1) This document summarizes an experiment to determine the center of pressure on a partially submerged plane surface. Tables of recorded data show close agreement between experimental and theoretical values. 2) A second part of the experiment aimed to determine the position of the center of pressure of a fully submerged plane surface, but results showed a 75% discrepancy between experimental and theoretical values. 3) Factors like parallax errors, random errors, water impurities, and bubbles could explain the discrepancies. Careful measurement and repeated trials could improve accuracy. The findings are relevant to submarine hull design to withstand high hydrostatic pressures at depth.

1. MECHANICALENGINEERINGDEPARTMENT
FLUID MECHANICS LAB
TITLE
HydrostaticPressure
INTRODUCTION
OBJECTIVE
 Thisexperimentiscarriedoutto determinethe centre of pressure onapartially
submergedplane surface. (PartA)
 The purpose of thisexperimentis todetermine the positionof the centre of pressure of
a plane surface immersedinwaterandtocompare the experimental positionwiththe
theoretical position.(PartB)
APPARATUS
1. HydraulicsBenchF1-10
2. HydrostaticPressure ApparatusF1-12
PROCEDURE
1. The quadrant wasplacedon the twodowel pinsandusingthe clampingscrew,itwas
fastentothe balance arm.
2. Value of a, L, depthdand widthb,of the quadrant endface were measured and
recorded.
3. Withthe Perspex tankonthe bench,the balance armwas positiononthe knife edges
(pivot).The balance panwashangedfromthe endof the balance arm.
4. A hose wasconnected fromthe draincock to the sump.
5. The tank was leveledusingthe adjustablefeetandspiritlevel.The counterbalance
weightwasmoveduntil the balance armwashorizontal.
6. The drain cock wasclosedand waterwasadmitteduntil the levelreachesthe bottom
edge of the quadrant.
7. For part A, weightof 50g was placedonthe balance pan,slowlyaddingwaterintothe
tank until the balance armwas horizontal.The waterlevel onthe quadrantandthe
weightonthe balance panwere recorded. (Fine adjustmentof the waterlevel was
achievedbyoverfillingandslowlydraining,usingthe stopcock)
8. Step7 wasrepeated 6 timesforweight100g, 120g, 140g, 160g, 170g and 180g.
9. For draining,eachincrementof weightinstep8 wasremovedone byone,andwater
levels were recorded after the weight was removed, until weight 50g on the balance pan.
10. The recordeddata was tabulatedinatable.

2. 11. Withthe table,Graphof m/y2
againsty wasplotted,then,the gradientandthe y-
interceptof the graphwere determined.
12. For part B, step7 wasrepeatedbyusingweightof 300g, 350g, 400g, 450g and 500g.
13. The recordeddata for part B was tabulatedintoatable.
RESULT
Part A
Heightof the quadrant fromthe top endface,a = 0.100m
Lengthfromthe pivottothe endof balance arm, L = 0.285m
Depthof the endface of quadrant,d = 0.100m
Widthof the endface of quadrant,b = 0.075
FILLING TANK DRAININGTANK AVERAGEVALUE CALCULATIONS
Weight
of load,
m (kgms-
2
)
Heightof
water,y
(m)
Weight
of load,
m (kgms-
2
)
Heightof
water,y
(m)
Weight
of load,
mA
(kg/ms-2
)
Heightof
water,yA
(m)
Wetted
surface
area,y2
(×10-3
m²)
Hydrostatic
Pressure,
m/y2
(Pa)
0.4905 0.044 0.4905 0.045 0.4905 0.0445 1.9803 247.69
0.9810 0.064 0.9810 0.065 0.9810 0.0645 4.1603 235.80
1.1772 0.071 1.1772 0.072 1.1772 0.0715 5.1123 230.27
1.3734 0.077 1.3734 0.078 1.3734 0.0775 6.0063 228.66
1.5696 0.082 1.5696 0.083 1.5696 0.0825 6.8063 230.61
1.6677 0.086 1.6677 0.086 1.6677 0.0860 7.3960 225.49
1.7658 0.089 1.7658 0.089 1.7658 0.0890 7.9210 222.93

3.  da
L
gb
y
L
gb
y
m

262

From the equation,
For a partiallyimmersedobject,
Compare thisequationwithgeneralequation,y=mX + C
Gradientof graph, m = -ρgb/6L
-ρgb/6L = -461.63kgm-2
s-2
Y-interceptof graph,C = ρgb(a+d)/2L
ρgb(a+d)/2L = 265.48Pa
Calculation of theoretical value
-ρgb/6L =-[(1000)(9.81)(0.075)]/6(0.285)
y = -461.63x + 265.48
220
225
230
235
240
245
250
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
HydrostaticPressure,m/y2(Pa)
Height of water, y (m)
Grapg of m/y² against y

4. =-430.26 kgm-2
s-2
ρgb(a+d)/2L= [(1000)(9.81)(0.075)(0.100+0.100)]/2(0.285)
= 258.16Pa
Percentage of discrepanciesof the gradient,
%discrepanciesof gradient=|[(-461.63)-(-430.26)] / (-430.26)| × 100%
= 7.29%
Percentage of discrepanciesof the y-intercept,
%discrepanciesof y-intercept=|[(265.48)-(258.16)] / (258.16)]|× 100%
= 2.84%
Part B
Equationof term
q = a+d-r
A = b × r
XpA = 2mL / ρrA
XpT = 2r/3 +q
For example,
q1 = 0.100+0.100-0.118 = 0.082m
A1 = 0.075 × 0.118 = 8.85×10-3
m2
XpA1 = 2(0.30)(0.285) / (1000)(0.118)( 8.85×10-3
) = 0.1637m
XpT1 = 2(0.118) / 3 + (0.082) = 0.1607m
No. Mass, m (kg) Height
of
water,
r (m)
Length
from
water
level to
balance
arm, q
Areaof
immersed
plane,A
(×10-3
m2
)
XpA (mm) XpT (mm)

5. (m)
1 0.300 0.118 0.082 8.850 0.1637 0.1607
2 0.350 0.130 0.070 9.750 0.1574 0.1567
3 0.400 0.143 0.057 10.725 0.1487 0.1523
4 0.450 0.155 0.045 11.625 0.1424 0.1483
5 0.500 0.168 0.032 12.600 0.1346 0.1440
From the graph of Xp Actual againstXp Theoretical,
Gradientof the graph, m = 1.752
Percentage of discrepancybetweenXp Actual andXp Theoretical,
% discrepanciesof ratio of Xp Actual / Xp Theoretical =|[(1.752)-(1.000)] / (1.000)| × 100%
= 75.2%
DISCUSSION
y = 1.752x - 0.1176
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.142 0.144 0.146 0.148 0.15 0.152 0.154 0.156 0.158 0.16 0.162
XpActual
Xp Theoretical
Graph of Xp Actual against Xp Theoretical

6. From the obtainedresult, the theoretical value of -ρb/6Lis-430.26 kgm-2
s-2
andρb(a+d)/2Lis
258.16Pa, whereasthe experimentalvalue of -ρb/6Lis-461.63kgm-2
s-2
andρb(a+d)/2Lis
265.48Pa. Bycomparingeach other,the percentage of discrepancyof -ρb/6Lis7.29%, while the
percentage of discrepancyof ρb(a+d)/2Lis2.84%. Since bothpercentagesof discrepanciesare
lowerthan10%, therefore the experimentpartA can be consideredassuccessful.
However,forpartB, the experimental ratioof the actual depthof centerof pressure to
the theoretical of thatis1.752. Since the theoretical ratiois1.000, thus the percentage of
discrepancyof the ratiois 75.2%. Due to the large percentage of discrepancy,the experiment
part B is consideredasunsuccessful.
The discrepanciesbetweenthe theoretical andexperimental resultinthisexperiment
are due to some errorsor factors that have beendone duringthe experiment.First, parallax
error mayoccur duringmeasurementof dimensionof quadrantandbalance arm, whichare a, L,
b and d. Thiserror occurs due to the eye level of the observerisnotperpendiculartothe scale
of the apparatus duringthe measurement,thusthe measuredvaluesare deviate withthe actual
value.Second, randomerrormayoccur in the experiment.Thiserroris causedbyunknownand
unpredictablechangesinthe experiment. Forexample,whenaddingthe waterintothe tank,
turbulentflowwill occurinthe tank,whichis unpredictable andcannotbe calculated.Asa
result,thisexperimentdoesnotobeythe assumptionof hydrostaticequilibriumand affecting
the resultindirectly.One of the factorsinthisexperimentisimpuritiesinthe water.The
assumptionsof thisexperimentisthe densityof the wateris1000kg/m3
,but the impuritiesin
the waterprovide extravolume andcause deviationof value of densitywiththe actual value,
thusthe resultbecomesinaccurate.Lastly,somewaterdropletsorairbubbleswill formonthe
quadrantwhenaddingthe waterintothe tank. Thisphenomenonwillcause the extraorless
force duringthe experiment.
To obtainmore accurate result,some precautionshave tobe done duringthe
experiment.Firstof all,topreventparallax error,the observershouldmake sure hiseye level is
alwaysperpendiculartothe apparatusscale duringmeasurement.Tominimize the effectof
randomerror, thisexperimentshouldbe repeatedseveral timestoobtainedaverage value
whichismore accurate. Also,inclinedplane shouldbe usedasa mediumduringaddingthe
water.Thisis because the inclinedplane canminimize the effectof turbulentflowandprevent
the phenomenonof formingwaterdropletandairbubble. Thisexperimentshouldalsobe
carriedout ina closedareawhichdoeshave minimumventilationtoobtainmore accurate
result.
Hydrostaticpressure isthe mostprioritized problemduringdesignationof the
submarine hulls.Fromthe equationof P = ρgh/A,where histhe depthof the submarine.So,the
pressure exertedonthe submarine,P,isdirectlyproportionaltothe depthof the submarine,h.
Generally,the submarine can dive thousandmetersbelow the sealevel,the worldrecordof the
submarine divingdepthis Trieste,whichdive 10911 meters.Thus,the exertedhydrostatic
pressure isverylarge. Asa result,submarine mustbe builttobe strongenoughtowithstand

7. such tremendouspressure.Towithstandlarge pressure,the hullof the submarine shouldbe
made ina shape whichcan withstandhighhydrostaticpressure.Nowadays,the submarinesare
built in cigar shape, which is also called “teardrop hull” and was pattern after the body of whales.
Thisshape can reduce the hydrodynamicdrag and noise of the submarine whendiving,while
decreasingthe seakeepingcapabilitiesand increasingthe dragforce whenat the watersurface.
For small submarines,aswell asthe oldestones,have asingle hull.Large submarinesnormally
have an extrahull.This external hull,whichactuallyformsthe shape of submarine,iscalledthe
outer hull or light hull, but it does not have to hold any pressure difference. Inside the outer hull,
there isa strong hull,orpressure hull,whichwithstandsseapressure andhasnormal
atmosphericpressure inside. The material of the hull will alsodetermine the capabilityof the
hull towithstandhydrostaticpressure. Ateraof WorldWar One,submarine wasbuiltbyusing
carbon steel,whichcannotdive below 100 meters.ForWorldWar Two,highstrengthalloyed
steel wasused,anditenable submarinestodive upto 200 meters.While,thisalloyedsteelis
still the mainmaterial forsubmarinesnowadays,withadepthlimitof from250 to 400 meters.
For militarysubmarines,theyare builtwithtitaniumalloy,whichallowsincrease indepth.
Titaniumisalmostas strongas steel,havinga lighterweight,andalsonotferromagnetic,which
enable tostealth.The testdepthof titaniumsubmarineisone thousandmeters.
CONCLUSION
The objectivesof thisexperimentare achieved.The centre of pressure isprovedthatitisalways
belowthe centroidforfullysubmergedbody.While,the presence of discrepanciesbetweenthe
actual andtheoretical resultsmaydue tosome errorsand factorsduringthe experiment,such
as, parallax error,randomerror,impuritiesof water,andothers.Toact as a reactiontothe
hydrostaticpressure,designof the submarine hullsshouldbe consideredintermof shape and
material of the hull.Titaniumalloyisastrongmaterial tobuildthe hull.The hull shouldbe built
incigar shape.
REFERENCES
1. Bruce R. Munson,DonaldF.Young, TedH. Okiishi,Wade W.Huebsch.(2010).
Fundamentalsof FluidMechanics(6thed.).US:JohnWiley&Sons,Inc.
2. (October2015). Submarine.Retrieved26December2015, from
http://www.newworldencyclopedia.org/entry/Submarine
3.