DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 1
Body of Report 1.0
Introduction
A worthwh!" #o$! %or $&' ($r&" "&#&""r) ) to r"*+," th" *r$# o% ($r&" "h,!") $) (+,h $) .o))/!" #"& th" o!+(" o% ($rt(" $,tt' & th" wor!* $&* th" ,o)t) o% %+"! to .ow"r %!""t) o% )h.) $&* oth"r ,r$%t A,,or*&# to S"% $&* T$$o! T$$o! &*4 %+"! ,o)t) $r" th" )",o&* !$r#")t t"( $%t"r )$!$r") o& $ /# "))"!5) /+*#"t wh"r"/' th" %+"! ,o&)+(.to& %or "6$(.!"4 $ !$r#" %"rr'4 r$&#") /"tw""& 1000 $&* 7000 !t"r) ."r ho+r Th) ("$&) th$t (!!o&) o% *o!!$r) t$") +. th" '"$r!' %+"! /+*#"t %or $ %"rr' r+&&&# 20 ho+r) ."r *$' D+" to th)4 t ) (.ort$&t th$t $ r"*+,to& & %+"! ,o&)+(.to& to &ot /" t$"& !#ht!' $&* '"t to t$" $,to& $) )oo& $) .o))/!" F+rth"r(or"4 $ r"*+,to& o% %+"! r"8+r"("&t) ) /"&"%,$! & t"r() o% r"*+,"* .o!!+to& I& or*"r to r"*+," th" %+"! ,o&)+(.to& ,o&)+(.to& & ($r&" "h,!")4 "h,!")4 ($r&" "&#&""r) "&#&""r) *"&t%"* *"&t%"* th$t th" *r$# %or," h$* ,$+)"* ($r&" "h,!") to +)" too (+,h o% %+"! Th" r"*+,to& o% %+"! ,o&)+(.to& ,orr"!$t") to th" r"*+,to& o% th" *r$# %or," Th" )($!!"r th" *r$# %or,"4 th" !")) %+"! ) &""*"* to (o" th" ($r&" "h,!" Th" *r$# %or," ) $& o..o)&# %or," o% th" *r&# %or," %or," th$t ($") th" "h,!" "h,!" (o" %orw$r*) %orw$r*) H"&,"4 *r$#-r"*+,t *r$#-r"*+,to& o& t",h&8+") t",h&8+") (+)t /" $..!"* & ""r' ($r&" "h,!" & or*"r to o/t$& $& "%%,"&t )$!&# I& th) th) r".ort r".ort44 thr"" thr"" t'.") t'.") o% ($r&" ($r&" "h,! "h,!") ") w"r" w"r" ,o"r" ,o"r"* * Th"' Th"' $r" ,r+)" ,r+)" )h.)4 )h.)4 )$!/o$t) $&* )+/($r&")
2.0
Objectives
Th" ($& .+r.o)" o% th) r".ort ) to "6$(&" $&* $&$!'9" th" *%%"r"&t t'.") o% *r$# %or,") $&* ,!$r%' how "$,h %or," ,r"$t") th" *r$# "6."r"&,"* /' "$,h ($r&" "h,!" Not o&!' th$t4 th) r".ort ) $!)o *o&" & or*"r to &")t#$t" th" *r$#-r"*+,to& t",h&8+") %or *%%"r"&t t'.") o% ($r&" "h,!")
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 2
3.0
Analysis of Marine Veicles
3.1
!ruise sips
Th" )h$." o% $ )h. .!$') r"$!!' (.ort$&t ro!" & or*"r to )t$/!9" & w$t"r Th" h+!! or /o*' /"!ow th" ($& *", ) t'.,$!!' "r' w*" h$) $ *"". /$)" !&" or /otto( A ro+&* /otto( *).!$,"("&t h+!! !oo) !" $ !$r#" r",t$&#!" wth ro+&*"* "*#") to *)).$t" *r$# "6"rt"* $#$&)t th" )h. Th" ro+&*"* "*#") (&(9" th" %or," o% w$t"r $#$&)t h+!! $&* $!!ow&# h+#" $&* h"$' )h.) to (o" )(ooth!' thro+#h th" o,"$&
Figure 1: Hull of a Ship Th" %or,") th$t $,t o& )h.) $r": /+o'$&,' %or,"4 #r$t$to&$! %or,"4 ),o)t' %or," $&* w&* %or," Th" "!o,t' o% $ )h. ) *"."&*&# o& th" w&* $&* ),o)t' %or," ;&* %or," ) &$t+r" %or," wh,h $!w$') ,o(" tow$r*) )h.) $&* $,t) o& ""r' )+r%$," o% th" )h. wh!" ),o)t' %or," o% w$t"r &or($!!' ,$+)" )& %r,to& $&* o,,+r & th" /otto( o% th" )h. How""r4 wth th" h"!. o% *"&)t'4 /+o'$&t %or," $&* #r$t$to&$! %or,"4 !$r#" )h. ,$& %!o$t & w$t"r I& or*"r to $,h"" /+o'$&,'4 !#ht w"#ht4 )t+r*' ($t"r$!) $&* *)."r)&# th" w"#ht o% )h.) $r" (.ort$&t *+r&# th" /+!* o% )h.) 000# o% .r"))+r" $&* .o..&# o+t .r"($t+r"!' $%t"r th" )h. )tr+, $& ,"/"r# <")*")4 th" r"t) w"r" &)"rt"* to th"r ho!*) /' h$&* H"&,"4 th" ,r$)h ,$+)"* ($))" !%" !o)) %or $/o+t 1>00 !%" & 1>12 U)/or&"4 D 200= Dr$# ) ($?or .ro/!"( to )h.) to (o" $&* )t$/!9" thro+#h th" w$t"r A %"w &"&to&) h$" to /" ,r"$t"* & or*"r to r"*+," th" *r$# o% th" )h.) Th" &"&to&) t$"& (+)t /" .$r$!!"! to Ar,h("*")5 Pr&,.!") Th" &"&t"* w$' to r"*+," *r$# $r": (,ro/+//!") $&* hot /o*' o% )h.)
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 3
M,ro/+//!") $r" $ *r$# r"*+,to& *"," th$t #") h+#" "%%",t to $ )o!* /o*' (o&# & w$t"r Sh.) )+,h $) t$&"r) .!$' ($?or ro!" & ($r&" tr$&).ort$to& Th"' $r" "r' /# & )9" $&* (o" "r' )!ow Th"' $r" ").",$!!' )+t"* to (,ro/+//!") <' &?",t&# th" (,ro/+//!")4 =0@ o% th" tot$! *r$# w$"-($&# *r$# $&* )& %r,to& ,$& /" ,o"r"* Th" U&"r)t' o% J$.$& &* <")*")4 )&," th" *"&)t' o% $r & /+//!") ) 11000 to w$t"r4 th" !$'"r o% ,!+)t"r"* /+//!") &"$r th" )o!* w$!! ,$& *",r"$)" th" )h"$r )tr")) ,r"$t"* /' w$t"r Th"r"%or"4 )& %r,to& ,$& $!)o /" r"*+,"*
Figure 2: An image of microbubbles for full-scale ship I& or*"r to $/!" to ")t($t" th" *r$# r"*+,to&) "%%",t o% (,ro/+//!") wh"& t ) $..!"* to $ %+!!-),$!" )h.4 t ) &","))$r' to ,$rr' o+t th" "6."r("&t /' +)&# (o*"! o% $ )h. I& th) ,$)"4 *("&)o&!")) &+(/"r "8+$to& ,$& /" +)"* & or*"r to ,$!,+!$t" th" %or," r"*+,to& π m= π a / p
ℜm = ℜa / p
( ) ( ) ρUD μ
=
m
ρUD μ
a/ p
CD m=CD a / p
(
F D 2
ρU D
2
) ( =
m
F D 2
ρ U D
2
)
a/ p
Equation adapted from Lecture Notes A hot /o*' ,$& h"!. )h.) r"*+," *r$# It ) *),o"r"* th$t wh"& !8+* ,o(") & ,o&t$,t wth )o!* /o*' th$t ) hott"r th$& t) /o!&# .o&t4 t w!! .ro*+," $& &)+!t&# !$'"r A,,or*&# to Pro%"))or D"r" Ch$&4 wh"& h" t")t"* th) "6."r("&t o& )o!* /$!!)4 h" %o+&* o+t th$t th" *r$# o% th" /$!!) ) r"*+,"* to $!(o)t (&(+( .o))/!" thro+#h th" ,r"$t&# o% $& &)+!t&# !$'"r wh"& t %$!!) thro+#h th" !8+* ;h"& th) ("tho* ) $..!"* to )h.4 &ot o&!' *r$# ,$& /" (&(9"* $) th" )h. .$))") thro+#h o,"$&4 /+t t .ot"&t$!!' ,$& r"*+,"
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 4
tr$&).ort$to& ,o)t) $&* #r""&ho+)" #$) "())o&) $) th" )h. ,$& (o" ""& %$)t"r How""r4 th) ("tho* ) $..!,$/!" o&!' %or ,"rt$& t"(."r$t+r" o% th" )o!* /o*' (o&# & w$t"r Th" t"(."r$t+r" h$) to /" ,o&tro!!"* $&* ($&t$&"* Too h#h & t"(."r$t+r" w!! ,$+)" *$($#") to th" )h.) Not o&!' th$t4 t ,$& ,$+)" ,orro)o& *+" to th" h+#" &,r"$)"* t"(."r$t+r" 3.2 "ailboats S$!/o$t) w"r" &"&t"* &t$!!' wth )8+$r" )$!) wh"r" th"' ,o+!* o&!' )$! w&*w$r* How""r4 th" )h$." o% th" )$!) w"r" th"& +.#r$*"* to tr$&#+!$r )h$." wh,h )how"* (.ro"("&t) $) th" )$!) w"r" $/!" to ,o&"rt w&* .ow"r %ro( $&' *r",to& &to %orw$r* thr+)t E$&) &* To*$'4 (o)t o% th" )$!/o$t) (.!"("&t"* tr$&#+!$r )$!) to "$)" th" )$!&# Th"r" $r" %o+r %or,") th$t $,t o& $ )$!/o$t4 &$("!' w&* %or,"4 ),o)t' %or," o% w$t"r4 #r$t' $&* /+o'$&,' No&"th"!"))4 th" w&* %or," $&* th" ),o)t' %or," o% w$t"r *r",t!' $%%",t th" (oto& o% th" )$!/o$t ,o(.$r"* to th" oth"r two ("&to&"* %or,") A,,or*&# to Ho Sailboats Sail Against the !ind &*4 Bth" %or," o% th" w&* .ro."!) th" /o$t $&* th" ),o)t' %or," )!ow) t *ow& $&* h"!.) t )t$' o& ,o+r)" A& "8+$! %or," o% #r$t' $&* /+o'$&,' $)))t) th" /o$t to %!o$t S$!) $r" +)"* $) "&#&") %or )$!/o$t) & wh,h w&* ) th"r ($& )o+r," o% "&"r#' & or*"r to ,r"$t" $ *r&# %or," th" %or," ) h$r&"))"* to (o" th" )$!/o$t $!o&# t) ,o+r)" S$!) ,$& /" +t!9"* $) $r%o!) %or +.w&* )$!&# $&* $) $r *$() %or *ow&w&* )$!&# "reating Lift and A#oiding $rag &* ;h"& th" )$!) $r" +)"* $) $r%o!)4 th"' "6."r"&," w&* %or,") & wh,h two ,o(.o&"&t) "6)t"* th" !%t ,o(.o&"&t $&* th" *r$# ,o(.o&"&t Th" !%t ,o(.o&"&t .+)h") th" )$! >0 ° ."r."&*,+!$r to th" w&* wh!" th" *r$# ,o(.o&"&t .+)h") th" )$! & th" *r",to& o% th" w&* Th" !%t ,o(.o&"&t ,$& /" "6.!$&"* /' +)&# th" <"r&o+!!5) .r&,.!" ;h"& th" w&* %!ow) $ro+&* th" )$!4 th" r"!$t" *%%"r"&," & w&* "!o,t") ,$+)") $ .r"))+r" *%%"r"&," th$t !%t) th" )$! %orw$r*4 th+)4 th" )$!/o$t $) w"!! Th" )$!) $r" )"t & $ "rt,$! .o)to& to "&)+r" th" !%t ) & $ %orw$r* *r",to& Th" %#+r" /"!ow !!+)tr$t") th" w&* %!ow o"r $& $r%o! )$!
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 5
!%t *r$#
tot$! w&* %or,"
Figure %: !ind flo o#er an airfoil sail Th" )*" "%%",t o% th" !%t ,o(.o&"&t ) th" *r$# ,o(.o&"&t Th" *r$# ,o(.o&"&t h$) two *%%"r"&t t'.") o% %or,") )*"w$') %or," $&* h""!&# %or,"4 & wh,h #o $#$&)t th" *r&# %or," Th" )*"w$') %or," ) *+" to th" &o&-+&%or( ).r"$*&# o% th" w&* &to th" )$!) Th" w&* ) ).r"$* & th" %orw$r* *r",to& $&* $!)o o%% to th" )*" o% th" )$!) O& th" oth"r h$&*4 th" h""!&# %or," r")+!t) %ro( th" )$(" %or," th$t th" w&* .r"))") &to th" )$!4 $,t&# +.o& th" h+!! to h""! th" )$!/o$t &h'sics of Sailing 200 Dr$# ) th" ($& ,o&,"r& %or )$!/o$t) $) too (+,h *r$# w!! ,$+)" th" )$!/o$t to /",o(" !")) ,o&tro!!$/!" $&* h"&,"4 ($&# t to (o" )!ow"r I& or*"r to r"*+," th)4 )$!/o$t) $r" &""*"* to h$" $ h#h"r *r&# %or," to o"r,o(" th" )*"w$') $&* h""!&# %or,") O&" o% th" ("tho*) to $,h"" th) ) to !"t th" w&* ,o(" %ro( th" )*") o% th" )$!) ;h"& th" )$!) $r" $t th" ,orr",t $&#!"4 t w!! "&$/!" th" w&* %or" to )t$' ,o&)t$&t4 th+) $!!ow&# th" )$!/o$t ).""* to "6,""* th" w&* ).""* A,,or*&# to &h'sics of Sailing &*4 )$!/o$t) ($&$#" to (o" two t(") %$)t"r th" w&* ).""* Not o&!' th$t4 th" *r&# %or," ,$& /" &,r"$)"* /' #oo* )$! tr((&# to ($&t$& $ )($!! $&#!" to th" w&* to ($" th" /")t +)" o% th" %or," (he &h'sics of Sailing &* ,!$("* th$t h$&# Btr+" w&* %or )$!&# ) th" (o)t "%%",t" w$' &ot o&!' to r"*+," *r$# /+t to ($" th" )$!/o$t (o" %$)t"r Tr+" w&* ) *"%&"* $) th" $**to& o% th" )$!/o$t ).""* $&* th" r"!$t" w&* w / r ;h"& th" )$!/o$t ).""* $..ro$,h") th" w&* ).""*4 th" r"!$t" w&* *ro.) to 9"ro ,$+)&# &o %or," o& th" )$! Th) ($") th" )$!/o$t to &ot /" $/!" to (o" %$)t"r th$& th" w&* How""r4 wh"& th" w&* ) $t $& $&#!"4 th"r" w!! /" ",tor ,o(.o&"&t) Th) ,$& /" %+rth"r "6.!$&"* /' r"%"rr&# to Appendices: Appendi) 1 H"&,"4 $) th" ).""* o% th" )$!/o$t &,r"$)")4 th" r"!$t" w&* &,r"$)") $) w"!!4 th+)4 (or" %or," ) $,t&# o& th" )$!) $&* )o #r"$t"r %or," ) .+)h&# th" /o$t %orw$r* &h'sics of Sailing &* Th" )$!/o$t w!! th"& $,,"!"r$t" +&t! to $ .o&t wh"r" th" *r$# %ro( th" w$t"r /$!$&,") th" %orw$r* ,o(.o&"&t o% th" %or," %ro( th" )$!) ($6(+( ).""*
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 6
L$)t!'4 th" )h$." o% th" )$!) &%!+"&,") th" *r&# %or," $&* *r$# Th, $r%o! )$!) #"&"r$t" (or" !%t $&* (or" *r$# & wh,h th" &,r"("&t ) *+" to th" h#h"r "!o,t' $&* th" !ow"r .r"))+r" O&" th" oth"r h$&*4 th& $r%o! )$!) #"&"r$t" !")) *r$# /+t !")) !%t ;h"& w&* ).""*) $r" & $ (o*"r$t" to h#h r$&#"4 )$!) )ho+!* /" ".t t#ht & $ )h$." o% $ th&# $r%o! wh!" *+r&# !ow ).""* w&* ,o&*to&)4 )$!) )ho+!* /" !"%t o+t $ /t to #"&"r$t" (or" !%t4 th+) (or" *r&# %or," Th" %#+r" /"!ow )how) th" !!+)tr$to& o% th" $r%o! )$!) E$&) &*
Figure *: Shape of different t'pes of airfoil sails 3.3
"ub#arines
V"rt,$! %or,") th$t $,t +.o& $ )+/($r&" $r" /$)"* o& th" Ar,h("*")5 .r&,.!" wh,h )t$t") th$t th" /+o'$&t %or," th$t $,t) +.o& $& o/?",t wh"& t ) )+/("r#"* ) "8+$! to th" w"#ht o% th" )+/("r#"* r"#o& o% th" o/?",t Ho*$&/o) 1>> V"rt,$! %or,") th$t $,t +.o& $ )+/($r&" *"t"r(&" th" "rt,$! .o)to& o% th" )+/($r&" $&* &%!+"&," th" .r"))+r" th$t $,t) +.o& th" )+/($r&" Th")" %or,") ,$& /" $*?+)t"* /' ,o&tro!!&# th" )+/($r&"5) *"&)t'
Figure +: &osition of ballast holes Th" t$& o+t)*" th" )+/($r&"5) /o*' ) ,$!!"* /$!!$)t t$& $&* wth th) t$& th" *"&)t' o% th" )+/($r&" ) $*?+)t"* ;$t"r ) %!!"* & th) t$& to &,r"$)" th" *"&)t' o% th" )+/($r&" $&* th" r$to o% w$t"r to $r ) (o&tor"* to $,h"" th" *")r"* "rt,$! .o)to& o% th" )+/($r&" ;h"& $ )+/($r&" ) $t r")t %!o$t&# o& w$t"r4 th) ) *+" to th" *"&)t' o% th" )+/($r&" ) !")) th$& th" w$t"r )+rro+&*&# th" )+/($r&" Surfacing and $i#ing &* Th)
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 7
,o&*to& ) &ow& $) h'*ro)t$t, <+o'$&,' $&* #r$t$to&$! %or,") .!$' ($?or ro!" %or )+/($r&" to )t$' & h'*ro)t$t, .o)to& Th) h'*ro)t$t, )t$t" ,$& /" )+(($r9"* /' %o!!ow&# "8+$!t': F< FG %!o$t&# o& th" )+r%$,"4 % ) F< K FG S&&# & th" /otto(4 % K ) F< FG %!o$t&# & th" %!+*4 % ) ;h"r": F< <+o'$&,' %or," FG Gr$t$to&$! %or," % %!+* *"&)t' ) )o!* *"&)t' Figure ,: H'drostatic states Th" %orw$r* hor9o&t$! %or," $,t) +.o& $ )+/($r&" ) th" "&#&" th$t .ow"r) th" )+/($r&" wh!" th" *r$# wh,h ) th" o..o)t" hor9o&t$! %or," ) ,o&tr/+t"* /' %r,to&) /"tw""& th" /o*' o% th" )+/($r&" wth th" )+r%$," o% w$t"r F!ow .$)t $& (("r)"* /o*' ,$+)") %or,") to /" $..!"* to th$t /o*'4 wh,h $r" *"."&*"&t o& t) )h$." $&* th" &$t+r" o% th" %!ow ;th r"#$r* to )+/($r&")4 th" )+/($r&" (o") thro+#h th" %!+*4 wh!" th" %!+* ) (or" or !")) )t$to&$r' How""r4 $&$!'9&# %!ow .$tt"r&) .$)t $ (o&# /o*' wth )t$to&$r' %!+* ) *'&$(,$!!' "8+$!"&t to $&$!'9&# th" %!ow .$tt"r&) $ro+&* $ )t$to&$r' /o*' $) th" %!ow (o") For "$)" o% CFD )(+!$to& th" !$t"r %r$(" o% r"%"r"&," ) "(.!o'"* to *"t"r(&" th" %or,") I& or*"r to ,o(.$r" *$t$ /"tw""& "6."r("&t$! t")t) r+& +)&# *%%"r"&t ).""*) or ""& %!+*) o&" ,$& ($" +)" o% *'&$(, )(!$rt' ;th *r$# $!+") th) ,o((o& #ro+&* ) %o+&* +)&# $ *("&)o&!")) ,o"%%,"&t CD4 wh,h ) *"t"r(&"* +)&# "8+$to& /"!ow C D =
DRAG 1 2
2
ρU A
DRAG QA
=
A) )how&4 th" *r$# %or," ) ($*" &o&-*("&)o&$! /' **&# /' th" *'&$(, .r"))+r" $&* th" $r"$ Th" .$rt,+!$r $r"$ +)"* *"."&*) o& th" )h$." &o!"* A) $ #"&"r$! r+!"4 th" %ro&t$! $r"$ ) +)"* %or /!+%% /o*")4 th" .!$&" %or( $r"$ o% th" )+/($r&" ) +)"* %or w&#) $&* th" w"tt"* $r"$ ) +)"* %or )+r%$," )h.) $&* /$r#") Th" !"&#th h$) &o .h'),$! ("$& /+t t )"r") th" .+r.o)" Th" DRAG $!+" & th" $/o" "8+$to& ) th" *r$# %or," o& th" /o*'4 wh,h ) ,$+)"* /' /oth ),o+) %r,to&$! $&* .r"))+r" %or( "%%",t)
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 8
Th" *r$# %or," ,$& /" r"*+,"* /' h$&# w$t"r )o!+/!"4 )+r%$,t$&t) (,ro/+//!") Tr+o&# 2001 Th) ("tho* ) r$th"r )(!$r to wh,h ) +)"* o& ,r+)" )h.) $) w"!! Th" (,ro/+//!") wor) $) th" *"&)t' o% $r & /+//!") ) 11000 to w$t"r4 th" !$'"r o% ,!+)t"r"* /+//!") &"$r th" )o!* w$!! ,$& *",r"$)" th" )h"$r )tr")) ,r"$t"* / ' w$t"r Th" )h$." )h%t&# ("tho* $!)o h$) /""& .ro"* to r"*+," *r$# o& )+/($r&" "h,!") Th" *r$# %or," o% th" "h,!" ,$& !"))"& th" *r$# %or," +. to 70@ % t ) ,o"r"* wth +&*+!$t&# )& Th) ("tho* ) &).r"* /' th" *o!.h& wh"r" th" ' wr&!" th"r )& to $o* w$t"r )t,&# o& th"r )& <$rr$) 200= Th")" ("tho*) o% *r$# r"*+,to& ) to &,r"$)" ).""* o% th" )+/($r&" wh,h ,o&)"8+"&t!' )$&# th" %+"!
$.0
!o#parison of te %ree Marine Veicles
Cr+)" )h.)4 )$!/o$t) $&* )+/($r&" $r" thr"" (o)t ,o((o& ($r&" "h,!") $$!$/!" to*$' Th" .+r.o)" o% "$,h *%%"r) $) ,r+)" )h. ) $ "h,!" th$t ,$rr") tho+)$&*) o% ."o.!" thro+#h $ ?o+r&"' thro+#ho+t th" )"$ wh!" )$!/o$t) o&!' ,$rr") two or thr"" ."r ?o+r&"'4 wh!" )+/($r&" h$) "&tr"!' *%%"r"&t .+r.o)" %ro( th" two to (o" +&*"rw$t"r For $!! th" thr"" ($r&" "h,!")4 th" "rt,$! %or,") $,t&# +.o& th"( $r" .r"tt' (+,h th" )$("4 th" /+o'$&,' $&* #r$t$to&$! wh,h ,$& /" )$* $) t) ow& w"#ht $) w"!! $) F($ ;th r"#$r* to ,r+)&# )h.) $&* )$!/o$t)4 th" "rt,$! .o)to& ) to /" (or" or !")) )t$to&$r' $&* %ro( th" "rt,$! %or,") .o&t o% "w4 th")" "h,!") $r" to )t$' $%!o$t A) %or th" )+/($r&" ,$)"4 th" "rt,$! %or,") &%!+"&," o& th" "h,!" ) $) (.ort$&t $) th" hor9o&t$! %or,") $) th" "rt,$! $&* hor9o&t$! .o)to& o% th" "h,!" ) to /" $r"* *"."&*&# o& th" ro+t" t$"& Th" hor9o&t$! %or,") $,t&# +.o& th")" thr"" $r") %ro( $ "h,!" to $&oth"r Cr+)" )h.) h$) th" "&#&" to %or," t %orw$r* $&* h$&# th" w&* %or," $&* ),o)t' %or," $) th" *r$# th$t o..o)" th" %orw$r* %or," Th" )$!/o$t h$) th" w&* $) t) *r&# %or," $&* th" ),o)t' %or," $) th" *r$# A) %or th" )+/($r&"4 th" %orw$r* %or," ) ,o&tr/+t"* /' th" "&#&" wh!" th" o..o)&# *r$# %or," ) ,o&tr/+t"* /' th" ),o)t' %or," $&* %r,to& %or," /"tw""& th" /o*' o% th" )+/($r&" wth th" w$t"r Th" *r$# r"*+,to& ("tho*) %or "$,h o% th" ($r&" "h,!") $r' %ro( o&" $&oth"r *"."&*&# o& ($&' .$r$("t"r) ),$!" o% w"#ht4 *r&# %or," $&* .r$,t,$!t' M,ro/+//!") $) $ *r$# r"*+,to& ("tho* ) +)"* & ,r+)" )h.) $&* )+/($r&") to &,r"$)" th" ).""* wh,h th"& !"$*) to )$&# (or" %+"! Th" ,r+)" )h. $!)o +)") $ hot /o*' $) $ *r$# r"*+,to& ("tho* Th"
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 9
)$!/o$t) $r" (.!"("&t&# th" $r%o! )h$.") to $*?+)t th" *r$# r"*+,to& $) w"!! $) th" !%t o% th" )$!/o$t) Th" .ro."r tr((&# o% th" )$! $,,or*&# to th" w&*) *r",to& $) w"!! $) th" t) ($#&t+*" w!! $!)o ,o&tr/+t" to th" *r$# r"*+,to& o% th" "h,!"
&.0
!onclusion
M$r&" "h,!") )h$r" .r"tt' (+,h )(!$r "rt,$! %or,") $,t&# +.o& th"( '"t (o)t o% th"( o&!' to /" $*?+)t"* to )t$' $%!o$t O&!' "h,!") )+,h $) )+/($r&" t$") "rt,$! %or,") to $r' t) "rt,$! .o)to& $) th$t .$rt,+!$r "h,!" .+r.o)" ) to )+r%$," $&* *" o+t $&* &to th" w$t"r Th" *r&# %or,") o& ($r&" "h,!") $r" ($&!' ,o&tr/+t"* /' "&#&")4 /+t )+,h "h,!" $) )$!/o$t) wh,h *o &ot h$" "&#&" to *o )o4 *"."&*) o& th" w&* $) th" *r&# %or," E$,h $&* ""r' ($r&" "h,!") h$) to "&,o+&t"r *r$# %or,"4 wh,h ) & th" o..o)t" % th" *r&# %or,"4 ($&# t )o("th&# th$t h$) to /" (&(9"* to ($6(9" th" *r&# %or," & %orw$r* *r",to& Th) *r$# %or," wh,h ) $!)o $ %r,to& %or," /"tw""& th" /o*' o% th" "h,!") wth th" w$t"r4 ) ,o&tr/+t"* /' th" ),o)t' %or," o% th" w$t"r Th"r" $r" ($&' *r$# r"*+,to& ("tho*) h$) /""& &"&t"* $&* /"&# (.ro)"* %ro( t(" to t(" $&* /"&# +)"* $,,or*&#!' to &","))t' o% "$,h "h,!" Th" *r$# r"*+,to& w!! (.ro" th" ).""* o% th" "h,!" wh,h ,o&)"8+"&t!' ,o&tr/+t") to )$&# th" %+"! +)$#" M,ro/+//!") $&* $r%o! )h$." $r" "6$(.!") o% th" *r$# r"*+,to& ("tho* &"&t"* %or ($r&" "h,!")
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 10
'.0
References
<$"r4 C 200 Estimating $rag Forces on Submarine Hulls htt..+/)*r*,#,,$PDFS+&,37.7227>.*% $,,"))"* M$' 14 2012 <$rr$)4 C 200= Shape-shifting Sin to .educe $rag on &lanes and Subs/ htt.www&"w),"&t)t,o($rt,!"*&13>3-)h$.")h%t&#-)&-to-r"*+,"-*r$#-o& .!$&")-$&*-)+/)ht(! $,,"))"* M$' 14 2012 2wwwr".ort))$!/o$t)$!/o$tht(! $,,"))"* M$' 174 2012 Histor': 0arro Ship'ards and Submarines 200 www)+/($r&"h"rt$#",o(h)tor'ht(! $,,"))"* M$' 14 2012
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 11
Ho*$&/o)4 C 1>> 0uo'anc': Archimedes &rinciple htt.www#r,&$)$#o;;;12;&*T+&&"!A,tt")/+o'Ar,h("*")ht(! $,,"))"* M$'4 1 2 012 Ho Sailboats Sail Against the !ind &* htt.www.h'),)%or$r,ht",t),o(S$!&#$#$&)tth"w&*.h. $,,"))"* M$' 174 2012 &h'sics of Sailing/ 200 htt.www),"&,"*$!',o(*"o)200120=-.h'),)o%)$!&#ht( $,,"))"* M$'4 17 2012 S"%4 MS $&* MT T$$o! &* N"w T",h&o!o#") For R"*+,&# F+"! Co&)+(.to& & M$r&" V"h,!") htt.www%)/+&9#hr)ort$200$/)tr$,tt=-1-t$$o!.*% $,,"))"* M$' 14 2012 Surfacing and $i#ing &* htt.%%*"&2.h')+$%"*+212%$!!2003w"/*r&$th$&"$r!))+r%$,&#$&**&#)!*"ht(! $,,"))"* M$' 14 2012 (he &h'sics of Sailing &* htt.www.h')+&)w"*+$+Q?w)$!&#ht(! $,,"))"* M$' 174 2012 (he ni#ersit' of (o'o &* Dr$# R"*+,to& /' M,ro/+//!") htt.www&(r#o?.($&,oo."r$to&+?&r2+?&r.$."r?.&o*$($.*% $,,"))"* M$' 174 2012 Tr+o&# V-T 2001 $rag .eduction (echnologies htt.www*t,(!,#-/&G"tTRDo,ADADA3>>0 $,,"))"* M$' 14 2012 U)/or&"4 D 200= "heap .i#ets 0lamed for 3assi#e Loss of Life as (itanic San htt.www&*"."&*"&t,o+&"w)wor!*$("r,$),h"$.-r"t)-/!$("*-%or-($))"!o))-o%-!%"-$)-tt$&,-)$&-=0>22ht(! $,,"))"* M$' 174 2012
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 12
(.0
Appendices
(.1
Appendi) 1
*et +or, ratio of #icrobubbles calculation r w=
¿
W net D U ∞ +W pump W o
+
Do U ∞
D W pump + D o D o U ∞
;h"r": ;o wor r$t" to .ro."! $ )h. & &o&-/+//!" ,o&*to& ;&"t &"t wor r$t" to .ro."! $ )h. & /+//!" ,o&*to& Do )h.5) *r$# & &o& /+//!" ,o&*to& D )h.5) *r$# & /+//!" ,o&*to& U )h.5) ).""* A))+(" to /" +&,h$&#"* /' /+//!" &?",to& ; .+(. wor r$t" %or /+//!" &?",to& r w 10 wh"& &"t *r$# r"*+,to& ) 9"ro
DRAG OF MARINE VEHICLES | FLUID MECHANICS 230 MINI-PROJECT | 2012 13
r w K 10 wh"& th"r" ) &"t *r$# r"*+,to& "%%",t
