TABLE OF CONTENT
No
Subject
Page
1 .1
Introduction
2
1 .2
Objective
3
1 .3
Learning Outcome
3
1.4 1.4
Theo Theore reti tica call Back Backgr grou ound nd
2 .1
roblem !tatement
8
3 .1
"##aratu$
%
3 .2
rocedure
%-1&
4 .1
'e$ult
1&-12
4 .2
"nal($i$
13-14 13
4 .3
)i$cu$$ion
1*
4.4
Conclusion
1+
4 .*
,#erimental #recaution
1+
4 .+
'eerence$
1+
4 ./
"##endi
1/
3-8 3-8
EXPERIMENT TITLE
)etermination o 0etacentric height.
1.1 INTRODUCTION
1
Level 1 laborator( activit( reer$ to condition here the #roblem and a($ mean$ are guided and given to the $tudent$. oever the an$er$ to the a$$ignment are let to the $tudent$ to $olve u$ing the grou# creativit( and innovativene$$. The activit( i$ ho#e to $lol( introduced and inculcate inde#endent learning among$t $tudent$ and #re#are them or a much harder ta$k o o#en-ended laborator( activitie$. In thi$ laborator( activit( $tudent$ ill be e#o$ed to the eu i#ment that u$ed to mea$ure the metacentric height o #ontoon. 5or $tatic euilibrium o the #ontoon6 the total eight6 W6 7 hich act$ through the centre o the gravit(6 G mu$t be eual to the buo(anc( orce
hich act$ through the centre o buo(anc(6 B6 hich i$ located at the centroid o the immer$ed cro$$-$ection. 9hen the #ontoon heel$ through a $mall angle6 the metacentre M i$ identiied a$ the #oint o inter$ection beteen the line$ o action o the buo(anc( orce 7 ala($ vertical and BG etend. 5or $table euilibrium6 M mu$t be above G.
Fgu!e ".#: " loating bod( i$ $table i the bod( i$ 7a. The centre o gravit( G i$ belo
the centroid B o the bod(; 7b The metacentre M i$ above G; 7c
1.$ OB%ECTI&E
To identi( the #o$ition o the metacentre 70 o a loating bod(6 b( reerring the di$tance rom the centre o gravit( 7=.
2
1.' LEARNING OUTCOMES
"t the end o the laborator( activitie$6 $tudent$ ould be able to: i. )etermine the $uitable laborator( te$t$ to be conducted to addre$$ the given #roblem. ii. "nal($e te$t data and #re$ent the $olution to the o#en-ended #roblem. iii. 9ork in a grou# to #roduce the relevant technical re#ort
1.( T)EORETICAL BAC*GROUND
ontoon i$ a term u$ed to denote a lat bottomed ve$$el hich i$ rectangular in cro$$ $ection and in #lan. >on$idering 5igure 26 e have the eight orce6 9 acting verticall( don through the ce+t!e o, g!a-t 6 G6 o the #ontoon. !ince the #ontoon i$ loating in ater ith a con$tant de#th immer$ion6 it ollo$ that there mu$t be an eual orce acting the o##o$ing direction o the eight orce6 knon a$ buoa+c ,o!ce 6 F 6 hich act$ verticall( u# through the centre o gravit( o the di$#laced ater.
Fgu!e ".1: " #ontoon loating on even keel ith 9 and 5 collinear.
!ince the #ontoon i$ a $im#le rectangle6 the $ha#e o the di$#laced liuid i$ al$o a rectangle ith it centre at the geometrical centre namel( the ce+t!e o, buoa+c/ B. The buo(anc( orce6 5 act$ u#ard$ through B. ?ote that 9 and 5 act collinearl( ith = $ituated $ome di$tance above B.
3
Fgu!e ".$: " #ontoon loating ith an im#o$ed angle o tilt6 $hoing the righting cou#le
9hen a #ontoon i$ tilted a$ $hon in 5igure 36 9 act$ verticall( don through = hich maintained at the $ame #o$ition but 5 no act$ through #oint B@ in$tead o B. Thi$ i$ becau$e act$ through the centre o gravit( o the di$#laced liuid hich i$ no tra#eAoidal in $ha#e ith it$ centre o gravit( at B@. "$ a re$ult 5 and 9 are no longer collinear6 but a cou#le o orce$ that return the #ontoon to an even keel are ormed. Thi$ i$ knon a$ righting cou#le. In thi$ ca$e the #ontoon i$ ca#able o righting it$el hen tilted6 hence it i$ $table.
Fgu!e ".'0 " #ontoon ith a rai$ed = and an im#o$ed angle o tilt6 $hoing the
overturning cou#le cau$ed b( 9 acting out$ide
It a relativel( tall #iece o eight i$ #laced on the #ontoon a$ $hon in 5igure 46 the combined eight6 9 o the #ontoon and it$ load act$ through the centre o gravit(6 = hich i$ relativel( high. 9hen = become$ higher and the angle o tilt increa$e$6 9 act$ urther and turn urther to the let. Thi$ mean$ that at the $ome #oint the movement o buo(anc( orce6 5 rom B to B@ i$ unlikel( to be large enough to #roduce a righting cou#le. 9hat e no have i$ the $ituation de#icted in 5igure *6 here the line o action 4
o 9 i$ out$ide 7nearer the edge o the #ontoon than the line along hich 5 act$. Thu$ 9 i$ tr(ing to overturn the #ontoon. The to orce$ 5 and 9 orm an overturning cou#le. Thu$ it i$ un$table.
Fgu!e ".( : The #o$ition o metacentre
" #ontoon loating on an even keel ha$ it$ center o buo(anc( at B and it$ centre o gravit( at =. " line joining B to = ould be a$ $hon in 5igure 46 that i$ vertical and at %& to the deck o #ontoon. Imagine line B= etend$ u#ard$ and ho con$ider the #ontoon in tilted #o$ition a$ in 5igure +6 the centre o buo(anc( moved rom B to B@. " line dran verticall( u#ard$ through B@ ill inter$ect the line B= at the #oint labelled 0 in the diagram. Thi$ called the metacentre. rovided the = doe$ not move6 then or all relativel( $mall angle o tilt; i.
The vertical line through u# B@ through 0. >on$euentl( i the location o B@ can be calculated6 the #o$ition o 0 can be ound gra#hicall(.
ii.
The di$tance o 0 above 0 con$tant.
iii. The di$tance =0 i$ called metacentric height o #ontoon.
9hen con$idering the $tabilit( o loating bod(6 it i$ u$ual to a$$ume that the angle o tilt θ $mall. Thi$ i$ nece$$ar( to $im#li( the theor( b( making the a$$um#tion that θ radian$ C $in θ C tan θ C θ radian$. >on$idering the re$toring moment that right$ a rectangular #ontoon to an even keel hen it i$ tilted6 the euation: B0 C I ws / V 5
9here: D C the volume o ater di$#laced b( the bod( I ws = the $econd moment o the area
Fgu!e ".": lan o the #ontoon here the tilt take$ #lace about the longitudinal ai$ E-E
I ws C
LB
3
12
It $hould be a##arent that B0 de#end$ onl( u#on: a.
I and b6 the dimen$ion$ o the #ontoon hich govern the value o I ws .
b.
D6 the volume o di$#laced ater hich de#end$ onl( u#on the eight o the #ontoon.
'eerring to 5igure /6 (ou $hould be able to $ee that B0 C B= F =0 or6 =0 C B0B=. I e can calculate B=6 then e can obtain =0 and hence determine i the bod( i$ $table or un$table. ?o6 B i$ the center o buo(anc(6 and ith the #ontoon loating on an even keel B i$ located at a height eual to hal the de#th o immer$ion 7hG2 above the #oint O on the bottom o the #ontoon.
6
Fgu!e ". : " #ontoon $hoing the ke( #oint$ and dimen$ion$
It i$ common #ractice to carr( out an e#eriment on ve$$el to a$$e$$ it$ $tabilit( b( calculating =0. Thi$ i$ a $im#le #rocedure utiliAing moveable eight #o$itioned on the deck at a##roimatel( the middle o the longitudinal centreline and a #endulum hanging in$ide the ve$$el. The eight namel( jocke( eight 7j i$ moved rom the centreline knon di$tance 7 ∂θ toard$ the $ide a$ $hon in 5igure 8. Thi$ move$ the centre o gravit( o the #ontoon rom = on the centreline to a ne #o$ition =@ and cau$e$ the ve$$el to tilt at the angle o
∂θ .
The magnitude o ==@ de#end$ u#on ho ar the jocke( eight i$ moved and it$ $iAe relativel( to the total eight o the #ontoon. <$ing the ratio o eight and ∂ x 6
wj ∂ x W
GG@ =
9here 9 i$ the total eight o the #ontoon including the #o ntoon GG@ = GM tan θ x
>ombining both euation$6
wj dx W d θ
GM = It i$ im#ortant to remember that
θ i$
in radian.
7
Fgu!e ".20 0ovement o the jocke( eight rom the centreline
$.1 PROBLEM STATEMENT
"n im#ortant a##lication o the buo(anc( conce#t i$ the a$$e$$ment o the $tabilit( o immer$ed and loating bodie$ hen being #lace in a luid. Hnoing metacentre6 0 location i$ vital and great im#ortance in the de$ign o $hi#$ and $ubmarine$. The bod( i$ $aid $table i 0 i$ above = and un$table i otheri$e. !tudent$ are reuired to #erorm a relevant e#eriment to ulil the objective $tated above u $ing both method namel( adju$table #o$ition traver$ed eight e#eriment and ba$ed u#on geometr( and de#th o immer$ion. 5or com#utation #ur#o$e6 the $tudent$ are a$ked to ind the euation rom the literature or eiting manual or luid and h(draulic laborator(.
'.1 APPARATUS
a. 0etacentric eight "##aratu$
8
1. ontoon Bod( 2. >ro$$ - bar 3. "dju$table 0a$$ 4. 0a$t *. !liding 0a$$ +. lumb - line /. Linear !cale Figure 1.0 - Metacentric Height apparatus
Figure 1.1 - Lael o! apparatus
'.$ PROCEDURE
1. 2. 3.
The tran$ver$e adju$table ma$$ i$ eighed. The #ontoon i$ a$$embled and eighed. The $liding ma$$ i$ #o$itioned along the ma$t $uch that the center o gravit( occur$ at the to# o the #ontoon. Thi$ can be determined b( u$ing either a knie edge or b(
4.
$u$#ending rom a light $tring around the ma$t. The ba$in i$ illed ith ater6 the #ontoon i$ loated en$uring that the adju$table
*.
ma$$ i$ in it$ central #o$ition. The D> #late$ #rovided i$ u$ed to level the loating bod( and Aero datum i$
+.
checked beteen #lumb line and $cale. The adju$table ma$$ i$ moved to the right o centre in *mm increment$ to the end o the $cale6 nothing the angular di$#lacement o the #lumb line or each #o$ition. "
/. 8.
The adju$table ma$$ i$ re#eated or movement to the let centre. 9ith the ece#tion o eighing the adju$table eight and em#t(ing and reilling the volumetric tank6 all the above i$ re#eated or the $liding ma$$ at dierent height$ u#
the ma$t6 i.e. or dierent centre$ o gravit(. %. "ll the reading i$ recorded in the re$ult $heet. 1&. The gra#h o lateral #o$ition o adju$table ma$$ again$t angle o li$t or each $liding ma$$ height i$ #re#ared. The value o
dx d θ
or each $liding ma$$ height i$ obtained6
the metacentric height6 =0 and di$tance beteen the centre o buo(anc( and the metacentre i$ calculated.
(.1 RESULTS
2.343 &.2&8 &.*11 2&& 3*& 2.3331&-4 2.3431&-3 &.&%%+ &.&33* &.&1+/
Tota3 4eg5t o, ,3oat+g a66e7b3 8W9 Weg5t o, a;ju6tab3e 7a66 8<9 Weg5t o, 63;+g 7a66 8< 19 B!ea;t5 o, =o+too+ 8B9 Le+gt5 o, =o+too+ 8L9 Seco+; 7o7e+t o, a!ea 8I9 &o3u7e o, 4ate! ;6=3ace; 8&9 )eg5t o, 7etace+t!e abo-e ce+t!e o, buoa+c 8BM9 De=t5 o, 77e!6o+ o, =o+too+ 8IP9 De=t5 o, ce+t!e o, buoa+c 8CB9
:g :g :g 77 77 7( 7' 7 7 7
)eg5t o,
Rea;+g o, 36t ,o! a;ju6tab3e 4eg5t 3ate!a3 ;6=3ace7e+t ,!o7 6a3 ce+t!e 3+e/
a;ju6tab3e
8779
4eg5t/ 1
>"#
>(#
>'#
>$#
>1#
#
1#
$#
'#
(#
"#
8779 #
*4
42
3&
2&
1&
&
-1&
-2&
-31
-42
-*+
-++
"#
-
-
-
+2
32
&
-18
-4+
-+&
-
-
-
1##
-
-
-
-
-
&
-*&
-+8
-
-
-
-
10
#
Table 1: Lateral di$#lacement o ro#eor each height o adju$table eight rom $ail centre line
In order to ind the angle6 e need to u$e trigonometr( rule. 9here6 JC3&& mm
)eg5t o,
A+g3e6 o, 36t ,o! a;ju6tab3e 4eg5t 3ate!a3 ;6=3ace7e+t ,!o7 6a3 ce+t!e 3+e/ ? 1
a;ju6tab3e
8779
4eg5t/ 1
>"#
>(#
>'#
>$#
>1#
#
1#
$#
'#
(#
"#
8779 #
-
-/.%/
-*./1
-3.81
-1.%1
&
1.%1
3.81
*.%&
/.%/
1&.8
12.4
/
1
-
-
-
-
-
-
1&.2 "#
& -
-
-
-
-+.&%
&
+.&%
8./2
11.+ 1##
-
-
-
11.3
#
1
8 -
-
&
%.4+
12./ /
Table 2: "ngle$ or each height o adju$table eight
11
-
)eg5t o, a;ju6tab3e
>"#
>(#
>'#
Metace+t!c )eg5t 8779 >1# # 1# $#
>$#
'#
(#
"#
#
4eg5t/ 1 8779 #
2*.&/ 2*.+& 2+./4 2+./% 2+./&
&
2+./% 2+./4 2*.+& 2*.&/
"#
-
-
-
8./%
8.34
&
2+./& 8.34
1##
-
-
-
-
-
&
*.41
11./4 13.*+
-
-
-
8.&*
-
-
-
Table 2: 0etacentric height or each height o adju$table eight
(.$ ANAL@SIS
12
24.8&
-
#lope !or 100$$
#lope !or 0$$
%&'%∅ ( )10 * 0+')".46 * 0+
%&'%∅ ( )20 * -20+ ' )3.81 * -3.81+
( 1.06 ( 5.25
#lope !or 50$$ %&'%∅ ( )10 * -20+')6.0" * -11.68+ (1.64
i !econd 0oment o "rea6 I
13
I =
LB 3
=
12
×1& −12
( 3*& )( 2&&) 3 12
×1& −12
= 2.333 ×1& − 4 m 4
ii Dolume o ater di$#laced6 D V =
=
W
H =
3
1& 2.343 1&
−3
m
3
x
=
*&6θ
−
=
*4
mx m p $in θ
= ( &.2&8
3
= 2.343 ×1&
iii 0etacentric eight6
)( *&&&* 1&.2& ( 2.343 ) $in = 25.07 $$1 iii 0etace ntric eight KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK KKKK 14
(
)
iv eight o metacentre above centre o buo(anc(6 B0 BM =
=
=
I V 2.333× 1& 2.343× 1&
−4
−3
&.&%%+m
v )e#th o immer$ion o #ontoon6 I IP =
=
V ×1& +
vi )e#th o centre o buo(anc(6 >B CB
LB 72.343 × 1& 8 × (1& −3
+
)
( 3*& )( 2&&)
= &.&33*m
=
=
=
V × 1&
+
2 LB
( 2.343
× 1&
(
−3
)(
) (1& ) +
×
2 3*& 2&&
)
&.&1+/ m
(.' DISCUSSION
i.
The eect o changing the #o$ition o = on the #o$ition o the metacentre 70.
>hanging the #o$ition o = on the #o$ition o the metacentre 70 ill cau$e change o $tabilit( o loating object.
• I 0 lie$ above = a righting moment i$ #roduced6 euilibrium i$ $table and =0 i$ regarded a$ #o$itive.
• I 0 lie$ belo = an overturning moment i$ #roduced6 euilibrium i$ un$table and =0 i$ regarded a$ negative.
•
ii.
I 0 coincide$ ith =6 the bod( i$ in neutral euilibrium.
9h( the value$ o =0 at loe$t value$ o the angle 7 are likel( to be le$$ accurate.
15
The angle7$ obtained during the e#eriment are directl( related to =0. T(#icall(6 the angle occur hen more o the hull on one $ide get dee#er into the ater6 and the hull on the other $ide move$ out o the ater. The re$ult i$ that the center o buo(anc( $hit$ to the $ide here more ater i$ di$#laced6 hile the center o gravit( remain$ in the $ame #lace at the #ontoon $ince the #ontoon it$el ha$ not changed. 9hen the centre o buo(anc( change6 thi$ make the re$ult =0 le$$ accurate and negative =0 ma( be re$ulted.
iii. 9hat i$ the mo$t $en$itive #arameter that aect$ the accurac( o the re$ult$M 0ake $ure the ater i$ in $tead( condition to #revent ei$tence o large ave$ on the ater beore taking the reading. Be$ide$6 hen taking the reading o the angle$ or adju$table eight lateral di$#lacement rom $ail centre line6 the e(e$ mu$t be #er#endicular to the #ontoon to get accurate reading.
(.( EXPERIMENTAL PRECAUTION 1 0ake $ure the ater i$ in $tead( condition to #revent ei$tence o large ave$ on the
ater beore taking the reading. 2 9hen taking the reading o the angle$ or adju$table eight lateral di$#lacement rom $ail centre line6 the e(e$ mu$t be #er#endicular to the #ontoon to get accurate reading. 3 Thi$ e#eriment involve$ large volume o liuid. Thu$6 en$ure that the ater lo$ accordingl( in the containerGa##aratu$ to #revent lood occur in the laborator(. (." CONCLUSION
Thereore6 e can conclude that the objective o thi$ e#eriment i$ achieved becau$e e are able to identi( the #o$ition o the metacentre 70 o a loating bod(6 b( reerring the di$tance o the adju$table eight rom the centre o gravit( 7=. 9e are al$o able to determine hether the #ontoon i$ $table or un$table b( getting the #o$ition o centre o gravit(. oever6 $ome #recaution$ are al$o $hould be taken to increa$ed the #robabilit( o our grou# re$ult$ $o that e can get the eact value$ and avoided more error$.
16
(. REFERENCES 1. Sir Embam A !a"#d$ Lab%ra&%r' Ma#a %* H'dra#i+s ad Wa&,r -#ai&'$
a+#&' %* Cii E0i,,ri0$ i&m Samara2a 3. 3. S#2aimi Abd# 4aib$ Hamid% A2mad$ 4#ra2im ABd Hamid ad 5#aida2 Ari**i$ #id M,+2ai+s$ 3d Edi&i%$ 3663 7. 5%2..!%#0as$ 5a#s8 M.Gasi%r,$ 5%2 A.Swa**i,d$ ad L', B.5a+ $ #id M,+2ai+s$ P,ars%$ 9&2 Edi&i%$ 366:. ;. 2&&pad>m,&a+,&ri+>2,i02&.p2p 9. 2&&p636/s&abii&'.pd*
",?)IE 17
