,University of Alaska, Pouch K, Kodiak, AK 99615.K. Hilderbrand is Seafood Technology ExtensionSpecialist, Oregon State University, HatfieldMarine Science Center, Newport, OR 97365.

ABSTRACT-This paper describes an an­alytical approach to estimate ice quantitiesrequired by fishing vessels using slush iceor chilled seawater (CSW) systems. The cal­culations specify ice required for differentvalues ofhold size, catch volume, and timeat sea, under varying conditions of watertemperature, hold insulation, and holdflood­ing strategy. Observations and measurementsrecorded during four trips on three differentsteel salmon packers were used to verify theprocedure and support several recommen­dations for CSW system operation.

47(4), 1985

transport vessels (or "packers") inCanada and, more recently, on bottom­fish draggers. Nearly all of these sys­tems use air, bubbled into the tanks froma grid of pipes on the tank or fish-holdfloor, to circulate cold water through themass of newly-loaded fish!. This basicdesign is increasingly being used in theAlaska fishing industry.

Adequate ice is necessary to chill thefish and water that will eventually floodthe hold (in most cases), and to main­tain low temperatures during the trip.One rule of thumb is to first fill the tankor hold 1/3 full of ice, then flood to thetop of the ice mass with water, and final­ly fill the tank with either fish or water(Dagbjartsson et aI., 1982; Kelman,Undated).

Canadian researchers have suggesteda formula l to aid in loading the correcttonnage of ice at the beginning of a trip.Commonly employed by U.S. CSWusers, the "Canadian Formula," in shorttons, is: TONS OF ICE NEEDED =(1/6) (MW + MF + TIME), where MW= tons of water to be chilled, MF =tons of fish to be chilled, and TIME =days duration of the trip.

In some cases the tank is first filledwith water and ice as the vessel awaitsthe loading offish; under most circum­stances, a full hold is necessary for ade­quate vessel stability. Excess water thenspills as fish are stowed in the tank.When operating in quiet water, a par­tially-filled tank may allow the operatorto load less ice, dump no water, andcompletely fill the tank or hold onlywhen it is time to begin the trip home.In these cases, the quantity of fish and

'Chilled sea water system data sheet. Undated (ca.1975). Techno!. Res. Lab., Can. Dep. Fish.Oceans, Vancouver, B.c. Unpubl. manuscr.

water (MW + MF) is taken as the cap­acity of the tank in short tons.

The Canadian Formula enables a ves­sel operator to get a generally conser­vative estimate of ice needs for typicalsummer British Columbia conditions,assuming a well-insulated hold (Gib­bard2). Subsequent experience thenallows the fisherman to adjust ice ton­nage to more closely match the needsas influenced by local conditions.

However, fishing conditions and CSWapplications in Alaska or California maydiffer substantially from those in BritishColumbia. Many boats are inadequate­ly insulated, thus requiring more ice dueto heat leakage into the hold during atrip. Conversely, sea, air, and fish tem­peratures in Alaska, for example, maybe lower during much of the fishingseason, thus calling for less ice thannecessary during summer months atlower latitudes.

This paper describes results of an an­alytical approach which enables one toproject ice usage for CSW systemsunder a variety of circumstances. Aseries of algebraic equations coupledwith appropriate simplifying assump­tions has been described in a BASICinteractive program operable on a per­sonal computer (see Appendix II). Theprocedure can evaluate the conse­quences of installing CSW withouthaving adequately insulated the hold,estimate ice expense saved when high­quality insulation is installed, project iceuse as environmental temperatures andfish volumes change, and, when condi­tions permit (e.g., aboard a docked pro­cessor vessel), investigate the effects of

2Gibbard, G. A. 1982. Personal commun. Form­erly with Techno!. Res. Lab., Can. Dep. Fish.Oceans, Vancouver, S.c.

33

The initial temperature of water addedto the tank, T(, would be the sea sur­face temperature. The final temperature,Tz, is the temperature of the CSW mix­ture, generally taken as -0.6°C (31°F),slightly below the ice-melt temperatureof O°C (32 OF) due to the salinity.

Based on recent measurementsaboard Oregon bottomfish trawlers, thisis also a good approximation for the ini­tial fish temperature prior to stowage inthe CSW tanks. While tests showed thatsome fish recently brought from theocean floor will be colder than the sea

operating at various fill-levels in thetank. A series of measurements aboardAlaskan salmon packers verified theanalytical procedure.

Model Development

The total tonnage of ice needed dur­ing any fishing trip must be adequate toserve four purposes: 1) Chill the ex­pected volume of fish, 2) absorb heatwhich leaks into the hold throughout thetrip, 3) absorb heat resulting from theenergy of bubbled air, and 4) chill sea­water taken aboard-first to "slush" theice (make a slurry into which fish canbe dumped), and then to fill the hold toa predetermined level. In most cases,the hold is completely ftlled to eliminatethe unbounded free water surface whichcan lead to capsizing of the vessel.

Ice Requirements forFish and Water

The mass of ice needed to cool fishor water to the final holding tempera­ture can be calculated from the follow­ing equation, written for the case offish:

Where MFCpfMIf

L

mass of fish added,specific heat of fish,mass of ice whichmelts,latent head of fusionfor ice,initial temperature ofwater added to tank,andfinal temperature ofthe mixture.

surface temperature, and that somelying on deck will be warmer due tosolar and air heating, the average ap­peared to be close to the temperature ofthe sea surface.

Ice Requirementsfor Heat Leakage

The mass of ice required to absorb theheat which leaks into the slush-ice tankduring the voyage can be calculated as:

(MID(L) = (U)(A) x(ToU! - T;n)(TIME) (2)

Where MIl mass of ice whichmelts,

L latent heat of fusionfor ice,

U an overall heat trans­fer coefficient,

A the boundary areathrough which heatis transferred,

ToU! external ambienttemperature,

T;n temperature of theslush ice mixture,

TIME = length of voyage.

The value for ToU! is assumed to equalthe sea surface temperature. This isbased on documentation of weather datafrom regions of Atlantic Canada whichindicated that for summer conditions,sea surface and air temperature averageswere quite similar (Merritt et aJ.3), anassumption verified by measurementstaken during the series of trips reportedbelow. The analysis ignored the fact thatengine room temperatures will be muchwarmer than those of the surroundingsea4• This is a reasonable simplificationsince the bulkhead separating the engineroom from the fish hold constitutes onlyabout 10 percent of the total boundaryarea3 and is typically insulated moreheavily than the other walls, floor, anddeckhead.

'Merritt, 1. H., E. Kolbe, and W. Robertson. 1983.Refrigerated storage of fish at sea with particularreference to thermal insulation. Unpubl. Res.Rep., Can. Inst. Fish. Techno!. Tech. Univ. NovaScotia, Halifax, 250 p.'Measurements during recent trips on Oregonbottornfish trawlers indicated engine room air tem­peratures of 18-39°C (65-102°F).

The total boundary area can be ex­pressed as a direct function of a cubictank volume:

A = (6) (V)(Z/3) (3)

Where A = the boundary area throughwhich heat is transferredand

V = tank volume.

However, holds or tanks which are notcubic in shape would have a greatersurface-to-volume ratio. Dimensions offishing boat holds compiled by Merrittet aJ.3 indicate that use of a coefficientof7.2 (rather than 6) in Equation 3 bet­ter describes the typical case; it is therelationship used in this analysis.

The overall heat transfer coefficientU accounts for thermal resistance ofthewall plus both inner and outer fluidftlms. However, resistances of the con­vective ftlms in water and wind will besmall compared with those of the wallsections and are thus neglected.

Our analysis has assumed three levelsof insulation for the representative wallsections shown in Figure 1 for the sidewalls and bulkheads of a 30 m (100-foot)steel vessel (Hanson, 1960; Merritt etaJ.3). Note that the "RESISTANCE"value given for each level in Figure 1is the reciprocal of the overall heat trans­fer coefficient U. Calculations to deter­mine these resistance values followedtwo procedures: For "Level I" and"Level 2" in which steel frames direct­ly contact inner and outer boundaries,the "Zone Method" outlined byASHRAE (1981); for "Level 3" inwhich insulation covers the ends of thesteel frames, an empirical method de­scribed by Munton and Stott (1978).

Heat LoadFrom Air Flow

To the quantity of heat leaking fromthe outside environment must be addedthe quantity of heat due to throttling ofcompressed air injected into the CSWmixture to effect circulation. This rateof heat addition is equivalent to the rateof energy supplied by the air pump.

The analysis first assumes the rate ofair flow to be 0.152 m3/minute (at 1atm and 21°C) per square meter of deck-

34 Marine Fisheries Review

Figure I.-Representative steel wall sections with calculated resistance values usedin the analysis of ice consumption.

bubbled air into a representative 30 m(lOO-foot) vessel having a hold volumeof 176 m3 (6,200 feet3) will be on theorder of om t/hour (0.08 short tons/hour).

Fill Strategies andEquation Development

As fish, water, and ice are added tothe tank, the heat balances that matchice with heat sources are coupled witha volume balance to ensure that allnecessary ingredients will fit into thetank. The analysis can select one ofthree cases for calculation: 1) Fill/Spill,2) Fill/No-spill, or 3) No-fill/No-spill.

Fill/Spill

In the Fill/Spill case, the tank is firstflooded to the top with water and ice.This ensures a stable vessel while oper­ating in the open sea before fish areloaded. This case will require the great­est tonnage of ice because it must in­clude a quantity to chill water that willbe dumped later.

Fill/No-spill

In this case, water is initially filled tothe level of the ice, creating a slush,after which fish are added. If the tankis not then full, more water plus thenecessary extra ice is added until thetank is full.

No-jill/No-spill

In rare circumstances, such as in adocked or anchored processing vessel,tanks can safely remain partially filled.In this case, water is first filled to thelevel of the ice to create a slush, andthen fish are added.

A summary of equations developedfor each of these fill strategies appearsin Appendix I.

Boundary Conditions

Throughout the calculation proce­dure, the program checks to ensure thatcertain boundary conditions are not ex­ceeded. One check warns if the volumeof the ice-water-fish mixture exceeds thetotal tank volume, a condition easilyreached when loading exc~ssive

amounts of fish.A second check warns if the volume

of the bulk-loaded ice exceeds the tank

7.9 mm STEEL PLATING

10.2em x 7.Gem x 7.9mmANGLE IRON FRAMES,SPACING = 53em

Air pressure required to overcomepipe friction and static head of water inthe hold is typically 35-48 kPa gage (5-7psig) I. Semi-empirical relationships(Baumeister and Marks, 1967) givepower into the air based on the requiredflow rate and supply pressure. The en­tire rate of energy supplied is assumeddissipated in the CSW tank. As an ex­ample, the rate of ice melt due to

~~~\19mm PLYWOOD~FIBERGLASS - LINEDTANK WALL

LEVEL 2-MEDIUM INSULATION

RESISTANCE = .657 m: K

URETHANE FOAM INSULATION

DENSITY RANGE = 24-40 kg/m 3

THERMAL CONDUCTIVITY = .025 mW

K

(ASHRAE, 1981)

LEVEL 3 MAXIMUM INSULATION

RESISTANCE = 2.933 m:K

head (0.5 standard foot3/minute persquare foot of deckhead) following Can­adian recommendations I. It next as­sumes deckhead area to be 30 percentof the boundary total, a figure represen­tative for vessel lengths in the range of25 m (80 feetp. These assumptions withEquation 3 can then indicate volumetricflow rate of air injected into the CSWtank.

LEVEL 1 - MINIMUM INSULATION

m 2 KRESISTANCE = .217 W

47(4), 1985 35

Table 1.-Specific volumes of loosely packed ice (fromFAO, 1975; Merrill, 1978). 11-,11 ~3 1 ~J ~U.J:JH'. 1'1 l-'hOGl-if·'l1"1 ru Cf.'tLCULAlE ICE. I~EOUJ r,CMENl S fOR CSW TAN" ED SYSTEMS

Type of ice Specific volume

Flake 2.1-2.3 m'll (67-74 feet'/short ton)LASE 2 FLLL/NO Sf'iLl.

'Collins, 1. 1983. Personal commun. Formerlywith Utilization Res. Lab., Northwest Alaska Fish.Cent., Nat!. Mar. Fish. Serv., NOAA, Kodiak,Alaska.6Lee, F. 1982. Personal commun. Formerly withTechno!. Res. Lab., Can. Dep. Fish. Oceans, Van­couver, B.C.

volume even before fish are added to thetank. Specific volumes (volume per unitmass) are given in Table I for varioustypes of ice. Excessive ice volumes canoccur when trips are long, tanks aresmall (and thus have high surface-to­volume ratios), and when insulation ispoor. Even if bulk ice volume does notexceed the tank volume, there may beproblems if so much ice were carriedthat inadequate space remained to ini­tially load a large volume of fish. Theprogram issues a warning if bulk icevolume exceeds 90 percent of the tankvolume.

Because an adequate chill rate of thefish will be achieved only if the bubbledair-driven cold water can circulate, athird check is on the fish packing dens­ity. If this is too great, it will preventadequate cold water circulation through­out the entire load. This analysis as­sumes a maximum permitted fish load­ing density of 670 kg/m3 (42 pounds/foot3), a value found by NationalMarine Fisheries Service researchers tobe valid for small tanks5. This is slight­ly lower than the value of 720 kg/m3

(45 pounds/foot3) given by Gibbardand Roach (1976) for refrigerated sea­water systems and used for large-tankedCSW systems as we1l2

.6

•

Calculation of Results

The analytical procedures describingice required under various conditionsand loading strategies have been writ­ten as a BASIC computer program (Ap-

H~NI' CAF'"(.'tC I 1'( J:] 1 N~)DELnJP, I L ru HOLD AL.L rHE F 1~3H f;:[(~U 1m:'D.rH( f'F':O[jf~Ar-1 HAS IKCF'<EASED THL 1NF'U r AI"IOUN r ClF FISH TO HE L(){~D[D.

Figure 2.-Sample output, representing the ice required for the center holdof Trip 4 (Table 4).

Results

Ice use rates, as well as data influ­encing these rates, recorded during thefour trips at sea appear in Table 3.

The schedule of air circulation wassimilar for each vessel and trip. Airblowers typically operated for 20-30minutes when the tank was first floodedwith water, then for about 10 minuteseach time a load of fish was added froma catcher vessel. Total air pumping timeranged from I to 3 hours per day. (This

istor sensing probes was placed in fishand water as loading proceeded. Thequantity of ice loaded at the trip startwas reported by the supplier of ice tothe vessel. The ice remaining at the endof the trip was an estimate based on thenumber of totes (boxes) filled with un­melted ice plus, in some cases, judge­ment of the vessel operator on theamount left aboard after draining thetanks.

All three vessels had commerciallyinstalled air blower and distribution sys­tems layed out in general agreementwith Canadian recommendations l . Alltravelled to areas having relatively quietwater before loading fish; all ended tripsby first draining tanks before returningto home port through unsheltered water.The vessels differed in hold size, lay­out, and insulation characteristics, andgeneral description of each is given inTable 2.

56 FI I ~j:;'~ CUD) C FEEl

::;:'1. ~, reIN!::;:::' DAYS:~ HOUf<SMJN;'. 1 lON!=:,?/ rONSO. I TONS

1.2 IONS7.? "ONS

Lt.1 [ r I f4l Of Et'IPEr...;H r UF.;[lANI VOLUME:r I bH 1 [J DE LO(4DEDNUMUl:..k or D"y'~j I 0 Ell-. HLLDflCJur-:s r'u, l)(-'lY OF Alf, BUrll:ILINGA::JSUMLD 11\l::;UU'l1 I LJN U:-'v'f IICE. MLL I Ff,OM r lS11lel MELI fROM IilAI tLAI-1L1:: ME.1. 1 F f,lJrl !:lUD8LED I·) t HrI~l MLL I I h:OM W~ I Eh: ADO[ I)

I Lli (~L LCE f,~.()U [1,[:1..>~" ·I-'h'O x r~'LFiCLN 1ACiL m I f·)NI'

UCCUF-' l CD i:lY LJf,yUULJ -I DfHH DIU.

7Mention of trade names or commercial ftnns doesnot imply endorsement by the National MarineFisheries Service, NOAA.

pendix II). Using thermodynamic valuesfrom ASHRAE (1981, 1982), and as­suming the use of flake ice (Table 1),the program allows the user to select in­sulation level, loading strategy, andother operating parameters to generatean output similar to that shown in Fig­ure 2. In this example, an attempt wasmade to in?ut 22.5 short tons (20.4 t)of fish to simulate the loading rate ob­served during a summer trip in Alaskanwaters. Because this exceeded the al­lowed packing density, the program hasadjusted the fish tonnage to maximumcapacity and has printed an appropriatemessage.

Methods and Materials

Four trips were made during summer1984 on three CSW salmon packersoperating out of Kodiak, Alaska. Thesetrips provided opportunities to observeprocedures, estimate ice use rates, andmeasure significant temperatures andchill rates aboard vessels having dif­ferent levels of insulation. These dataallow a comparison of observed ice re­quirements with those predicted usingthe calculations described.

Temperatures were recorded manual­ly using a YSI Telethermometer Model42-SC (Yellow Springs InstrumentCo.?). Typically, an array of nine therm-

1.6-2.0 m'll (51-64 feet'/short ton)

1.7-1.8 m'll (55-58 feet'/short ton)

1.4-1.6 m'lt (45-51 feet'/short Ion)

Plate

Tube

Crushed block

36 Marine Fisheries Review

'As reported by vessel operator.'Forward hold-not loaded with fish.'Center hold.'Aft hold.

Recorded values Computer Calculations

Ice Fiillevel Fill level Ice AssumedTrip no. and used after load- after load- used insulation

vessel (letter) (t) ing (0/0) ing (%) (t) level (Fig. 1)

l(A) 7.5-8.4 60 42 6.8 Medium60 '8.1

2(A) 5.5-6.4 60 46 6.1 Medium60 '7.4

3(B) 10.0-10.9 100 100 11.8 Maximum100 '11.0

4(C)Fwd. hoid 82 19 3.0 MinimumCtr. hold 5.5-6.4 100 100 6.6 MinimumAft hold 3.6 80 47 2.6 Medium

80 '3.3

'Corrected value.

47(4), 1985

Fish loaded (t) 22.7 26.8 51.8Ice loaded (t) 13.9 9.1 16.4Est. ice remaining

at trip's end (t) 5.5-6.4 2.7-36 5.5-6.4Est. ice used (t) 7.5-8.4 5.5-6.4 10.0-10.9Fill level of tank

after ioading (%) 60 60 100

1 2 3Item A A B

Trip length, days 3 2 1.5Avg. SST (DC) 12.8 11.7 12.2Avg. air temp. (DC) 12.8 12.8 13.3Core temp. of several

fish before loading (DC) 133-15.6 12.8-15.0 13.3-16.7

'Operation of "Champagne" systems. Tech. Inf.Bull. 80-1 (unpubl.). Technol. Servo Branch, Dep.Fish. Oceans, Environ. Can. 5 August 1980.

period of air bubbling is shorter thanthat generally recommended from theCanadian experience2

,8). Additional ob­servations specific to individual trips aregiven below.

Trip 1

The 15 compartments within the holdof Vessel A were not initially fllied withequal quantities of ice. Several had noice remaining at the end of the trip, al­though CSW temperatures appeared tostay close to O°C (32OF) owing to watercirculation between compartments.

37

Trip 2

The loading and air pumping sched­ule for Vessal A was similar to that forTrip 1. Before the start of this trip, thevessel operator separated the bin boardsslightly, enabling better circulation ofcold water between the 15 compart­ments. This improvement, plus betterinitial ice distribution, led to unmeltedice remaining in each compartment attrip's end.

Trip 4

Vessel C's uninsulated forward hold,not loaded with fish, had no tempera­ture probes so meltwater temperature attrip's end was unknown. Both fish andice were poorly distributed in the centerand aft tanks. Although some ice re­mained in the center tank at trip's end,it was all massed at one corner. Also,a small volume of chilled water wasdumped from the center tank as the finalfish loading took place. Temperatures inboth tanks holding fish (center and aft)were uneven throughout the trip.

Comparisons

Table 4 compares recorded ice userates with values calculated both withthe analysis described above and withthe Canadian formula. In addition to theinfluencing conditions reported aboveand data given in Table 3, the analysisused bulk ice volumes for flake ice, andan air pumping schedule of 2 hours perday.

The analysis for the case of partially-5.95.95.3

100 15.7

100 15.2

100 150

100100100

Calculations fromCanadian formula

Fill level Iceafter ioad- used

ing (%) (t)

Insulation'

20 em (8 inches) of urethane foamon sides, floor, lazaret bulkhead,and deckhead; 30 em (12 inches)of urethane foam on the engineroom bulkhead. Insulation undercenter floor sump is unknown.

15 em (6 inches) of urethane foamon all boundaries, including areaunder center sump.

Except for tank liner and enclosedair space there was no insulationon boundaries of the forward andcenter holds. Boundaries of the afthold had 15 em (6 inches) of ure­thane foam.

4C

212.8-13.312.2·18.3

128-16.7

Forward Center Afthold hold hold

0 20.5 8.68.2 8.2 7.3

0 1.8-2.7 3.68.2 5.5·6.4 3.6

100 80

Tank layout

Each of three holds is separatefrom the other. None of the holdshad separating boards or parti­tions.

Bin boards to a height of 1.2 m(4 feet) Irom the floor separate onehold into smaller sections.

Fiberglass partitions or bin boardsseparated one hold into smallercompartments, each approximate·Iy 2.1 m (7 leet) high, and eachhaving air supply pipes on thefloor.

feet'

3,200

3,037

'1,152'1,15241,024

Table 3.-0bservatlons during four trips at sea.

Trip no. and vessel (letter)

Table 4.-Recorded and calculated ice use rates.

Tankedhold volume

86

m'

90.9

'32.6'32.6429.0

Table 2.-Characteristics of vessels A-C used in trips 1-4.

82

75

75

feet

Length

25

22

m

22

4

1,2

Tripno.

3

C

B

A

Vessel

filled tanks (No-fill/No-spill) assumesfish to be loaded at the maximum allow­able density, or minimum volume ofwater and ice. However for trips 1, 2,and 4 (aft hold), the operator loadedmore ice and more seawater than neces­sary to achieve this maximum density,thus filling the tank fuller than thecalculations would indicate. If the cal­culated "Fill level after loading" is cor­rected to match observed levels by add­ing seawater and the necessary extra iceto chill it down, the results (Table 4)allow comparison of calculated values("corrected") with observed values atthe same tank fill level.

Similarly, the analysis for the filledtank of trip 3 assumed that no unmeltedice remained at the end of the trip. Infact, unmelted ice did remain, occupy­ing a volume that the analysis assumedwas occupied by chilled water. The cor­rected value shown (Table 4) resultedfrom subtracting the amount of ice re­quired to chill a volume of water occu­pied by the observed excess ice.

Discussion

Perhaps the greatest uncertainty incalculating ice consumption lies in esti­mating the heat which leaks into thehold during a trip. This is because thesecalculations depend strongly on severalfactors which may be unknown by thevessel operator-perhaps the second orthird owner of the vessel-or which arehighly variable during a trip. Examplesinclude:

1) Nature of the fish hold boundarystructure (e.g., frame spacing; connec­tions between hold liner and frames;presence and thickness of concretefloor; deck covering; nature of pene­trating structure like piping, manholes,and stanchions) and type, thickness,quality, or existence of insulation;

2) Nature and degree of separation ofadjacent compartments (e.g., warm fueltanks or net lockers, hot engine room,additional cold CSW tanks);

3) Area of the hold or tank boundary;4) Level to which the flooded CSW

38

tank is filled;5) External heat transfer film coeffi­

cients-generally low and variable withwind speed if in air, and high if the sur­face is hit by spray or is below thewaterline;

6) External sea temperature and airtemperature which may vary from dayto day or from day to night; and

7) Solar load on the deck or wall ofthe vessel.

Despite these uncertaInties and theapproximate nature of some observa­tions documented in Table 3, the predic­tion of ice consumption shown in Table4 for these documented trips at sea areclose to recorded values. The predictedconsumption in the uninsulated forwardhold of Trip 4 shows the poorest agree­ment with the observed result. Thishold, which was unused, uninsulated,and adjacent to the engine room, ob­viously had much worse heat leakagerates than what was described using theresistance value for the "minimum"level of Figure 1. Structural penetrationsand an uninsulated shaft tunnel couldaccount for most of this difference.

Although good insulation was re­ported by the operator of vessel A (Trips1 and 2), the use of "medium" ratherthan "maximum" insulation resistance(Fig. 1) provided a closer calculation ofthe ice consumption rate. Again, undoc­umented structural penetrations wouldhave decreased the effective boundarythermal resistance.

As shown by Table 4, the CanadianFormula did not match observed resultswell at all. This was expected becauseit was not intended for these situations.

The example calculation of Figure 2presents values (in British units) corre­sponding to ice consumption in thecenter hold of Trip 4 and gives relativequantities for the different heat sources.With the short air bubbling periods ex­perienced on these trips, expected iceconsumption due to injected air isminor.

For most calculations using the "max­imum" insulation level, ice consump-

tion due to heat leakage is a minor frac­tion of the total. It is with less efficientinsulation, as considered in the exam­ple of Figure 2, that heat leakagebecomes significant and uncertaintiesmore important. Research to gain a bet­ter understanding of thermal resistancesof fish hold boundaries is presentlyunderway at the Department of Agricul­tural Engineering, Oregon State Univer­sity, Corvallis.

Acknowledgments

This work is a result of research spon­sored by the Office of Sea Grant,NOAA, U.S. Department of Com­merce, under Grant NA8IAA-D-00086,and by The University of Alaska FisheryIndustrial Technology Center, Kodiak,Alaska.

Literature Cited

ASHRAE. 1981. Handbook of fundamentals. Am.Soc. Heating, Refrigerating, Air ConditioningEngr., Atlanta,. Ga., 926 p.

____ . 198L. HandbooK of applications.Am. Soc. Heating, Refrigerating, Air Condi­tioning Engr., Atlanta, Ga., 706 p.

Baumeister, T., and L. S. Marks (editors). 1967.Standard handbook for mechanical engineers.McGraw-Hill, N.Y., seventh ed.

Dagbjartsson, B., G. Valdimarsson, S. Arason.1982. Icelandic experience in storing fish inchilled seawater, p. 233-242. In Advances inthe refrigerated treatment of fish. Proc. Int. Inst.Refrig. Conf., Boston.

Eddie, G. c., and A. G. Hopper. 1974. Contain­erized stowage on fishing vessels using chilledsea water colling, p. 69-74. In R. Kreuzer(editor), Fishery products. Fish. News BooksLtd., Surrey, Eng!.

FAa. 1975. Ice in fisheries. FAa Fish. Rep. 59,Rev. 1,57 p. Food Agric. Organ., UN., Rome.

Gibbard, G. A., and S. W. Roach. 1976. Stand­ards for an R.SW. system. Environ. Can., Fish.Mar. Servo Tech. Rep. 676, Vancouver, B.c.,12 p.

Hansen, P. 1982. Containers for chilling, stowageand transport of fresh fish in ice water, p.251-258. In Advances in the refrigerated treat­ment of fish. Proc. Int. Inst. Refrig. Conf.Boston.

Hanson, H. C. 1960. Steel and wood scantlingtables (west coast of USA), p. 137-145. In J.Traung (editor), Fishing boats of the world, vo!.2. Fish. News (Books) Ltd. Lond.

Kelman, 1. H. Undated. Stowage of fish in chilledsea water. Torry Advisory Note 73, 10 p.

Merritt, 1. H. 1978. Refrigeration on fishingvessels. Fish. News Books Ltd., Farnham, Sur­rey, Eng!. Rev. ed., 161 p.

Munton, R., and 1. R. Stott. 1978. Refrigerationat sea. Second ed., App!. Sci. Pub!. Ltd.,Lond., 238 p.

Marine Fisheries Review

Appendix I

Relationships for the mass of ice re­quired to chill fish and to absorb heatleakage from the warm sea and air am­bient are presented in Equations (l) and(2) respectively. The mass of ice re­quired to absorb the energy of bubbledair is represented by the followingequation:

cupying the available volume in thetank, depends upon the fill strategy, asoutlined in the report. The additionalequations corresponding to these fillstrategies appear below.

Fill/Spill

The mass of ice required to chill wateroriginally added to flood the tank isgiven by:

v,

T,

(6)

(5)

Pf

MF

Fill/No-spill

In this case the volume occupied byanticipated ice, water, and fish is firstcalculated by Equation (6). The com­puter routine adjusts quantities up ordown to achieve a balance. The ice re­quired for added water then results fromEquation (7).

No-fill/No-spill

An estimated volume is first calcu­lated using Equation (6); ice quantity foradded water follows from Equation (7).But for this case, there is no concern tobalance the volume to completely fIll thetank.

VP

where 0.08 = ice consumption rate (inshort tons/hour) in a typical 30 m(lOO-foot) vessel; and 6,200 = a typicalhold volume (in feet 3) of the same ves­sel. Other symbols are defined in Ap­pendix Table 1.

The additional ice required to absorbthe heat of added seawater while oc-

Appendix Table 1.-Symbols used In Equations (4)through (7).

MIa = (0.08)(V/6,200)2/3(TIME)(TAIR) (4)

Cpw = Specific heat of seawater.L = Latent heat of fusion of ice.MF = Mass of fish.MI. = Mass of ice required to absorb bubbled air

energy.Mi, Mass of ice required to cool stowed fish.Mi, = Mass of ice required to absorb heat leakage.M/w = Mass of ice required to cool added water.T, = Initial temperature of fish or water before

stowage.= Final temperature of fish and water in CSW

tank.= Hours per day that air is pumped.= Duration of holding period in CSW tank.= Specific volume of bulk loaded ice (see text

Table 1)."" Tank or hold volume.= Partial volume occupied by fish/ice/water mix­

ture in the "Fill/No-spill" and "No-fill/No-spill"cases.

= Density of ice particles.= Density of seawater.~ Average density of fish flesh.

TAIRTIME

vVP

P,

P

P~

47(4), 1985 39

Appendix II

This Appendix describes "SLUSH,"a computer program which calculatesice required in chilled seawater (or slushice) fish holding systems.

Holding fish in flooded-tank chilledseawater (CSW) systems provides sev­eral benefits. One is elimination of theneed to shovel and distribute ice throughthe volume of bulk-loaded fish. Anotheris enabling rapid chilling of fish, es­pecially significiant when large catchesare brought aboard. A third is providingbuoyancy to the fish and thus avoidingcrushing that can occur in bulk-loadediced fish systems.

Several conditions affect the successof these CSW systems. One is that theoperator be aware of the vessel instabil­ity risks associated with partially-filledtanks. Another is that the bubbled airsystem normally used to bring aboutadequate circulation of cold waterthrough the newly-loaded fish be prop­erly designed and installed. And a thirdcondition is that the operator use suffi­cient ice and avoid overloading the tankswith fish. Use of program SLUSH ad­dresses this last condition and enablesthe user to learn how predicted ice con­sumption will vary with:

1) Fish hold or tank volume,2) level of insulation in the bound­

aries,3) filling strategy (whether the tank

will be full or partially full),4) seawater temperature,5) amount of fish to be loaded,6) length of time fish is to be held,

and7) length of time air is bubbled into

the tank.

The program in BASIC language ap­pears as Appendix Table 2 at the end ofthis section. It is "interactive," whichmeans that the user enters informationin response to questions which appearon the screen, and it requires a printer,since output appears both on screen andon printer. Input and output values areexpressed in British ("Inch-Pound")units.

Program Operation

To operate the program, the user must

40

enter information in response to requestsappearing on the screen. The requestswith required information arc:

OCEAN TEMPERATURE (in OF). Theexpected sea surface temperaturedescribes not only the warm seawaterthat will be chilled by ice in the hold,but also the approximate temperatureof fish to be chilled.

HOLD OR TANK VOLUME (in feet3).

NUMBER OF DAYS ICE WILL BE INTHE TANK.

NUMBER OF HOURS PER DAYBUBBLED AIR IS TO CIRCU­LATE.

CASE NUMBER TO BE CALCU­LATED, whereCASE 1 IS FOR FILL/SPILL,CASE 2 IS FOR FILL/NO-SPILL,CASE 3 IS FOR NO-FILL/NO­SPILL.FILL/SPILL refers to a tank that isfirst filled to the top with sea waterand ice before any fish are loadedaboard. This is the usual case wherevessel stability dictates that the tankmust ref.1ain full at all times. As fishare loaded, cold water is spilled­overboard or to another tank.FILL/NO-SPILL refers to a tank thatis loaded with fish, water, and ice insuch a way that the tank is full at theend of loading. In this case a partially­filled tank is tolerated during loading;no cold water is spilled.NO-FILL/NO-SPILL refers to a tankthat can be filled to whatever level isnecessary to exceed the minimumallowed fish loading density-con­sidered by the program to be 670kg/m3 (42 pounds/foot3).

INSULATION DESCRIPTION ASMIN, MED, OR MAX, where'MIN' DESCRIBES A TANK HAV­ING ESSENTIALLY NO ("mini­mum") INSULATION,'MED' DESCRIBES A MARGIN­ALLY ("medium") INSULATEDTANK, and'MAX' DESCRIBES A WELL-IN-

SULATED ("maximum") TANK.The levels represented by these three

descriptors appear in Figure 1 in themain text. Values of U, the overall heattransfer coefficient, were calculated fortypical bulkhead and sidewall construc­tion of a 30 m (lOO-foot vessel).

TONS OF FISH TO ~E ADDED TOTHIS CSW TANK.

Program Output

For each case, program output willappear on the printout sheet; Figure 2in the main text presents an example ofthis output.

During calculation, the programchecks to see that certain limits are notexceeded, and if they are, issues a warn­ing. These warnings include the follow­ing:

WARNING: FISH LOADING DEN­SITY EXCEEDS MAXIMUM AL­LOWED VALUE OF 42 LBM/FTI.TRY LOADING LESS FISH.

Experience has shown that filling thetank more than about two-thirds full offish will prevent the bubbled air frompromoting adequate water circulation.The result is that fish in the center aretoo slowly chilled. If the user enters anexcessive mass of fish for the tank, theprogram will print the above warning onthe screen and then await a new valueof "TONS OF FISH TO BE ADDED".

WARNING: INITIAL BULK ICEVOLUME EXCEEDS TANK VOL­UME BY - %. TRY BETTER INSU­LATION OR LESS FISH.

In a few circumstances of small tanks,poor insulation, or overloading, calcu­lations indicate a required amount of icehaving a bulk volume which is simplygreater than the volume of the tank.When this happens, the above warning(or one similar, depending on the fillstrategy being considered) appears onthe screen, then returns to await newvalues of insulation level and fish. Theprogram presently assumes the use of"flake ice" having a specific volume of2.1 m3/t (67 feet3/short ton).

WARNING: INITIAL BULK ICE

Marine Fisheries Review

VOLUME EXCEEDS 90% OF TANKVOLUME. MAY HAVE DIFFICULTYLOADING INITIAL CATCH.

This message, which appears on theprinter for Case 1 (FILL/SPILL) warnsif the initially-loaded ice exceeds 90 per­cent of the volume (but occupies lessthan the full tank volume). If this oc­curs, the crew will have difficulty load­ing fish until sufficient ice melts to pro­vide the space. The program does notreturn for new input in this case, butcontinues on; the message appears withthe printed output.

TANK CAPACITY IS INADEQUATE

TO HOLD ALL THE FISH RE­QUIRED. THE PROGRAM HAS DE­CREASED THE INPUT AMOUNTOF FISH TO BE LOADED.

Calculations in Case 2 (FILL/NO­SPILL) automatically balance either thevolume of fish or the amount of addedwater to arrive at a full tank. If theamount of fish was automatically de­creased, the above printed message ap­pears with the output of Case 2. If water(plus the required ice) is added to ar­rive at a full tank, the following mes­sage appears with the printed output:EXTRA WATER HAS BEEN ADDEDTO FILL THE TANK.

Appendix Table 2.-Program listing.

PROGRAM HAS ADDED EXTRAWATER AND ICE TO REDUCE FISHPACKING DENSITY TO AN AC­CEPTABLE VALUE.

The amount of water initially used incalculations for Case 3 (NO-FILL/NO­SPILL) has a volume equal to the voidswithin the bulk ice-that is, the wateris filled to the level of the ice. If thevolume of fish loaded exceeds the max­imum loading density of 670 kg/m3 (42pounds/feet3) in this partially-filledtank, the program adds more water (plusice to chill it), and prints the abovemessage with the calculation results.

10 'PROGRAM SLUSH VERSION 7/118530 'THIS PROGRAM CALCULATES ICE REQUIREMENTS IN CSW TANKS40 E. KOLBE50 OREGON STATE UNIVERSITY60 SEA GRANT EXTENSION70 'Begin program by defining variables that are unlikely to change.71 'Note that all quantities are in British units.80 CF = .85 'Specific heat of fish90 CW = .964 'Specific heat of sea water100 LI = 144 'Latent heat of fusion of ice110 RHOW = 64 'Density of seawater120 RHOI = 57.5 'Density of ice130 RHOF = 64 'Density of fish140 MIN .811 'Thermal transmittance for uninsulated wall, Btu/hr-ft2·F150 MED .268 'Thermal transmittance for partialily160 'insulated wall. Btu/hr-ft2-F170 MAX .06 'Thermal transmittance for well-insulated wall (Btu/hr-ft2·F)180 CLS190 PRINT "THIS IS 'SLUSH', A PROGRAM TO CALCULATE ICE REQUIREMENTS FOR

CSW TANKED SYSTEMS"200 LPRINT210 LPRINT220 LPRINT "THIS IS 'SLUSH'. A PROGRAM TO CALCULATE ICE REQUIREMENTS

FOR CSW TANKED SYSTEMS"230 PRINT240 PRINT "SPECIFIC HEAT OF FISH ";CF;"BTU/LBM-F"250 PRINT "SPECIFIC HEAT OF SEA WATER ";CW;"BTU/LBM-F"260 PRINT "HEAT OF FUSION OF ICE ";L1;"BTU/LBM"270 PRINT "DENSITY OF SEAWATER ";RHOW;"LBM/FT3"280 PRINT "DENSITY OF ICE ";RHOI;"LBM/FT3"290 PRINT "DENSITY OF FISH ";RHOF;LBM/FT3"300 PRINT "THERMAL TRANSMITIANCE,MIN. INSULATION ";MIN;"BTU/HR-FT2·F"310 PRINT "THERMAL TRANSMITIANCE,MED. INSULATION";MED;"BTU/HR-FT2-F"320 PRINT "THERMAL TRANSMITIANCE,MAX. INSULATION";MAX;"BTU/HR-FT2-F"330 'Next define variables that will change only under program development340 TF,j 31 'Final temperature of slush ice mixture, Fahrenheit350 D = 42 'Maximum allowed fish loading density, Lbm/Ft3360 VOLBKLlCE = 67 'This is the volume (Cubic feet per ton) of dry bulk flake ice370 PRINT380 PRINT "CSW TEMPERATURE ";TF;"F"390 PRINT "MAXIMUM PERMITIED FISH PACKING DENSITY";D;"LBM/FT3"400 PRINT "SPECIFIC VOL OF DRY BULK-LOADED ICE ";VOLBLKICE;"FT3/TON"410 PRINT420 PRINT430 'Now define variables that may vary with each case440 INPUT "TYPE IN OCEAN TEMPERATURE, IN DEGREES FAHRENHEIT";TI450 PRINT460 INPUT "TYPE IN HOLD OR TANK VOLUME, IN CUBIC FEET"; VTOT470 PRINT480 INPUT "TYPE IN THE NUMBER OF DAYS ICE WILL BE IN THE TANK";TIME490 PRINT491 INPUT "TYPE IN THE NUMBER OF HOURS PER DAY BUBBLED AIR IS TO

CIRCULATE";TAIR492 PRINT

47(4), 1985

500 PRINT "IF CASE 1 IS FOR FILUSPILL:'510 PRINT" CASE 2 IS FOR FILUNO-SPILL:'520 PRINT" CASE 3 IS FOR NO-FILL/NO-SPILL:'530 PRINT531 INPUT "TYPE IN THE CASE NUMBER TO BE CALCULATED";CASE538 LPRINT539 LPRINT540 LPRINT541 LPRINT "CASE";CASE;542 IF CASE = 1 THEN LPRINT "FILUSPILL:'543 IF CASE = 2 THEN LPRINT "FILUNO-SPILL:'544 IF CASE = 3 THEN LPRINT "NO-FILUNO-SPILL:'545 LPRINT550 PRINT560 PRINT "IF 'MIN' DESCRIBES A TANK HAVING ESSENTIALLY NO INSULATION"580 PRINT" 'MED' DESCRIBES A MARGINALLY INSULATED TANK,"590 PRINT" 'MAX' DESCRIBES A WELL-INSULATED TANK,"600 PRINT610 INPUT "TYPE INSULATION DESCRIPTION AS MIN, MED, OR MAX";U$620 IF U$ = "MIN" THEN U = MIN621 IF U$ = "min" THEN U = MIN630 IF U$ = "MED" THEN U = MED631 IF U$ = "med" THEN U = MED640 IF U$ = "MAX" THEN U = MAX641 IF U$ = "max" THEN U = MAX650 PRINT660 INPUT "TYPE IN THE TONS OF FISH TO BE ADDED TO THIS CSW TANK"; MF670 IF MF'2000IVTOT <= D GOTO 740680 PRINT"690 PRINT "WARNING FISH LOADING DENSITY EXCEEDS MAXIMUM ALLOWED

VALUE OF";700 PRINT D; "LBM/FT3"710 PRINT "TRY LOADING LESS FISH"720 PRINT"730 GOTO 660740 PRINT750 PRINT760 MIFISH = MF'CF'(T1-TF)/LI 'Total ice melt for fish770 MILKDA = .0864·U·VTOTl.6678·(TI-TFJ/LI 'Ice melt per day for heat leak780 MILEAK = MILKDA'TIME781 MIAIR = .08·((VTOT/6200lt.667)"TAIWTIME 'Ice melt per trip due to air790 ON CASE GOSUB 1110.1370.1700860 L PRINT "INITIAL TEMPERATURE ";TI;"F"870 LPRINT "TANK VOLUME ";VTOT;"CUBIC FEET"880 LPRINT "FISH TO BE LOADED881 LPRINT USING "###.#";MF;882 LPRINT" TONS"890 LPRINT "NUMBER OF DAYS TO BE HELD ";TIME;"DAYS"891 LPRINT "HOURS PER DAY OF AIR BUBBLING ";TAIR;"HOURS"900 LPRINT "ASSUMED INSULATION LEVEL910 IF U=MIN THEN LPRINT "MIN"920 IF U=MED THEN LPRINT "MED"930 IF U=MAX THEN LPRINT "MAX"

(Continued on next page.)

41

Appendix Table 2. continued.

940 LPRINT "ICE MELT FROM FISH950 LPRINT USING "##.#";MIFISH;960 LPRINT" TONS"1000 LPRINT "ICE MELT FROM HEAT LEAK1010 LPRINT USING "##.# "; MILEAK;1020 LPRINT" TONS"1021 LPRINT "ICE MELT FROM BUBBLED AIR1022 LPRINT USING "##.#"; MIAIR;1023 LPRINT" TONS"1030 ON CASE GOSUB 1300, 1630, 19501040 VOUCE ~ VOLBLKICE'MI'100IVTOT1050 LPRINT ''APPROX PERCENTAGE OF TANK ..1060 LPRINT" OCCUPIED BY DRY "1070 LPRINT" BULK-LOADED ICE1080 LPRINT USING "###"; VOUCE1081 CLS1082 PRINT ..

1083 PRINT1084 PRINT" IF YOU'RE FINISHED RUNNING CASES,"1085 PRINT"TYPE 'CANCEL: (WANG) OR 'CONTROL - BREAK' (IBM)"1086 PRINT1087 PRINT .. •• .. • .. •••••••••••••• .. ••••••••• ..1088 PRINT1089 PRINT1090 GOTO 4401091 STOP1092 END1100 END1110 'Case 1 is for continually flooded tank; cold water spilled as fish added1120 MIWATVOL = (RH01/2000 - (MILEAK + MIAIR + MIFISH)IVTOTj I (1 +

(RHOI'U)/(RHOW'CW'(TI -TF») 'Mass of ice per unit volume to chill water1130 MIWAT = MIWATVOL'VTOT1140 MI = MIFISH + MILEAK + MIAIR +MIWAT1150 IF VOLBLKICE'MI <= VTOT GOTO 12101160 PRINT ..1170 PRINT" WARNING: INITIAL BULK ICE VOLUME EXCEEDS TANK VOLljME BY'"1171 PRINT USING "###."; (VOLBLKICE'MI-VTOTjIVTOT"100;1172 PRINT" %"1180 PRINT" TRY BETTER INSULATION OR LESS FISH."1190 PRINT ..1200 GOTO 5601210 IF VOLBLKICE'MI <= .9·VTOT GOTO 8601220 LPRINT "1230 LPRINT "WARNING: INITIAL BULK tCE VOLUME EXCEEDS 90% OF TANK

VOLUME,"1240 LPRINT" MAY HAVE DIFFICULTY LOADING INITIAL CATCH."1250 LPRINT "1260 GOTO 8601300 LPRINT "ICE MELT FROM WATER ADDED1310 LPRINT USING "##.#"; MIWAT;1320 LPRINT "TONS"1330 LPRINT "TOTAL ICE REQUIRED1340 LPRINT USING "##.#";MI;1350 LPRINT" TONS"1360 RETURN1370 'Case 2 is for an ultimately flooded tank; no water is spilled1380 'as fish is added1384 VOLPRIME = (VOLBLKICE'(MILEAK+MIAIR+MIFISH)'U)/(U+(RHOW/RHOI)'CW'

(TI-TF)-(VOLBLKICE/2000)'RHOW'CW'(TI-TF»1385 MIWAT = ((RHOW'CW'RHOI'(TI-TF)/2000)/(RHOI'U+RHOW'CW'(TI-TF)))'

(VOLPRIME-(MILEAK+MIAIR+MIFISH)'2000/RHOI)1386 IF VOLPRIME < VTOT GOTO 13941387 PRINT"1388 PRINT "WARNING: ICEIWATER MIXTURE EXCEEDS TANK VOLUME. NO ROOM

FOR FISH,"1389 PRINT" TRY BETTER INSULATION OR LESS FISH"1390 PRINT"1391 GOTO 5601394 N=O1395 VOLWAT ~ MIWAT"U'2000/(RHOW'CW'(TI-TF»1400 IF (VOLPRIME + MF'2000/RHOF) < VTOT GOTO 14401405 IF (VOLPRIME + MF'2000/RHOF) = VTOT GOTO 14701410 IF N< 0 GOTO 14701415 MF = .99·MF1420 MIFISH = MF'CF'(TI-TF)/U1425 VOLPRIME = (VOLBLKICE'(MILEAK+MIAIR+MIFISH)'U)/(U+(RHOW/RHOI)'CW'

(TI-TF)-(VOLBLKICE/2000)'RHOW'CW'(TI-TF»

42

1426 MIWAT = «RHOW·CW·RHOI·(TI·TF)/2000)/(RHOI·LI+RHOW·CW·(TI-TF»)·(VOLPRIME-(MILEAK+MIAIR+MIFISH)'2000/RHOI)

1430 N = 11435 GOTO 14001440 IF N > 0 GOTO 14701445 VOLWAT = 1.01·VOLWAT1450 MIWAT = VOLWAT"RHOW'CW'(TI-TF)/(U'2000)1455 VOLPRIME ~ (MIWAT + MILEAK + MIAIR + MIFISH) '2000/RHOI + VOLWAT1460 N ~ -11465 GOTO 14001470 MI = MIFISH + MILEAK + MIAIR + MIWAT1472 IF N<l GOTO 15001475 LPRINT"1480 LPRINT "TANK CAPACITY IS INADEQUATE TO HOLD ALL THE FISH REQUIRED."1485 LPRINT "THE PROGRAM HAS DECREASED THE INPUT AMOUNT OF FISH TO

BE LOADED."1490 LPRINT "1495 GOTO 8601500 LPRINT "1505 LPRINT "EXTRA WATER HAS BEEN ADDED TO FILL THE TANK"1510 LPRINT"1515 GOTO 8601630 LPRINT "ICE MELT FROM WATER ADDED1640 LPRINT USING "##.#"; MIWAT;1650 LPRINT" TONS"1660 LPRINT "TOTAL ICE REQUIRED1670 LPRINT USING "##.#"; MI;1680 LPRINT" TONS"1690 RETURN1700 'Case 3 is for a partially flooded tank1710 VOLPRIME = (VOLBLKICE'(MILEAK+MIAIR+MIFISH)'U)/(U+(RHOW/RHOI)'CW'

(TI-TF)-(VOLBLKICE/2000)'RHOW'CW'(TI-TF»)1711 MIWAT = «RHOW'CW'RHOI'(TI-TF)/2000)/(RHOI'U + RHOW'CW'(TI-TF)))'

(VOLPRIME-(MILEAK+MIAIR+MIFISH)'2000/RHOI)1720 IF VOLPRIME < VTOT GOTO 17801730 PRINT"1740 PRINT "WARNING: ICEIWATER MIXTURE EXCEEDS TANK VOLUME. NO ROOM

FOR FISH,"1750 PRINT "TRY BETTER INSULATION OR LESS FISH"1760 PRINT"1770 GOTO 5601780 VOL = VOLPRIME +MF'2000/RHOF1790 IF VOL <~ VTOT GOTO 18501800 PRINT"1810 PRINT "WARNING: VOLUME OF FISH AND CSW EXCEEDS TANK VOLUME."1820 PRINT "TRY PACKING LESS FISH"1830 PRINT"1840 GOTO 6601850 VOLWAT ~ MIWAT"U'2000/(RHOW'CW'(TI-TF»)1851 N=O1852 IF MF'20001V0L <= D GOTO 19301855 VOLWAT ~ 1.01·VOLWAT1860 MIWAT = VOLWAT"RHOW'CW'(TI-TF)/(U'2000)1865 VOLPRIME = (MIWAT + MIAIR + MILEAK +MIFISH)'2000/RHOI + VOLWAT1870 VOL = VOLPRIME + MF'2000/RHOF1875 N = 11880 GOTO 18521930 MI ~ MIWAT + MILEAK + MIAIR + MIFISH1931 IF N < 1 GOTO 19401932 LPRINT "1933 LPRINT "PROGRAM HAS ADDED EXTRA WATER AND ICE TO REDUCE FISH

PACKING DENSITY"1934 LPRINT" TO AN ACCEPTABLE VALUE"1935 LPRINT "1940 GOTO 8601950 LPRINT "ICE MELT FROM WATER ADDED1960 LPRINT USING "##.#"; MIWAT;1970 LPRINT" TONS"1980 LPRINT "TOTAL ICE REQUIRED1990 LPRINT USING "##.#";MI;2000 LPRINT" TONS"2010 LPRINT "FISH LOADING DENSITY2020 LPRINT USING "##.#";MF·20001V0L,2030 LPRINT" POUNDS PER CUBIC FOOT"2040 LPRINT "PERCENTAGE OF VOLUME OCCUPIED"2050 LPRINT "BY ICEIWATER/FISH MIXTURE2060 LPRINT USING "##.#"; VOL'100IVTOT2070 RETURN

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