UNIVERSIDAD RICARDO PALMA Facultad de Ingeniería
ESCUELA ACADÉMICO PROFESIONAL DE INGENIERÍA CIVIL
LAORA!ORIO N" #$
VELOCIDAD DE CAÍDA DE PAR!ICULAS CURSO%
INGENIERIA HIDRÁULICA
ALUMNA% C&DIGO%
PACHAS YLLISCA MANUEL 201020579
DOCEN!E% ING. CIP. MANUEL CASAS VILLALOBOS FEC'A%
16/01/15
SEMES!RE% 2015 - 0
LIMA(PER)* SURCO + $#,,. IN!RODUCCION% Un !"#$%&' ()'*+ *n#",+&%*+ n ' (n, + &n &*+, n "!,(, !," %#, + ' "++ *n*%* &n 3,*3*n#, + (n#3*n#, , +(%n(, 4& +!n+ + '( "'%*,n( n#" '( +n(*++( + ' !"#$%&' +' &*+,. L( !",!*++( $(*%( + ',( (+*3n#,( n#" ''( ' ',%*++ + %$+ + !"#$%&'( (,n + *3!,"#n%* &n+3n#' n ',( #",( + ' *nn*"$ *+"8&'*% n 3'(( +("n+,"( %n'( !",%(,( &*'( '%&(#" %,(#",( %,n("%*)n +' 3*n#.
$. O/E!IVO% E' ,#*, +' ',"#,"*, ( ,("" ' %,3!,"#3*n#, + '( !"#$%&'( , (+*3n#,( n ' +#"3*n%*)n !"*3n#' + ' ',%*++ #"3*n' + !"#$%&'( n &( 4&*#( ($ %,3, ' ',%*++ #)"*% &(n+, %"*#"*,( %,""(!,n+*n#( ' %(,. E(#'%" n ' ',"#,"*, ' !",!*++ + ' %$+ + !"#$%&'( n &( #"n4&*'( : (& "*%*)n %,n ' #3!"#&".
0. FUNDAMEN!O !E&RICO% L +#"3*n%*)n + ' ',%*++ + %$+ !,( n&3",(( !'*%%*,n( n ' *nn*"$ %**' %,3, !," 3!', n ' +*(;, + +("n+,"( 4& (,n (#"&%#&"( %&: &n%*)n ( "#n" , #"!" ',( (+*3n#,(. E' 3#"*' #"n(!,"#+, !," '( %,""*n#( + & !,( %#,( !"&+*%*'(< +*(3*n&: ' 8" + !(, + ',( %,n+&%#,( n "n '( #*""( + %&'#*, !",+&% 4& ' 3#"*' *3!%# n ',( '( + '( #&"*n( !",+&%*n+, (& "(*)n. S#,=( (&!&(, 4& !" ' &(, + &n (" 3)*' + +*83#", D> (*#&+ n &n %,""*n# %&: ',%*++ ( *&' U 1 !" n?3",( + R:n,'+( !4&;,( *n"*,"( ' &n*++ ( !,(*' +(!"%*" ',( #@"3*n,( + *n"%* "n# ',( + *(%,(*++ ''n+, (#'%" ' !"(*)n + ' "(*(#n%* ' n% + &n (" n ' (n, + &n &*+,< W
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L,( '*3*#( + !'*%%*)n + ' !"(*)n (,n< 2 3 D 50 3. 3 3*%" L3n#'3n# '( '*3*#%*,n( + ' !"(*)n + S#,=( ' +n (# %8'%&', &n "n, + !'*%%*)n 3&: (%(,. En ' !"8%#*% !" ' +#"3*n%*)n + ' ',%*++ #"3*n' + &n !"#$%&' ( "%&""n ,#"( "'%*,n( 3!$"*%( (*n 3", ', 38( "%,3n+' ( !",%+" !"*3n#'3n#. L ',%*++ !"*3n#' ( +#"3*n "'%*,nn+, ' +*(#n%* FH "%,""*+ !," ' !"#$%&' : ' #*3!, F# 4& #"+. V e=
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VELOCIDA DE CAIDA DE PAR!ICULAS EN AGUAS 5UIE!AS%
E( I3!,"#n# n ',( #",( + ' *nn*"$ *+"8&'*% #n" n %&n# '( !",!*++( $(*%( + ',( (+*3n#,( n ', 4& ( n%&n#" ' ',%*++ + %$+ + '( !"#$%&'(. S !&+n (#'%" n #"( #*!,( + !",!*++( + '( !"#$%&'(< Pr67iedad indi8idual de la3 7artícula3%
A'&n( + '( !",!*++( $(*%( *3!,"#n#( + '( !"#$%&'( ()'*+( %,n(*+"+ *n+**+&'3n# ( !"(n#n %,3,< a9 La :6r;a de una 7artícula* #*n &n *3!'*%n%* +*"%# n ',( (*&*n#( n#,( *+"8&'*%,(< • • • •
V',%*++ + (n#3*n#, n ' (n, &n &*+,. In*%*%*)n +' 3,*3*n#, + &n !"#$%&' n &n %,""*n#. E(#*'*++ , 4&*'*"*, n &n #'&+. A%,3,+, +n#", + &n "&!, n (&(!n(*)n .O#"( 4& #*nn 4& " %,n !",%(,( *+", : ",+*n83*%,( : n ' 3,",',$ : !",%(,( + (,%%*)n : (+*3n#%*)n.
M%N,n : In'*= #"( &n ("* + #",( !"*3n#'( %,n%'&:",n 4& la ;e<6r re7re3entaci=n de la :6r;a de la3 7artícula3 *n ++, !," 3+*, + ' "'%*)n +*3n(*,n'< +n,3*n+ :act6r de :6r;a +Jn*+, > +,n+ KK% (,n ',n*#&+( ',"+( n ( 3&3n# ,"#,,n'( (,%*+( &n !"#$%&'. Y ,#", %#," *n#"(n# !" ' +*(;, + ' (#*'*++ + &n n",%+, ( ' +n,3*n+, "'%*)n + C6re> FF C / 4& *n+*% ' l6ngitud relati8a de una 7artícula. ?9 La den3idad + ' 3( 4& +(%"* ' 3( ()'*+ !," &n*++ + ,'&3n @(# n, "$ (*n*J%n#3n# %,n ' #3!"#&" !," ', 4& ( (&3 %,n(#n# n ',( %8'%&',( ( %,n(*+" *&' ' +n(*++ + '( !"#$%&'( + %&", ( +%*" 2650 =/3. c9 El Pe36 e37ecí@c6 * %,""(!,n+ ' !(, !," &n &n*++ + ,'&3n +' ()'*+, &n '," #$!*%, (&3*+, !"'*3*n"3n# ( 26.5 =N/3
D#"3*n%*)n +' !(, (!%$J%,< d9 La gra8edad e37eci@ca G ( ' ")n +' !(, (!%$J%, + ' !"#$%&' ()'*+ ' !(, (!%$J%, + &n &*+, &n #3!"#&" (#8n+" + ""n%* %,3?n3n# ( #,3 ' & C.
D#"3*n%*)n + ' "++ (!%$J%< e9 El Pe36 3u;ergid6 de una 7artícula* ,#n*+ !," ' !'*%%*)n +' !"*n%*!*, + A"4&$3+(> "'%*,n ' !(, (!%*J%, + ' !"#$%&' ()'*+ %,n ' !(, (!%*J%, +' '*4&*+, n ' %&' ( n%&n#" (&3"*+ *&'n+, ' +*"n%* n#" ',( +,( !(,( (!%$J%,( ($> :9 El !a;a6 de 7artícula3* d3 ( &n + '( !",!*++( $(*%( 38( *3!,"#n#( + ',( (+*3n#,(.
Pr67iedade3 de ;iBtura3 de 3edi;ent63% a9 Di3tri?uci=n > ta;a6 de 7artícula3 Un 3!', + ' +*(#"*&%*)n + !"#$%&'( ( 3&(#" +&n#, n ' n,. M&(#" ' !,"%n# n !(, +' 3#"*' 38( Jn, 4& !( !," ' "#&" + &n #3* ++,. ?9 L 7artícula de ta;a6 d3 ( *+n#*J% !," 3+*, + ' %&" "n&',3@#"*% %,3, !," 3!', +50 %,""(!,n+ 4&'' %&:, #3;, ( #' 4& ' 50 n !(, +' 3#"*' + ' 3*#&" ,("+ ( *&' , 3n,". D *&' ,"3 ' +90 ' +10 (,n #3;,( + !"#$%&'( #'( 4& ' 90 : ' 10 +' !(, #,#' (,n *&'( , 3n,"(. c9 C6e@ciente3 de graduaci=n% ( &n 3+*+ + ' n, &n*,"3*++ + &n 3%' + (+*3n#,(. :
%,J%*n#( +
G" ( ' "+&%*)n
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"+&%*)n ( "+&%n ' &n*++ !" &n 3%' &n*,"3 + (+*3n#,( ( +%*" %&n+, +Q+50+16> ( *n%"3n#n %,n ' n, &n*,"3*++ &n %,J%*n# '#, +(%"* &n 3%' *n "+&+. d9 Angul6 de re7636* * ',"( #$!*%,( + 8n&',( + "!,(, + 3#"*' "n&'" &",n ++,( !," S*3,n( : ,#",( *n(#*+,"(. Pr67iedade3 de 3edi;ent63 en 3u37en3i=n
a9 Vel6cidad de 7artícula3 en agua3 uieta3* # ',%*++ + (n#3*n#, (#,( "* !," +*"n#( !"83#",(< a.,9 La 8el6cidad de a3enta;ient6 de una 7artícula en agua3 uieta3 a ,#"C % ( %'%&' %,n ' !"(*)n + G," St6e3 1Q5-1Q51 n ' ,"3 (*&*n#<
L( li;itaci6ne3 de la :=r;ula ' &(, %#*, + ' !"(*)n n#"*," (#8 "(#"*n*+, !"#$%&'( + #3;,( +( !4&;,( n ' "n, . D*%, *n#"', % &" + ',( &(,( + ' *+"8&'*% !"8%#*%. P", (* ( *3!,"#n# !" ' (#&+*, 3+*, 3*n#'. a.$9 La 8el6cidad ter;inal de una 7artícula dada 76r Gi??3 1971. *n ' !"(*)n<
Li;itaci6ne3 de la :=r;ula .- ' !"(*)n (*+, ',"+ !" !"#$%&'( (@"*%( +n#", +' "n, + +*83#",( D6nde* 7ara a;?a3 :6r;ula3 d3 e3 el di;etr6 de 7artícula* e3 la 8i3c63idad* G e3 la gra8edad e37eci@ca* > g e3 la aceleraci=n de la gra8edad. a.09La 8el6cidad de 3edi;entaci=n de Ru?e>% #*n ' ,"3%
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0.79
?9 L 8el6cidad de a3enta;ient6 de un gru76 de 7artícula3 En &n%*)n + ' %,n%n#"%*)n (# ++, !,"<
D,n+ 0 w ( ' ',%*++ + (+*3n#%*)n + &n !"#$%&' ( &n &n%*)n +' %#," + ,"3 + ' !"#$%&' +'
#3;, ' +*(#"*&%*)n : ' n?3", + R:n,'+( + ' !"#$%&' +,n+ .65 !" R:n,'+( 3n,"( 4& &n, R1 : 2.2 !" ',"( + RK 1000. E(# %,n(*+"%*)n ( 3&: *3!,"#n# !" (#&+*,( + (+*3n#%*)n n 3'(( : ',( #",( + "3,%*)n + (+*3n#,(. c9 G"J%, + (n#3*n#, + !"#$%&'( !" ' !",*3%*)n !"'*3*n" + '( ',%*++( + %$+ + !"#$%&'( n ' (n, + &n &*+, *(#n +*"n#( !",!&(#( %,3, ',( + S&+": : ,#",( %,3, ',( + P",%+*n In#"n%: R N 12 57. 4& ( 3&(#" n ,"3 +&n#.
N)MERO DE RENOLD%
E( &n n?3", +*3n(*,n' *'*+, n 3%8n*% + &*+,( +*(;, + "%#,"( : n)3n,( + #"n(!,"# !" %"%#"*" ' 3,*3*n#, + &n &*+,. C,3, #,+, n?3", +*3n(*,n' ( &n %,%*n# &n %,3!"%*)n. En (# %(, ( ' "'%*)n n#" ',( #@"3*n,( %,n%#*,( : ',( #@"3*n,( *(%,(,( + '( %&%*,n( + N*"-S#,=( 4& ,*"nn ' 3,*3*n#, + ',( &*+,(. A+38( ' n?3", + R:n,'+( !"3*# !"+%*" ' %"8%#" #&"&'n#, , '3*n" n %*"#,( %(,(. A($ !," 3!', n %,n+&%#,( (* ' n?3", + R:n,'+( ( 3n," + 2000 ' &, ("8 '3*n" : (* ( 3:," + 000 ' &, ("8 #&"&'n#,. E' 3%n*(3, : 3&%( + '( ",n( !," '( %&'( &n &, ( '3*n" , #&"&'n#, ( #,+$ ,: ,#, + (!%&'%*)n.
S?n ,#",( ,"(< •
•
•
P" ',"( + ' &, ( 3n#*n (#%*,n"*, : ( %,3!,"# %,3, (* (#&*" ,"3+, !," '83*n( +'+( 4& *n#"%#?n ()', n &n%*)n + ',( (&",( #nn%*'( *(#n#(. P," (, (# &, ( ' ''3 &, '3*n". E' %,',"n# *n#",+&%*+, n ' &, ( 3& (*&*n+, &n +'+ '$n !"'' '( !"+( +' #&,. P" ',"( + ' '$n +' %,',"n# !*"+ (#*'*++ ,"3n+, !4&;( ,n+&'%*,n( "*'( n ' #*3!, 3n#n*@n+,( (*n 3", +'+. E(# "@*3n ( +n,3*n + #"n(*%*)n. P" ',"( + +(!&@( + &n !4&;, #"3, *n*%*' %,n ,(%*'%*,n( "*'( ' %,',"n# #*n+ +*&n+*"( n #,+, ' &,. E(# "@*3n ( ''3+, #&"&'n#, ( +%*" %"%#"*+, !," &n 3,*3*n#, +(,"+n+, n, (#%*,n"*, : #"*+*3n(*,n'. E(# n?3", "%* (& n,3" n ,n," + O(,"n R:n,'+( 1Q2-1912 4&*n ', +(%"**) n 1QQ. V*n ++, !," (*&*n# )"3&'<
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*(%,(*++ %*n38#*% +' &*+,
H. E5UIPO U!ILIADO% (!er;=;etr6 < ( &n *n(#"&3n#, + 3+*%*)n + #3!"#&". D(+ (& *nn%*)n ,'&%*,n+, 3&%, !"*n%*!'3n# !"#*" +' +("",'', + ',( #"3)3#",( '%#")n*%,( +**#'(. In*%*'3n# ( "*%",n !",%n+, ' n)3n, + ' +*'#%*)n !," ', 4& ( !""$ ' &(, + 3#"*'( %,n '+, %,J%*n# + +*'#%*)n + 3,+, 4& ' &3n#" ' #3!"#&" (& (#*"3*n#, " 8%*'3n# *(*'. E' 3#' ( 4& ( *'* n (# #*!, + #"3)3#",( (*+, ' 3"%&"*,
n%""+, n &n #&, + *+"*, 4& *n%,"!," &n (%' "+&+. (Cr6n=;etr6% E' &n%*,n3*n#, &(&' + &n %",n)3#", %,n(*(# n 3!" %,n#" +(+ %", ' !&'("( ' 3*(3, ,#)n 4& ', +#*n. A+38( *#&'3n# !&+n 3+*"( "*,( #*3!,( %,n ' 3*(3, %,3*n, : +*(#*n#, Jn'. P" '', ( %,n' ',( (&%(*,( #*3!,( %,n &n ,#)n +*(#*n#, n,"3'3n# %,n ' + "*n*%*, 3*n#"( (*& %,n#n+, n (&n+, !'n, (# 4& ( !&'( ' ,#)n + %,3*n,.
-Mue3tra de 7artícula3 de granul6;etría 3elecci6nada% '( 3&(#" 4& *'*3,( &",n ',( (*&*n#(< !AMI DE PAR!ICULAS KH
DJ;9
K,#
00075 0002
K$#
0001
KH#
0000Q
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-!u?6 7ara 6?3er8aci=n de 8el6cidade3 de caída%N,( :&+ +#"3*n" ' ',%*++ + !"#$%&'( %,n +*"n# "n&',3#"$ T+*83#", : %,3!,(*%*)n n &( 4&*#(. C,n ', 4& ' *(%,(*++ +' '*4&*+, ( &n %#," *3!,"#n#. E3te eui76 tiene c6;6 c6;76nente3%
- #&, + *+"*, Su3 di;en3i6ne3%
- '", 1.15 3. - +*83#",
-. PROCEDIMIEN!O DE LAORA!ORIO DE GAINE!E % Para e3te eB7eri;ent6 3e di8idi= en cuatr6 gru763 ue 3iguier6n e3t63 7a363%
R%,n,% : +(%"* '( !"#$%&'( +' "&!, + '( 3&(#"( "%**+( n ' ',"#,"*, %,n ' :&+ +' "n*" : + ' *n%. - ,3 n,# + ',( #3;,( +' "&!, + !"#$%&'( 4& ("*"8n + 3&(#"( !" ' n(:, + ',%*++ + %$+ + '( !"#$%&'( n #"n4&*'(. - R*(#" ' #3!"#&" +' & n ' !",#. - D#"3*n ' +*(#n%* + ,("%*)n. -
S&'# n ' & '( !"#$%&'( n ,"3 *n+**+&' : n "&!,. - ,3 ' #*3!, + "%,""*+, + &n !"#$%&'. - ,3 ' #*3!, + "%,""*+, + &n "&!, + !"#$%&'(. - R!*# ' ,("%*)n +' !&n#, 5 +&"n# ' 3n,( #"( ,("%*,n( !" ',( +*"n#( #3;,( + !"#$%&'(. -
Dat63%
In#"!,'n+, ',( +#,( + ' #'< • • • • • •
ρ
997.5 /%3 0.951 10 - PW( -6 2 υ 0.95 10 3 /( H #"3, +' & 0.50 3 3!"#&" 1QC ρ( 2650 /%3
F=r;ula3 V D*(#n%*/#!",3 V# Xρ( T ρ. . D2/1Q R V.D/
. !OMA DE DA!OS%
N. !AMICES H , $# 0# H# # ,##
ρ3
ρa
2600 2600 2600 2600 2600 2600 2600 2600
1000 1000 1000 1000 1000 1000 1000 1000
ρ3
( ρa
1600 1600 1600 1600 1600 1600 1600 1600
Jρ3 ( ρa9 B g 156Q0 156Q0 156Q0 156Q0 156Q0 156Q0 156Q0 156Q0
D
D$
2t
00075 0002 00011Q 000059 0000295 0000177 0000 000017
225625E-05 000000 192E-06 Q1E-07 Q7025E-0Q 129E-0Q 000000009 21609E-0Q
1Q67Q 0592 115079 02Q770 007192 0025Q9 007Q 0017Q6
. CLCULOS RESUL!ADOS
N. !AMICES
t
8eQt
H , $# 0# H# # ,##
160 1Q1 275 21 92 59 1220 25
01 0276 01Q2 0216 0127 00Q 001 0021
N. !AMICES
PRUEA N.
D J;9
! J39
H , $# 0# H# # ,##
1 2 5 6 7 Q
00075 0002 00011Q 000059 0000295 0000177 0000 000017
160 1Q1 275 21 92 59 1220 25
Re>n6ld3 R V D Qν 00001QQ 552Q6E-05 212Q6E-05 127706E-05 75956E-06 1921E-06 1229QE-06 01QQ9E-07
2 eB7eri;ent al 01 02Q 01Q 022 01 00Q 00 002
. PRESEN!ACI&N DE LOS GRFICOS
2 te6ric6
N. Re>n6ld3
1Q67Q 0592 115079 02Q770 007192 0025Q9 007Q 0017Q6
000016725 000005QQ0 0000029Q 000000Q217 0000002915 00000015Q0 0000001Q27 000000069
DIAME!RO VS. VELOCIDAD !EORIA 20 1Q Q26Q1.1 Z2 16 R[ 1 1 12 VELOCIDAD 10 Q 6 2 0 0 0 0 0 DIAME!RO
P,"
0
0.01
DIAME!RO VS. VELOCIDAD EPERIMEN!AL 0.M5 0.M0
CE D 1M.91 Z0.65 R[ D 0.6Q
0.25 0.20 VELOCIDAD EP.
P,H-" CE
0.15 0.10 0.05 0.00 0
0
0
0
0
0.01
DIAME!RO
. CUES!IONARIO A. Enc6ntrar la 8el6cidad li;ite de una e3:era de di;etr6 D #.;; > den3idad ;edia de cae en el aire de den3idad ρ3,0.grQcc* ue ρaire,.$grQcc > 8i3c63idad igual a ,.H$-T,# (- ;$Q3.
V*(%,(*++ 1.25W10-5 32/( 0.125%32/( X1.6-1.26W9Q0.60.0Q 2/ 2.96%3/(
1QW1.7955W10-1
. Enc6ntrar la 8el6cidad lí;ite de la ;i3;a e3:era* ue cae en agua c6n 8i3c63idad de ,.,HT,# (0 N.3 Q;$* > den3idad de ., g. Q; 0.
1.1W10- N(/32 1.107W10 -5/%3.( \ Q5.196 %3/(.
,#.
CONCLUSIONES
,,.
E( I3!,"#n# n ',( #",( + ' *nn*"$ *+"8&'*% #n" n %&n# '( !",!*++( $(*%( + ',( (+*3n#,( n ', 4& ( n%&n#" ' ',%*++ + %$+ + '( !"#$%&'(. E' #3;, + '( !"#$%&'( (#8 %,3!"n+*+, n#" ',( +*83#",( + 0.00753 : 0.000153. En !'n, !"*3n#, n,#3,( 4& ' ',%*++ + %$+ + &n !"#$%&' ( + %&"+, ' #3;, + (#8 + %&"+, (# %, (%3,( %,3, %,n%'&(*)n 4& ' +*(3*n&*" ' +*83#", ' #*3!, + (+*3n#%*)n &3n#. A($ 3*(3, !,+3,( +%*" 4& (* ' & &" '+ , &n #3!"#&" 38( 4& ' #,3+ '( !"#$%&'( +3,""$n 3( n " : ' #*3!, ("* 3:,". L,( 3''( 4& &",n &(+( (,n '( ] ]Q]16 ]20]0]0]60]100. S +#"3*n, ' ',%*++ + %$+ !"*3n#' %,3, #)"*% + !"#$%&'( %,n +*83#",( %,n,%*+,( n &( 4&*#(. L ',%*++ !"*3n#' ( +#"3*n "'%*,nn+, ' +*(#n%* FH "%,""*+ !," ' !"#$%&' : ' #*3!, F# 4& #"+. E' n&3", + R:n,'+( (# #3*@n n &n%*)n +' +*83#", + '( !"#$%&'( ' %&' ( 3:," %&n+, ' +*83#", + ' !"#$%&' ( 38( "n+. L,( #*3!,( 4& "%,"" '( !"#$%&'( ( %n 38( %,"#,( %,n,"3 (,n 38( !4&;(. E' n(:, & "'*+, &n #3!"#&" + 1Q ^ C !" ' %&' +n(*++ & ' (*&*n#< ρ 997.5 /%3 ' 0.951 10 - PW( : ' *(%,(*++ υ 0.95 10-6 32/( L,( ',"( + R _ 2000 !," ', #n#, ' &, ( 3n#*n (#%*,n"*, : ( %,3!,"# %,3, (* (#&*" ,"3+, !," '83*n( +'+( 4& *n#"%#?n ()', n &n%*)n + ',( (&",( #nn%*'( *(#n#(. P," (, (# &, ( ' ''3 &, '3*n". E' #*!, + &, ( &, '3*n" (# "(&'#+, ('*) n 1 "&!,.
RECOMENDACIONES •
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