UNIVERSIDAD NACIONAL DEL CENTRO DEL PERU
CÁLCULOS METALURGICOS EN LAS PLANTAS CONCENTRADORAS ING. MARIO A. CERRON MADUEÑO ING. FIDEL CORDOVA CORDOVA CABRERA ING. MANUEL RUBEN GUERREROS MEZA
HUANCAYO- PERU JUNIO 2005
DERECHOS RESERVADOS Es! "#$%& '& ()!*! s!% !' (+%! & &+" %!(%&*),#*& & !&%#+*& !' s#s!+s *! +%,/#& & %+'s##*& !' ,)+"1)#!% &%+ & !*#& !"!,%3'#,&4 !,'#,&4 &&,&(#+*& & ,)+"1)#!% &%& s#s!+ s#' "+ (%!#+ +)&%#+,#3' *! "&s AUTORES
HECHOS TODOS LOS DEPOSITOS DE LEY N6 25728
INTRODUCCIÓN
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& ,&' )' (%&(3s#& *!#'#*&4 "+ *! $%#'*+% + "&s !s)*#+'!s *! "+ Es(!,#+"#*+* *! I'=!'#!%<+ M!+"?%=#,+ ; &%&s +#'!s4 )' %!(!%&%#& s#s!#,& ; $#!' ("+'!+*&s *! "&s (%#',#(+"!s ,",)"&s 1)! s! %!+"#+' !' )'+ ("+'+ *! P%&,!s+#!'& *! M#'!%+"!s. E' !" ,&'!'#*& *! !s! !:&4 s! /+ %++*& *! s#("##,+% +" :#& "&s *!s+%%&""&s +!#,&s (+%+ ""!+% + "+s 3%)"+s (+%+ s) +("#,+,#3' ,&' !>!("&s s#("!s ; (%,#,&s. N&s (!%##&s +*!%#% 1)! !" ,&'!'#*&4 '& !s )'+ ,&s+ &%#=#'+"4 s#'& 1)! s! %++ *! )'+ +*!,)+*+ (%!s!'+,#3' *! "&s ,&'&,##!'&s !' !" ,+(& *! P%&,!s+#!'& *! M#'!%+"!s4 (+%+ "+s !'s!@+'+s !'s!@+'+s 1)! s! #(+%!'4 (+%+ 1)! + %+9s *! 9s&s s! "&=%! ,%!+% )'+ ')!+ !s,)!"+. LOS AUTORES
CAPITULO I
DESCRIPCIONES GENERALES E" (%!s!'! %+$+>& !s+ *!*#,+*& + *!s,%#$#% "+s (%#',#(+"!s !+(+s ; ,",)"&s $s#,&s 1)! s! %!+"#+' !' "+s P"+'+s *! B!'!#,#& *! #'!%+"!s4 *!s*! "+ %!*),,#3' *! ++@&s4 /+s+ !" %++#!'& )s)+" *! "+ ,&',!'%+,#3'. L+ %!*),,#3' *! ++@& *! "&s #'!%+"!s s! !!,?+4 (&%1)! !" #'!%+" !:%+<*& *! "+ #'+ s&' +;&%!'! *!+s#+*& =%+'*!s (+%+ s!% s&!#*&s + "&s %++#!'& *! ,&',!'%+,#3'4 ; s! /+,!' /+,!' (&% "+s !+(+s !+(+s *! %#)%+ %#)%+,#3 ,#3'' ; M&"#!' M&"#!'*+4 *+4 /+s+ /+s+ +",+' +",+'+% +% )'+ =%+')" =%+')"&! &!%<+ %<+
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+*!,)+*+4 1)! (!%#+ "+ "#$!%+,#3' *! "+s (+%<,)"+s +"#&s+s !'+s *! )' #'!%+" *! "+ =+'=+. L+ %#) %#)%+ %+,# ,#3' 3'44 =!'! =!'!%+ %+" "!' !'! ! s! !!, !!,? ?+' +' !' "+s "+s 1) 1)#' #'+s +s ""+ ""++* +*+s +s C/ C/+' +',+ ,+*& *&%+ %+ss & )!$%+'+*&%+s4 *&'*! s! %!*),!' "&s ++@&s =%+'*! *! #'!%+"!s + !*#+*&s ; ")!=& + =%+*&s #'!%!*#&s *! s)$*##s#&'!s4 !' +%#+s !+(+s4 +("#,+'*& "+ )!%+ !,'#,+ *! ,&(%!'s#3'. L+ M&"#!'*+ s! ""!+ + ,+$& !' "&s &"#'&s4 "&s ,)+"!s ()"!%#+' & *!s#'!=%+' !" #'!%+" /+s+ !" ++@& 3(#& *! "#$!%+,#3'. P+%+ "& ,)+" !" M#'!%+" s!=)#% "+ s!,)!',#+ *! "+s s#=)#!'!s &(!%+,#&'!s )'#+%#+s ,&& s! #'*#,+ !' !" D#+=%++ *! %++#!'&4 ; s! #!'!
1.- ABASTECIMIENTO Y DESCARGA DEL MINERAL DE MINA D! *&'*! !" M#'!%+" !s +$+s!,#*& ; %+'s(&%+*& + "+ P"+'+ C&',!'%+*&%+ (&% !*#& *! s#s!+s *! ,+$"!s ,+%%#"!s4 ,+%%&s ,+%=)!%&s ) &%& s#s!+ *! %+'s(&%! !" ,)+" "& *!(&s#+ !' "+ T&"+ *! G%)!s&s4 1)! ()!*! s!% *! &%+s *#!%!'!s4 *! )'+ *!!%#'+*+ ,+(+,#*+*. U'+ ! *!(&s#+*& !" #'!%+" !' !s+ T&"+4 !s *!s,+%=+*+ *! 9s+ (&% "+ (+%! #'!%#&%4 + %+9s *! )' S/)4 & *! &%&s !,+'#s&s *! *!s,+%=+ *!s,+%=+ ; !s %+'s(&%+*+ /+,#+ /+,#+ "+ C/+',+*&%+ C/+',+*&%+ P%#+%#+ (&% !*#& !*#& *! +"#!'+*&%!s +"#!'+*&%!s *! O%)=+ O%)=+ ) &%&s !*#&s !*#&s *! +"#!'+,#3'.
2.- CHANCADO O QUEBRANTAMIENTO DEL MINERAL
.- Chancado P!"a!o .- !" #'!%+" %+'s(&%+*& !s +"#!'+*& + "+ C/+',+*&%+ P%#+%#+ *! )#>+*+ & *! !>! s)s(!'*#*+. T#(& U'#!%s+"4 !" #'!%+" !s +"#!'+*& (&% !" G+(!4 ; "+ *!s,+%=+ *!s,+%=+ s! /+,! (&% !" S! *! "+ C/+',+*&%+4 1)! !s+ +,,#&'+*+ (&% )' &&%4 *! *&'*! !" #'!%+" !s %+'s(&%+*& !*#+'! +>+s /+,#+ )'+ Z+%+'*+ V#$%+&%#+.
2. 2.-- Ta"!#ado d$% &%'(o P!nc!)a% d$ M!n$a% T!*'ado .- !" +#+*& s! /+,! +;&%!'! !' )'+ Z+%+'*+ V#$%+&%#+4 *&'*! !" #'!%+" 1)! (+s+ (&% "+ +""+ s! "! +s#='+ ,&' !'&s - ; !" #'!%+" 1)! !s %!,/++*& s! "! +s#='+ s +""+ .
D! +1)< !" #'!%+" 1)! s&$%! !' !" T+#4 (+s+ + "+ C/+',+*&%+ S!,)'*+%#+ ; !" #'& s! +"+,!'+ (&% !*#& *! +>+s !' "+ T&"+ *! F#'&s.
7.- Chancado S$c'nda!o .- P+%+ !s+ !+(+4 +;&%!'! s! )#"#+' "+s C/+',+*&%+ G#%+&%#+s *! !>! s)s(!'*#*&4 !" ,)+" %!,#$! !" #'!%+" (%&!'#!'! *! "+ +%+'*+ #$%+ #$%+&%# &%#+4 +4 !' s) ("+& ("+& & ,+$! ,+$!+" +" *! +"#!' +"#!'+, +,#3' #3'44 *!" ,)+" ,)+" ,&#! ,&#!'+ '+ + ,+!% ,+!% #'!%#&%!'! *!$#*& +" *!s("++#!'& =#%&s,3(#,& *!" M+'"! 3%=+'& 3#"4 *&'*! "&s %+&s *! #'!%+" !s+%' s&!#*&s + (!%,)s#&'!s s),!s#+s +"=& *! +%%+s%! !'%! !""+s ; + "&s !s)!%&s *! ,&(%!s#3' &%#=#'+*& (&% !" +,!%,+#!'& *! (#s#"& + "+ ,3',++. T&*& !" +,,#&'+#!'& *! "&s ()'&s 3#"!s *! "+ C/+',+*&%+ s! *!$! + )' s#s!+ *! !'=%+'+>!s ,&'!,+*&s + )' &&%4 (&% !*#& *! )' !>! /&%#&'+" 1)! !%#'+ !' )' (#@3' ; !s !" 1)! %+s#! &*& !" &## &##!' !'&& (&% !*#& *! "+ !:,9' !:,9'%#, %#,+4 +4 1)! !s &'+* &'+*&& !' )' ,&>#' ,&>#'!! !! ; +,,#&'+*& (&% "+ ,&'!:#3' *! "+ ,++"#'+ ,&' !" (#@3' *!" ,&'%+ !>!. T+'& !" M+'"! ; !" ,3',+& s&' *! +,!%& +" +'=+'!s& ; "+s s)(!%#,#!s &"!*&%+s #!'!' '!%+*)%+s (+%+ "+ !>&% +,,#3' *! %#)%+,#3'. T&*& !" #'!%+" %#)%+*& +" ++@& s & !'&s *! !s *!s,+%=+*& (&% "+ (+%! #'!%#&%4 ; %+'s(&%+*& + "+ &"+ *! #'&s4 "+ ,)+" *!$!% !'!% 7 !,!s s 1)! "+ ,+(+,#*+* *! "+ ("+'+ (+%+ +'!'!%"+ !' &(!%+,#3' s# s! (%!s!'+' *!s(!%!,&s !' "+s ,/+',+*&%+s. ,/+',+*&%+s.
+.- MOLIENDA DEL MINERAL, .- Mo%!$nda P!"a!a .- L+ ,)+" s! !!,?+ !' &"#'&s *! $+%%+s 4 *&'*! !" #'!%+" !s s&!#*& + "+ +,,#3' &"!*&%+ *! "+ ,+%=+ *! $+%%+s4 "+s ,)+"!s s&' "!+'+*+s +" =#%+% !" &"#'& s&$%! "+s &'*)"+,#&'!s *! "&s &%%&s ; +" ,+!% &%#=#'+' )' !!,& &"!*&% #'!'s& *!$#*& + s) (!s&4 9s&s &"#'&s s&' +,,#&'+*&s (&% )' &&%4 !" &##!'& !s %+'s##*& (&% !*#& *! )'+ +>+ !' V + )' (#@3' 1)! /+,! =#%+% !" &"#'& (&% !*#& *! )'+ ,++"#'+ *!'+*+. E" #'!%+" &"#*& s! *!s,+%=+ (&% !" )@3' *! *!s,+%=+4 *!s,+%=+4 !' &%+ *! ()"(+ !" ,)+" ""!+ )' %&!" =#%+&%#& 1)! %+$+>+ ,&' +=)+ + (%!s#3' 1)! ,+! s&$%! "+ s)(!%#,#! !' &%+ *! ,/#s=)!!4 !" %&!" s!(+%+ "+s $+%%+s4 (!%'&s ; #'!%+"!s *)%&s 1)! '& /+' s#*& &"#*&s. L+ ()"(+ *!" #'!%+" &"#*& (+s+ + )' +'1)! *! *!s,+%=+ + >)'+%s! ,&' "+s +%!'+s *!" C#,"3' & C"+s##,+*&% ,&'s#);!'*& "+ ,+%=+ *! +"#!'+,#3' *!"
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M&"#'& *! B&"+s. Es&s &"#'&s %+$+>+' !' ,<%,)"& +$#!%&4 (%&*),!' (%&*),&s $+s+'! =%+')"+*&s =%+')"+*&s ; )'#&%!s #(&%+'!s #(&%+'!s (+%+ )'+ ,&',!'%+,#3' =%+#9%#,+. =%+#9%#,+. 2.- Mo%!$nda S$c'nda!a .- S! /+,!' !' "&s " &s &"#'&s *! $&"+s4 ; "+ *!s,+%=+ (%&#!'! *!" &"#'& *! $+%%+s 1)! !s "+ +"#!'+,#3'4 s "+s +%!'+s *!" C#,"3' & *!" C"+s##,+*&%. A1)< !" #'!%+" !s s&!#*& *)%+'! "+ &"#!'*+ + +,,#3' *!s#'!=%+*&%+ *! =&"(!4 %#,,#3' ; (%!s#3' *! "+s $&"+s. E" #'!%+" &"#*& !s *!s,+%=+*& +" ,+>3' *#s%#$)#*&%4 (+%+ ")!=& s!% $&$!+*& $&$!+*& +" C#,"3' & *!s,+%=+ *!s,+%=+%% *#%!,+!'! +" ,"+s##,+*&% ,"+s##,+*&% /!"#,&#*+" & *! %+s%#""&.
7.- C%a!&!cac!n.- C&& "+ &"#!'*+ '& !s )'#&%! '# &+"4 s! !'*% (+%!s #'+s ; =%)!s+s =%)!s+s !' "+ ()"(+ *! *! *!s,+%=+ *!s,+%=+ *!" &"#'&4 &"#'&4 (&% (&% "& ,)+" !s '!,!s+ '!,!s+%#& %#& ,"+s##,+ ,"+s##,+%"&s %"&s !s+s (+%!s4 s# !s ,&' )' ,#,"3'4 "+ ()"(+ s! $&$!+ + =%+' (%!s#3' (&% !*#& *! )'+ $&$+ ; 9s+4 *&'*! ,#%,)"+ "+ ()"(+ + +"+ !"&,#*+* +"%!*!*&% *! "+s (+%!*!s *!" ,#,"3' (&% !!,& *! "+ )!%+ ,!'%<)=+ 1)! s!(+%+ + "+ ()"(+ !' )'+ (+%! #'+ ; &%+ =%)!s+. L+s =%)!s+s (&% s) +"& (!s& s! (!=+%' + "+s (+%!*!s ; s! /)'*!' ; s! *!s,+%=+' *!s,+%=+' (&% !" APEK ; %!&%'+' +" &"#'& ,&& ,+%=+ ,#%,)"+'!. L+s #'+s (+s+' + "&s +,&'*#,#&'+*&%!s (+%+ ")!=& (+s+% + "+ ,&',!'%+,#3' (&% "&+,#3' ) &%&s 9&*&s *! ,&',!'%+,#3' s!=?' "+ (%&(#!*+*
/.- CONCENTRACIÓN DEL MINERAL, L+ ()"(+ ()"(+ *! %!$&s! %!$&s! *!" ,"+s# ,"+s##,+ #,+*&% *&% 3 "&s #'&s #'&s 1)! s+"!' s+"!' *!" V&%!: &%!: *!" *!" ,#," ,#,"3' 3' +,&'*# +,&'*#,#& ,#&'+ '+*&s *&s (+s+' (+s+' + "&s $+' $+',&s ,&s *! ,!"*+s ,!"*+s s!=?' s!=?' "&s !"!!' !"!!'&s &s 1)! s! *!s!+' *!s!+' ,&',!'%+% (&% "&+,#3'. T+$#9' s! ()!*! ,&',!'%+% )#"#+'*& &%&s 9&*&s ,&& (&% =%+#!%<+4 !"!,%&s#,+4 !,. D!" ,)+" s! &$#!'!' "&s (%&*),&s *! ,&',!'%+*& ; !" %!"+!.
0.- ELIMINACIÓN DEL AGUA EN LOS CONCENTRADOS T+'& "&s "&s ,&',!'%+*&s ,&',!'%+*&s ; "&s %!"+!s %!"+!s s+"!' +,&(+@+*&s +,&(+@+*&s *! +=)+4 "& ,)+" ,)+" s!% !"##'+*& /+s+ 04 (&% !*#& *!" Es(!s+*& ; F#"%+*&.
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CAPITULO II CLCULOS METALRGICOS EN LA SECCIÓN DE PREPARACIÓN MECANICA 1.- CUBICACIÓN DE TOL3AS Es '!,!s+%#& *!!%#'+% "+ ,+(+,#*+* *! "+s &"+s !' !" 1)! s! +"+,!'+ !" #'!%+" + #' *! ,&(%&$+% s# 9s+s #!'!' "+ s)#,#!'! ,+(+,#*+* *! +"+,!'+>! ; (%!!'#% ,&'%+ #!(&s !' "&s !*#&s *! %+'s(&%! *! "+ #'+ ; &%&s *!s(!%!,&s 1)! ()!*+' &,)%%#% !' !" (%&,!s& ; +s< !'!% !' s&, (+%+ !" '&%+" )',#&'+#!'& *! "+ ("+'+. L+s &"+s ()!*!' s!% *! *#!%!'!s &%+s ; ++@&s4 (+%+ !!,)+% "&s s#=)#!'!s ,",)"&s !s '!,!s+%#& ,&'&,!% +'& !" &")!' *! "+ &"+ ; "+ =%+!*+* !s(!,##,+ *!" #'!%+" +(+%!'!.
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D&'*! P P&!',#+ !' HP W A A"#!'+,#3' A"#!' +,#3' !' TC/ 5.5 E'!%=<+ *! %#)%+,#3' !' -/TC 0.708 R!!("++'*& R!!("++'* & P 0.708 : 5.5 : .7 7.0 HP - R!'*##!'& R!'*##!' & *!" M&&%4 s#!'*& !" *! "+ #'s+"+,#3' #'s+"+,#3 ' *! 0 HP. HP. E#,#!',#+ & %!'*##!'& E
HP B práctico práctico xG00 HP Binstalada
7.0xG00 G0
70.L
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T&'!"+>! T&'!"+>! M:.
HP Binstalada WxG.I7G HP O Kw
G0 HP 0.7N08 Kw h O TCxG.I7G HP O Kw
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R!!("++'*& R!!("++'*& A 0.8 : : 2. TM/
07.- La )o*$nc!a )o*$nc!a $'$ $'$!da !da $n $% Mo*o d$ 'na Chancado Chancadoaa .- S! ()!*! ,+",)"+% +s#='+'*& +" HP !',&'%+*& 0 (&% (9%*#*+s *! %+'s#s#3' *! &##!'& *!" &&% + "+ ,/+',+*&%+4 20 ,&& !*#*+ *! s!=)%#*+* ; 200 (+% )'+ ))%+ +("#+,#3' *! "+ P"+'+. P #'s.
7.0BG0 20 200 G00
Q.0 HP
/.- CALCULO PARA HALLAR LA E5ICIENCIA DE UNA ARANDA 3IBRATORIA. P+%+ +("#,+% "+ s#=)#!'! s#=)#!' ! &%)"+ *! TAGGART AGGART e
G0.000 a b a G00 b
D&'*! ! E#,#!',#+ *!" +# + *!" !%*+*!%& U'*!%s#*! !' "+ +"#!'+,#3' $ *!" U'*!%s#*! !' !" +,)+" O!%s#*!. Es '!,!s+%#& '!,!s+%#& ,&'& ,&'&,!% ,!% "+ ,+%=+ ,+%=+ +" +#4 +#4 ,&& ,&& s! ()!* ()!*!! !% !' !" !s1)!+ !s1)!+ s#=)#!'! s#=)#!'! E>!("& D+&s M+""+ *! .5 : .5 -
A"#!'& 5.20 =
-
O!%s# %s#*! 75.5 =
-
U'*!%s#*! .05 = =
M+""+ *! X : -
O!%s#*! .2 =
-
U'*!%s#*! .5 = =
17.- C?%c'%o d$ %a $&!c!$nc!a $&!c!$nc!a d$ %a "a%%a 1.0 < 1.0. C&'s#*!%!&s 1)! )' +'"#s#s =%+')"&9%#,& *!" #'!%+" %!,!(,#&'+*& %!,!(,#&'+*& (!s+*& *+ !" s#=)#!'! %!s)"+*& A"#!'+,#3' 5.20 =
.5 72.05 = - .5 22.5 =
O!%s#*!
75.5 =
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5.20
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.05 =
U'*!%s#*! 2 7 : .80 = -7 : 2.80 =
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Ma%% Ma%%aa E E*a6% *a6%$$c!da !da 2.50 =
Ma%%a a%%a !>'a !>'a%% a %a "!*a "!*ad d d$ d$ %a %a an* an*$$!o !o 28.80 =
- 0.50 = T&+" 75.00 =
- .0 = 75.000 =
TABLA PARA DETERMINAR LOS 5ACTORES DE CORRECCIÓN 5ACTOR A 5ACTOR B F '$ no 5ac*o F '$ )aa %a 5ac*o )aa $% *a"!# 0 20 70 0 50
A 0. 0.Q .07 .0 .
"!*ad d$ a6 0 20 70 0 50
B 0.Q0 0.0 0.0 .00 .20
5ACTOR C A6$*'a TC5* 0.02 0.077 0.08 0.085 0.07
0.0 0.50 0.80 0.Q0 0.5
7
80 Q0 0 0 -----
.72 .55 2.00 7.80 -----
80 Q0 0 0 -----
.0 .80 .0 2.00 -----
0.7 0.5 X 2 7
.0 .50 2.00 7.0 7.Q0 .75 5.Q0 Q.25
a.- C?%c'%o d$ C.- S!=?' "+ +$"+ )' #'!%+" *! *!'s#*+* 00 L$ 7 ; (+%+ )'+ +$!%)%+ *! 4 ,&%%!s(&'*! )' +,&% *! 7.0 TC 2 : /. C&& C +%#+ (%&(&%,#&'+"!'! + "+ *!'s#*+* s! #!'! 00 L$7 ------ 7.0
7.0 TC2: /
Q L$7 ------ :
: 5.QQ TC2 : /
6.- C?%c'%o d$ A.- S!=?' !" +'"#s#s =%+')"&9%#,& !" (&%,!'+>! 1)! '& (+s+ (&% "+ +""+ *! +$!%)%+ s!% 00 ------- 75.0 = K
------- 2.5 =
K Q0
T%+s"+*+'*& T%+s"+*+'*& !s! +"&% + "+ +$"+ /+""+&s !" +"& F+,&% A .55
c.- C?%c'%o d$ B .- E" (&%,!'+>! 1)! (+s+ + )'+ +""+ *! 4 !s #=)+" + "+ #+* *! "+ +'!%#&% 4 s!% /+""+*& s!=?' "+ +$"+ 00 ------- 75.0 = K
------- . =
K 2
T%+s"+*+'*& !s! +"&% + "+ T+$"+ /+""+&s !" +"&% 1)! (+s+ "+ +""+
F+,&% B
20.0
0.
2.0
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70.0
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d.- C?%c'%o d$% ?$a R$'$!da .- A("#,+'*& "+ &%)"+ (%,#,+
AREA
5.5GG5TC O h 2
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&.- C?%c'%o d$ %a d!"$n!on$ d$ %a aanda, AREA R!+" L+%=& : A',/& S#!'*& !" A',/& %!,&!'*+$"! .5 L+%=& .5 2 .5 7.0 L+s *#!'s#&'!s *! "+ +%+'*+ s&' *! .5[ : 7[ ; s!=?' "&s C+"&=&s T;%& C&. R!,&#!'*+ (+%+ !s+ +%+'*+ )' &&% *! .0 HP.
0.- CLCULOS PARA DETERMINAR LA POTENCIA DE UNA 5AA TRANSPORTADORA. P+%+ !!,)+% !s&s ,",)"&s '!,!s+%#+!'! s! &+ !' ,&'s#*!%+,#3' ,&'s#*!%+,#3' %!s (&!',#+s ; s&' H&%#&'+"4 !%#,+" ; P&!',#+ %#((!%4 1)! (!%#+ !',&'%+% !" &&% ,+(+ ,&' "+ )!%+ '!,!s+%#+ (+%+ (&'!% !' &##!'& + "+ +>+.
17.- Po*$nc!a Ho!#on*a% !s "+ '!,!s#+*+ (+%+ (&'!% !' &##!'& "+ +>! !'%! *&s ()'&s /&%#&'+"!s /&%#&'+"!s ; !s !:(%!s+*+ !:(%!s+*+ (&% "+ !,)+,#3' !,)+,#3' s#=)#!'! HP / F+,&% C : L+ : TC/
D&'*!. F+,&% C Es )'+ +%#+$"! *!s+%%&""+*+ (&% "+ !:(!%#!',#+ 1)! #',");! !" (!s& *! &*+s "+s (+%!s !' &##!'& (&% (#! *! "+%=& *! "+ +>+. L+ L+ *#s+',#+ +>)s+*+ !'%! "&s ,!'%&s *! "+s (&"!+s ; 1)! !s ,&(!'s+*& (&% !" +,&% *! (&!',#+ %!1)!%#*+. S! ()!*! ,+",)"+% + (+%#% *! L+ 0.2 L 7.5 S#!'*& L "+ *#s+',#+ &%#=#'+" !'%! "&s ,!'%&s *! (&"!+s. TC/ Es "+ ,+(+,#*+*. ,+(+,#*+*.
5
27.- Po*$nc!a 3$*!ca% Es "+ '!,!s+%#+ (+%+ +"+% & $+>+% "+ +>+ ,+%=+*+ ; s3"& s! "! !("!+ !' "&s ,",)"&s *! "+s +>+s #',"#'+*+s. Es+ !:(%!s+*+ (&% "+ &%)"+
HP V
TC O hxH NN0
D&'*! H Es "+ !"!+,#3' & "+ +")%+ *! "+ +>+ %+'s(&%+*&%+ !' (#!s. (#!s.
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HP F+,&% A : :
TC O hxH hxH NN0
*&'*! F+,&% A Es )'+ ,&'s+'! $+s+*+ !' %!s#s!',#+ %!s#s!',#+ %#,,#&'+" *! "+s (&"!+s *!" %#((!%. V!"&,#*+* *! "+ +>+ !' #'. / A")%+ *!" T%#((!%. P+%+ )'+ +>+ #',"#'+*+ #',"#'+*+44 s) P&!',#+ P&!',#+ &+" !s+ *!!%#'+ *!!%#'+*+ *+ (&% "+ s)+ *! "+ (&!',#+ /&%#&'+" /&%#&'+" s "+ (&!',#+ !%#,+". P+%+ !!,)+% ')!s%&s ,",)"&s '&s $+s+%!&s !' "+ s#=)#!'! T+$"+ 1)! #'*#,+ "+ +%#+,#3' *! "+ ,+(+,#*+* *! *!s,+%=+ *! )'+ +>+ %+'s(&%+*&%+ !' )',#3' *!" A',/& *! "+ +>+ !' ()"= ; !" (!s& *!" +!%#+" %+'s(&%+*& (&% )'#*+* *! &")!' !' L$s 7. Es&s +"&%!s s! /+' &$!'#*& + %+9s *! +%#+s (%)!$+s !:(!%#!'+"!s s&$%! +>+s 1)! !'<+' %!s %&*#""&s "&,&s *! s&(&%! F&%+'*& )' '=)"& *! 20\ ; 1)! ""!+$+' )'+ !"&,#*+* *! 00 #'.
TABLA DE CAPACIDAD DE DESCARGA DE UNA 5AA 5AA TRANSPORTADORA E' TC/ + 00 (#!s#' ; ,&' %&*#""&s "&,&s *! 20\
Ancho d$ 5a(a 9)'%>7 20 2
0 2 7 50
P!$ )o 'n!dad d$ 3o%'"$n d$% "a*$!a% 9L6&* +7 J0 1 120 2 58 Q0 5 5 5 Q5 00 25
10 02 50
8
70 Q 78 Q 2 82 27 /7.- C?%c'%o )o)!a"$n*$ )o)!a"$n*$ d!cho,
5 22 72
25 05
27Q 72 8
D+&s - A',/& *! "+ +>+ 78 ()"=. -
L&'= L&'=# #)* )* *! "+ +>+ +>+ 200 200 (#!s (#!s
-
D#s+' D#s+',#+ ,#+ !'%! !'%! ,!'%& ,!'%&ss *! *! (&"! (&"!+s +s 5.5 5.555 (#!s (#!s
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P!s& P!s& *!" *!" #'!% #'!%+" +" (&% (&% )'#* )'#*+* +* *! *! &") &")!' !' 0. 0.52 52 L$ L$ 7.
-
V!"&,#* !"&,#*+* +* (%,# (%,#,+ ,+ *! "+ +>+4 +>+4 !'#! !'#!'*& '*& !' !' ,)!'+ ,)!'+ 1)! 1)! )' ()'& ()'& *! *! "+ +>+ +>+ s! *!&%+ !' *+% )'+ )!"+ ,&("!+ 50 s!=.
P&% "& ,)+" V 200 (#!s50 s!=: 80 s!=#'. 20 =#'. -
S+$#!' S+$#!'*& *& !" '=)" '=)"&& *! #',"#' #',"#'+,# +,#3'4 3'4 s! ()!*! ()!*! *!! *!!%# %#'+% '+% "+ +")% +")%++ *! "+ +>+ +>+ *! "+ s#=)#!'! &%+ /5.55 : S!' \5[ 5.55 : 0.7 2.8 (#!s.
C&'s#*!%+'*& P!s& *!" #'!%+" (&% (#! *! "&'=#)* *! +>+ 5.0 =(#!. -
Ca)ac!dad d$ d$ca>a d$ 5a(a $?,
C+( 5.0 =(#!20 (#!s#'80 #'/TM000 =.02TCTM Q.7 TC/ -
C?%c'%o d$ %a Po*$nc!a Ho!#on*a%, a7 D$*$ D$*$"!n "!nac! ac!n n d$% d$% &ac &ac*o *o C, P+%+ "& ,)+" s! &+ "&s +"&%!s *! "+ +$"+ ! #'!%(&"+'*& s! #!'! )'+ *!'s#*+* *! 0.52 L$(#! ,?$#,& ,&%%!s(&'*! )'+ ,+(+,#*+* :#+ *! *!s,+%=+ *!s,+%=+ *! 720.78 TC/ + )'+ !"&,#*+* *! 00 (#!s#'. C+( TC/
D!'s#*+* L$(#! ,?$#,&
25.00
25.00
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0.52
72.0
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C&& "+ !"&,#*+* *! %+$+>& !s *! 20 (#!s#'. S! ("+'!+ 00 (#!s#' -----------
720.78TC/
20 (#!s#' -----------
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L+ ,+(+,#*+* :#+ *! *!s,+%=+ *!s,+%=+ + "+ !"&,#*+* *! %+$+>& !s *! Q0. TC/ S!=)#*+!'! (+%+ !% !" *! ,+%=+ !'!&s
Q
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0.1.- OTROS METODOS PARA DETERMINAR LA POTENCIA DE UNA 5AA TRANSPORTADORA, + S!=?' S!=?' "+ F&%)"+ F&%)"+ *! J. J. P!%%; P!%%; (+%+ )'+ #',"#' #',"#'+,#3' +,#3' *! *! 25\4 s! #!'! #!'! HP TC/H : 0.00Q7 V : 0.007Q , D&'*! 0.00Q7 ; 0.007Q s&' +,&%!s *! ,&'!%s#3' ,&'s+'!s H Es "+ "&'=#)* *! "+ +>+ !' (#!s 5 (#!s V Es "+ !"&,#*+* *! "+ +>+ !' (#!s#' 75 (#!s#'. C Es "+ ,&'s+'! *! (!s& *! "&s #'!%+"!s 1)! ,);& %+'=& !s+ !'%! 2 + 2.5 ,&& :#&. S# "+ ,+%=+ !s *! 25.5 TC/ %!!("++'*& !' s)s +"&%!s s! #!'!
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HP
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J.- CALCULOS EN LOS MOLINOS 9DE BOLAS Y DE BARRAS7, + C?%c'%o d$ %a 3$%oc!dad C=*!ca d$ 'n Mo%!no. - L+ !"&,#*+* ,%<#,+ *!" &"#'& !s "+ :#+ !"&,#*+* !"&,#*+* !' "+ ,)+" "+s $&"+s $&"+s & $+%%+s ,&' !" &"#'& (!=+*&s (!=+*&s + "&s &%%&s *!$#*& + "+ )!%+ ,!'%<)=+4 /+,#!'*& )"+ "+ &"#!'*+. Es #(&%+'! "+ !"&,#*+* ,%<#,+ (+%+ !% !" %+$+>& '&%+" *! "&s &"#'&s4 (&%1)! +$#9' + $+>+s !"&,#*+*!s "+s $&"+s & $+%%+s '& )!"!' s&"& (%&*),!' %&*+*)%+ s! !"!+' ; %!s$+"+' (!%& + )'+ !"&,#*+* &*!%+*+ s! )!"!'. S! ,+",)"+ !*#+'! "+ &%)"+ s#=)#!'! Vc
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M+""+ 7 2 7 8 0 20 2 80 00 50
ALIMENTACION A6$*-M!c F P$o .050 8. 2.Q00 20.7 4525 .50 48 .5 7472Q 7. 4855 0.0 77 0. 5 7.8 2 . Q .02 0 0.
FAc9-7 00.00 7.5 Q2.5 8.0 52.5 7.Q 2.8Q .27 .5 0.75 .QQ
Ma%%a 8 0 20 2 75 85 00
DESCARGA A6$-M!c F P$o .8 0.5 7472Q 0.Q 24782 .7 4855 .Q0 48 2.8 77 .28 5 .22 .7Q 25 . 20 0.5 Q .
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22
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Ta"ao d$ Bo%a TOTALES
P$o d$ Bo%a F G .2 54Q2.7 2.8 74QQ. 22.0Q 24. 00.00 400.00
N d $ Bo%a 2 7Q 0
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28
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CICLO 2 7 5
RE3OLUCIONES 00 252 7 70 72
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: 7 577 87
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.- D!$! (!%##% "+ %!,!(,#3' ; +!%!+,#3' *! "+ ()"(+ s#' (!%##% "+ s!*#!'+,#3' *! "&s s3"#*&s. 2.- *!$! (!%##% "+ *!s,+%=+ *!s,+%=+ *! "&s %!"+!s !(&$%!,#*&s ")!=& 1)! "+ +!%!+,#3' *! "+ ()"(+ /+;+ (%&*),#*& (%&*),#*& "+ !s()+ !s()+ #'!%+"#+*+. 7.- D!$! D!$! (!%##% !" (+s! *! "+ ()"(+ ()"(+ *!s*! *!s*! "+ !'%+*+ !'%+*+ + "+ s+"#*+ s+"#*+ *! "+ ,!"*+ ,!"*+ s#' 1)! !s! !' &(!%+,#3' )',#&'+#!' )',#&'+#!'&. &. .- S)#'#s%+% +" &")!' &+" *! ()"(+ "+s $)%$)>+s *! +#%! *! ++@& ,&'!'#!'!4 ,&'!'#!'!4 ,&("!+!'! *#s(!%s+s ; !' )'+ ,+'#*+* +*!,)+*+ (+%+ "+ ,&',!'%+,#3' *! "+ ,&")'+ *! !s()+s. 5.- D!$ D!$!! *#s(&' *#s(&'!% !% *! )'+ &'+ &'+ !' 1)! ()! ()!*+ *+ &%+% &%+%s! s! )'+ ,&")' ,&")'++ *! *! !s()+ !s()+ss #'!%+"#+*+s 1)#!+s4 *! *&'*! ()!*+ ,+!% "+ =+'=+ "#(#!+ s!,)'*+%#+. 8.- D!$! *!s,+%=+ *!s,+%=+ !" +!%#+" "&+*& ; !" /)'*#*& (&% s!(+%+*&s. Q.- D!$! *#s(&'!% *#s(&'!% *! )' ,&'%&" ,&'%&" *!" *!" '#!" '#!" *! ()"(+ ; *! *! "+ "+ +")%+ +")%+ *! "+ ,&")' ,&")'++ *! "+ !s()+. .- P!%##% "+ +!%!+,#3' s#' "+ &%+,#3' *! $)%$)>+s ); =%+'*!s4 3 s#' ,+#*+*!s *! +#%! 1)! (%&*),!' (!%)%$+,#&'!s. .- D!$! s!% *! ,#" +%%+'1)! ")!=& *! )'+ +""+ !,'#,+4 s#' !" +%!'+*& *! "+s (+%! !,'#,+s ; &%##,#&s *! *!s,+%=+. *!s,+%=+. 0.- D!$! s!% ,#" +'!'##!'&4 s#' !s1)#'+s *!s#=)+"!s *&'*! ()!*+' +,))"+%s! %!s&s *! +*!%+4 *!s!,/&s 3 ,+".
7
.- D!$! (!%##% !" )s& !#,#!'! *! "+s )!%+s &&%+s4 *!" !s(+,#& *! "+ ("+'+ ; *! "&s #()"s&%!s. 2.- D!$!' D!$!' s!% "!:#$"!s "!:#$"!s +" ,+$#& ,+$#& %(#*& %(#*& ; ,#" *! +"#!'+, +"#!'+,#3' #3' ; !'!% !'!% ,+'+" ,+'+"!s !s *! #'!%,#%,)"+,#3' !' !" ,#%,)#& $+',+*+ *! "+ 1)! &%+ (+%! "+ ,!"*+. 7.- T!'!% ,+(+,#*+* (+%+ ,)$%#% )'+ +"#!'+,#3' *! (+%<,)"+s =%+'*!s s#' %#!s=& *! +,))"+,#3' ; +&%+#!'&. .- P!%##% !" +>)s! *!" %+$+>& !'%! "+ ')!+ +"#!'+,#3' ,#%,)"+'! !' !" ()'& *! !'%+*+ *! +#%! ; *! "+ ()"(+ 1)! %!,#%,)"+% *!'%& *! "+ ,!"*+. 5.- D!$! D!$! *#s(&'!% *#s(&'!% *! )'+ )'+ *!s,+%=+ (!%#3*#,+ (&% !" !" &'*&4 &'*&4 (+%+ "+s +%!'+s +,))"+*+s. +,))"+*+s.
2.- CLASI5ICACIÓN DE LAS CELDAS DE 5LOTACIÓN. A,)+"!'! !:#s!' *#!%s&s &*&s *! ,"+s##,+% ,"+s##,+% "+s ,!"*+s *! "&+,#3'4 "&+,#3'4 !" !" s s#("! ! #(&%+'! !s $+s+*& !' !" 9&*& *! A!%!+,#3' *! "+ ()"(+4 ()!s& 1)! !s+ !s "+ ,&'*#,#3' $s#,+ !s!',#+" *! "+s 1)#'+s *! "&+,#3'. As< ,&& s! #'*#,+ !' !" ,)+*%& s#=)#!'! *! ,"+s##,+,#3' *! "+s ,!"*+s *! +,)!%*& + "+ &%+ *! +!%!+,#3' *! "+ ()"(+ ; *! s) &%#=!' *! +$%#,+,#3'. TIPO DE CELDA .- MECANICAS L+ ()"(+ !s +!%!+*& (&% !,"+*& *! +#%!
ASPECTO DEL DISEÑO .- C&' #()"s&% 2.- C&' #()"s&% !s(#%+" 7.- I()"s&% *! ,+>+ *! +%*#""+
2.2.- NEUM NEUMA ATICAS TICAS "+ .- R&&% ,#"<'*%#,+ (&%&s& ()"(+ s! +!%!+ ,&' 2.- T)$!%<+ (&%&s+ #>+. #';!,,#3' *! +#%! 7.- C&' #%& *! +#%!
FABRICANTE +. M#'!%+" S!(+%+#3' M.S. $ D!'!% , M.S. S)% A!%!+,#3' S)$-A + D!' D!'!% !% M+ss M+ss,& ,&44 H)$ H)$& &.. A=#+#%. * R&&. %+)s F+=!%=%!'.
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")>& *! '#!" #>+ ; !" #(& ,+%+ & ,!"*+. E'%! !s&s *&s ?"#&s s! !',)!'%+' "+s ,!"*+s D!'!% F%!!-"& ; C!"" & C!"". F+%=!%=%!'4 A=#+#%. A=#+#%. A !*#*+ 1)! )!%&' +(+%!,#!'*& 1)#'+s ,+*+ ! s !#,#!'!s4 )!%&' 1)!*+'*& )!%+ *! ,&(!!',#+ ),/+s (+%#,)"+%!'! *!" #(& N!)#,&4 *! +,<& ; &%&s s +'#=)&s ,&& *! ,+s,+*+4 *! =!'!%+,#3' *! =+s (&% %!+,,#&'!s % !+,,#&'!s 1)<#,+s4 !,. A,)+"!'! s&' *! !%*+*!%+ #(&%+',#+ T!,'&"3=#,+ (&% "&s !'&s !' "& 1)! s! %!#!%! +" C&'#'!'! A!%#,+'& ; !' ')!s%& (+
a7 M?'!n M?'!na a D$n4$ D$n4$ S'6-A, S'6-A, C&'s#s! !' ,!"*+s ,)+*%#,+s /!,/+s *! +*!%+ & +,!%&4 ,+*+ )'+ ,&' s) (%&(#& +=#+*&% ; %!)'#*&s !' 2--8 ; & s s!=?' "+s '!,!s#*+*!s. S! +"#!'+ !*#+'! )' )$& "+!%+" #',"#'+*&4 1)! !s+'*& !' )',#&'+#!'& *!s,+%=+ "+ ()"(+ *#%!,+!'! s&$%! !" +=#+*&% I()"s&% 3 %&&% 1)! !s )' *#s,& ,&' 8 (+"!+s &%#!'+*+s /+,#+ +%%#$+4 1)! s! !',)!'%+ *!$+>& *! )' D#)s&% Es+&% !s+,#&'+ !s+,#&'+%#& %#& ,&' &%##,#&s &%##,#&s 1)! s#%!' (+%+ "+ !>&% !>&% *#s(!%s#3 *#s(!%s#3'' *! "+s $)%$)>+s $)%$)>+s *! +#%! ; ,&' (+"!+s &%#!'+*+s /+,#+ +$+>& (+%+ "+ !>&% *#s(!%s#3' *! "+ ()"(+ ; *!s,+%=+' *!s,+%=+' !" %!"+! (&% &%& )$& !' )' '#!" s $+>& +" 1)! !" &##!'& *! "+ ()"(+ *!'%& *! "+s 1)#'+s s! !!,?+ (&% =%+#+,#3'. E" ,&',!'%+*& s! %!#%+ *! "+ (+%! s)(!%#&% *! "+s ,!"*+s + )'+ ,+'+"!+ (&% !*#& *! (+"!+s =#%+&%#+s & $#!' (&% "++*& ,&' ,&' +=)+. E" +=#+*&% !s +,,#&'+*& (&% )' &&% + %+9s *! )' !>! ,!'%+" 1)! s! !',)!'%+ !' )' )$& 1)! s#%! (+%+ /+,!% ""!=+% !" +#%! !:!%#&% /+s+ "+ ()"(+ ,)+'*& /+,!&s )',#&'+% !" +=#+*&% ,&' )'+ !"&,#*+* (!%#9%#,+ !'%! 500 + 800 #'4 !(#!+ + s),,#&'+% !" +#%! (&% !" &%##,#& s#)+*& !' "+ (+%! s)(!%#&% *!" )$& *!" !>!. E" +#%! &+ ,&'+,& ,&' "+ ()"(+ !' "+ &'+ *!" +=#+*&% 1)! "+'+ "+!%+"!'! "+ !,"+ 1)! s! *#s(!%s+ ,&' "+ +;)*+ *!" *#)s&%. L+s $)%$)>+s #'!%+"#+*+s s)$!' + "+ s)(!%#,#! ; "&s %!"+!s >)'&s ,&' "+s (+%<,)"+s '& %!,)(!%+*+s s#=)!' s) ,+#'& (&% =%+!*+* $+>& "+ (%!s#3' *! "+
5
()"(+ ')!+ 1)! ""!=+ + "+ ,!"*+ + %+9s *! )'+ ,&()!%+ +>)s+$"! ; !'%+% (&% !" )$& + "+ s#=)#!'! ,!"*+. As< #s& !s+s ,!"*+s #!'! )'+ (#!+ !"#,+ #>+ s#)+*+ s&$%! !" +=#+*&% 1)! "& (%& (%&!= !=!! *! "+ s!*# s!*#! !' '+, +,#3 #3''
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)',#&'+#!'& ; 1)! (!%#+ s) (&s!%#&% ()!s+ !' +%,/+. G!'!%+"!'! !s+s (+%!s #+"!s !s' %!!s#*&s %!!s#*&s ,&' =&+ (+%+ *#s#')#% *#s#')#% s) *!s=+s!. S! #!'!' s *!+""!s s&$%! !s+s 1)#'+s !' "+ T+$"+. $ M?'!na 5a>$>$n S&' +$#9' ,!"*+s ,)+*%#,+s *! 2 + 8 3 +s s!=?' '!,!s#*+*!s +" #=)+" 1)! !" +'!%#&% 1)#'+. L+ (+%! )'*+!'+" *!" !1)#(& !s+ !' s) %&&% ; Es+&% 1)! !s' ,&"&,+*&s ,&',9'%#,+!'!4 ,&',9'%#,+!'!4 ,&' )'+ *#s+',#+ <'#+ !'%! +$&s. T+'& !" R&&% ; Es+&% s&' *&s ,#"#'*%&s /)!,&s ,&' $+s!s *! +'#""& 1)! s! )'!' !'%! s< (&% +%#""+s !s(+,#+*&%!s *! +,!%& %!!s#*&s ,&' =&+. E" %&&% #!'! +*!s !' "+ (+%! s)(!%#&% ! #'!%#&% %+;&s !' &%+ *! ,%)4 #',"#'+*&s *! +" &*& 1)! "+ (+%! s)(!%#&% s),,#&'! !" +#%! ; (+%! #'!%#&% "+ ()"(+. F)',#&'+ ,&' 00 + 00 RPM4 "& 1)! ,&%%!s(&'*! + )'+ !"&,#*+* (!%#9%#,+ *! 8Q0 #'. ,&' "+ ,)+" s! +",+'+ s),,#&'+% !" +#%! *! "+ +3s!%+ + %+9s *! )' ,#"#'*%& ,&' +"=)'+s (!%&%+,#&'!s 1)! !',#!%%+ !" !>! ,!'%+" !' ,);& !:%!& #'!%#&% !s+ !" R&&% ; s),,#&'+ *!s*! +%%#$+ !" +#%! ; *!s*! +$+>& "+ ()"(+ 1)! ,/&,+' !' !" #'! #'!%# %#&% &% (%&* (%&*), ),#9 #9'* '*&s &s!! "+ #(% #(%!= !='+ '+,# ,#3' 3' *! "+ ()"( ()"(++ ,&' ,&' !" +#%! +#%!.. L+ ()"( ()"(++ =+s##,+*+ s+"! %+*#+"!'! *!" R&&% ; +" (+s+% (&% s)s !s(+,#+*&%!s ; (&% "+s *!" Es+&% s! *#s(!%s+ s +?'. Es+s Es+s ,!"*+s !s' s!(+%+*+s s!(+%+*+s !'%! s< (&% ,&()!%+s +>)s+$"!s 1)! (!%#!' ,&'%&"+% !" '#!" *! ()"(+. Es+s ,&()!%+s ""!=+' /+s+ "+ #+* *! s) +")%+ *! &*& 1)! !' s) (+%! #'!%#&% "+ ()"(+ ()!*+ ,#%,)"+% "#$%!!'!. A"=)'+s !,!s !' "+ (+%! s)(!%#&% s! ()!*!' $+>+s "+s ,&()!%+s (+%+ 1)! "+ !s()+ +$#9' ()!*+ ,&%%!% "#$%!!'!. L+ ?"#+ ,!"*+ 1)! *!s,+%=+ "+ ,&"+ "& /+,! (&% !%!$&s! ; !s! '#!" (!%#! !" +>)s+ *! "+ ()"(+ !' "+ 1)#'+. Ms *!+""!s *! 9s+s 1)#'+s s! *+' !' "+ T+$"+. , M?'!na A>!*a! .
8
A" #=)+" 1)! "+s "+s +'!%#&%!s +'!%#&%!s s! )s+' !' )'#*+* )'#*+*!s !s *! 2- 3 +s ,!"*+s ,!"*+s s!=?' s!=?' "+ '!,!s#*+*4 ; *#s(&'!' *! )' +=#+*&% (&% !*#& *!" ,)+" s! #'%&*),! !" +#%! ; s! !!, !!,? ?++ "+ +=# +=#+, +,#3 #3'' *! "+ ()"( ()"(++ ; *! )' ,)!% ,)!%(& (& !s+ !s+,# ,#&' &'+% +%#& #&44 ""+ ""++* +*&& Es+$# Es+$#"# "#+* +*&% &%44 1)! s#%! s#%! (+%+ (+%+ s) *#s(!% *#s(!%s#3 s#3'' ; !s+$# !s+$#"# "#+,# +,#3'. 3'. L+ *#!%! *#!%!', ',#+ #+ )'*+!'+" !'%! !s ; &%+s 1)#'+s %!s#*! !' !" /!,/& *! 1)! "+s A=#+#% (+%+ "+ +#%!+,#3' )s+' +#%! ,&(%##*& + (!1)!@+ (%!s#3'. E" +=#+*&% !s )' )$& /)!,& *! +,!%& %!!s#*& *! =&+ 1)! *!s,+'s+ s&$%! %&*#""&s. E' s) (+%! #'!%#&% #!'! )' *#s,& ,&' *#!'!s *#!'!s &%#!'+*&s &%#!'+*&s /+,#+ +$+>& 1)! s#%! (+%+ "+ *#s(!%s#3' *! "+ ()"(+ +#%!+*+. T%+$+>+' + )'+ !"&,#*+* (!%#9%#,+ *! 770 + Q0 #'. s) (+%! #'!%#&% s! ()!*! s!(+%+% *!" !>! /)!,& ; '& %!1)#!%! +'!'##!'& !s(!,#+"4 s#'& 1)! ,)+'*& s! *!!%#&%+ s! %!!("++. E" !s+$#"#+*&% ,&'s#s! !' ("+',/+s *! +,!%&4 %!!s#*&s *! =&+ *#s%#$)#*&s !' &%+ %+*#+". N& &,+' !" &'*& *! "+ ,!"*+ s#'& 1)! !s' s)s(!'*#*&s + )'+ +")%+ *! +s & !'&s 5 ,s. P+%+ (&*!% *!>+% "#$%!!'! "+ ()"(+. S) )',#3' !s "+ *! !#+% "+ )%$)"!',#+ *!'%& *! "+ &'+ #'!%#&% *! "+ 1)#'+ 1)! s! !',)!'%+ )!%!!'! +=#+*+ ; +s!=)%+% "+ *#s%#$),#3' (+%!>+ *! "+s $)%$)>+s + %+9s *! &*+ "+ s)(!%#,#! *! "+ ,!"*+. E" s#s!+ *! +#%!+,#3' +#%!+,#3' +%##,#+" $+>& (%!s#3' #!'! !'+>+ !'+>+ s&$%! "+ +#%!+,#3' +#%!+,#3' (&% s),,#3' *! 1)! s! ()!*+ %!=)"+% ,&' =%+' s!'s#$#"#*+* ; s! ()!*+ /+,!% +s +$)'*+'! ,)+'*& "& %!1)#!%+ "+s ,&'*#,#&'!s. E" +#%! !s %+'s(&%+*& (&% )$!%<+s *! 8 ()"=+*+s ; +"#!'+*&s !' "+s ,!"*+s #s+s (&% )$!%<+s *! 2 ()"=+*+s + %+9s *!" !>! /)!,& *!" +=#+*&%4 !" +#%! s! ,&'%&"+ (&% !*#& *! ")"+s. L+ +"#!'+,#3' ; *!s,+%=+ *! "+ ()"(+ s! !!,)+ + %+9s *! ,&()!%+s !s(!,#+"!s s#)+*+s !' "+ ,+$!+ ; ,&"+ *! "+ 1)#'+ %!s(!,#+!'!. E" '#!" *! "+ ()"(+ !s %!=)"+*+ !' ,+*+ "<#! *! ,!"*+ ; !" %!$+"s! *! *!s,+%=+ !*#+'! !%!*!%&s *! +,!%& *! +")%+ +%#+$"!. L+ +")%+ *! "+ !s()+ s! ()!*! ,&'%&"+% (&% !*#& *! "+s "+s " ")" )"+s +s *! +#%! +#%!.. S! )s+' )s+' *#s *#s#' #'& &ss $+', $+',&s &s *! ,!"* ,!"*+s +s (+%+ (+%+ ,+*+ ,+*+ #(& #(& *! &(!%+,#3'. M+;&%!s #'&%!s s! *+' !' "+ +$"+. G!'!%+"!'! "+s ,!"*+s s! &%*!'+' !' s!%#! &%+'*& )' ,<%,)"& & $+',+*+ ,#%,)#& 3 $+',&s *! ,!"*+s 1)! %!,#$!' "&s %!"+!s *! "+ (%&,!*!',#+ ; s! !'*% 42 ; 7 ,#%,)#&s 3 $+',&s *! ,!"*+4 s!=?' "+s ,"+s!s *! +!%#+"!s +"#&s&s 1)! s! *!s!+ %!,)(!%+% *! )' #'!%+". As< (&% !>!("&
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CELDAS CELDAS ROUGHER ROUGHER F"&+ F"&+,#3 ,#3'' P%#+% P%#+%#+ #+..- Es *&' *&'*! *! s+"! s+"! !" ,&' ,&',!' ,!'%+ %+*& *& (%#+%#&4 !s *&'*! s! +"#!'+ "+ ()"(+4 !s "+ ,!"*+ +*%! 1)! %!,#$! "+ ,+%=+ *! ()"(+ *!" +,&'*#,#&'+*&% +,&'*#,#&'+*&% & *#%!,+!'! *#%!,+!'! *!" ,"+s##,+*&%. ,"+s##,+*&%.
CELDAS ESCA3ENGHERS A=&+*&%!s 3 M!*#&s.- S&' "+s ,!"*+s *&'*! s! %!+"#+ "+ %!,)(!%+,#3' *! "+s (+%!s +"#&s+s 1)! '& s! /+' %!,)(!%+*& !' "&s %&)=/!%.
CELDAS RECLEANER R!"#(#!+. R!"#(#!+.- C!"*+s *&'*! s! /+,! "+ "#(#!+ *! ,&',!'%+*& (%&!'#!'! *! "+s C!"*+s C"!+'!%. E>!("& *! )' C#%,)#& *! C!"*+s
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+.- CAPACIDAD DE LAS CELDAS L+ ,+(+,#*+* *! "+s ,!"*+s *! "&+,#3' *! %++#!'& *! ,)+"1)#!% #'!%+" *!(!'*! *! +%#&s +,&%!s 3 ,&'*#,#&'!s4 "+s ,)+"!s ()!*!' s!% *!!%#'+*&s !:(!%#!'+"!'!. As< ,&& !" &'!"+>! + %++%s!4 #!(& *! ,&'+,& %!1)!%#*& !'%! "&s %!+,#&s *! "&+,#3' ; "+s !'+s +"#&s+s. D!'s#*+* *! ()"(+ 1)! ");! (&% "+ 1)#'+ ; !" &")!' *! ()"(+ /?!*+ (&% &'!"+*+ *! #'!%+" s!,&.
/.- CALCULO DEL NMERO DE CELDAS 9Banco d$ C$%da .
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57
CAPITULO IV
BALANCE METALRGICO EN LA CONCENTRACIÓN DE MINERALES 1.- CONCEPTOS GENERALES. Es &*& %++#!'& *! #'!%+"!s ,)+"1)#!%+ 1)! s!+ !" (%&,!*##!'&4 ,);+ #'+"#*+* !s ,&',!'%+%"&s (+%+ &$!'!% )' (%&*),& #'+" !,&'3#,&4 '!,!s+%#+!'! #'!%#!'!' "&s s#=)#!'!s !"!!'&s C+$!+ & A"#!'+,#3'4 !" C&',!'%+*& 3 P%&*),& +"#&s& 1)! s! *!s!+ &$!'!%4 !" R!"+! 3 C&"+ 1)! #!'! + s!% !" +!%#+" #'s!%#$"! !' !s! #'s+'!. D!#'#!'*& !s&s (%&*),&s s! #!'!
Ca6$#a.- Es !" #'!%+" (%&!'#!'! *! "+ #'+ 1)! s! +"#!'+ + )'+ ("+'+ *! %++#!'&4 ; !s *! )'+ "!; *!!%#'+*+ !' !" !"!!'& *! #'!%9s. C&',!'%+*&.- Es !" (%&*),& #'+" +"#&s& !,&'3#,& &$!'#*& *!" %++#!'& *! "!; s +"+ 1)! "+ ,+$!+ !' !" !"!!'& +"#&s&.
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5
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CAPITULO V
MAQUINAS Y EQUIPOS AUILIARES EN LA 5LOTACION DE MINERALES
1.- SECCION DE ACONDICIONAMIENTO L+ #'+"#*+* *!" +,&'*#,#&'+#!'& +,&'*#,#&'+#!'& !s !,"+% "&s %!+,#&s ,&' "+ ()"(+ (%!(+%'*&"+s (+%+ !" (%&,!s& *! "&+,#3'. L+s (+%<,)"+s !s+%' !' ,&'+,& ,&' "&s %!+,#&s !" #!(& #!(& '!,!s '!,!s+%# +%#&& (+%+ (+%+ 1)! s)%+' s)%+' %!+,,# %!+,,#&'! &'!ss ! !' 2 /&%+s TC T T#!(& *! +=#+,#3'
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ACONDICIONAMIENTO EN EL CIRCUITO DE PLOMO O BUL 9 P6 V C' L&s L&s %!+, %!+,# #& &ss (+%+ (+%+ !s! !s! ,#%, ,#%,)# )#& & s! +,&' +,&'*# *#,# ,#&' &'+% +%+' +' +;& +;&% %!' !'! ! !' "+ &"# &"#!' !'*+ *+44 !s(!,#+"!'! "&s %!+,#& s3"#*&s ; "&s "<1)#*&s (&,& s&")$"!s !' !" +=)+4 +s< #s&4 "&s *!(%!s&%!s *!" Z#', *! "+ (#%#+ !,. D+'*& *! !s+ +'!%+ +;&% #!(& *! ,&'+,& ,&' !" #'!%+" ; 1)! !' ,#!%&s ,+s&s #'+"!'! !' )' +'1)! *! +,&'*#,#&'+#!'& s! ,&("!+' "+s !,"+s '!,!s+%#+s.
0
L&s s #(&%+'! *! !s+ s!,,#3' !s !" *#s!@& *! +,&'*#,#&'+*&% 1)! s! %!1)#!%! ,&' ,#!%&s %=!'!s *! s!=)%#*+* !'#!'*& !' ,)!'+ "+ ,+(+,#*+* +,)+" ; "+s (&s#$"!s +("#+,#&'!s ))%+s. Siguiendo el método de la Denver Equipament. Co. Para los calculos se aplica la siguiente formula: Volumen (ft 3)
= R x T x Factor de Agitación.
D&'*! R T&'!"+>! !' 2 /&%+s TC. T T#!(& *! A=#+,#3'. F+, F+,&% &% *! +=# +=#+, +,#3 #3'' s! /+"" /+""++ !' "+s "+s +$" +$"+s +s %!s( %!s(!, !,# #+ +ss *! +,&' +,&'*# *#,# ,#&' &'+* +*&% &%!s !s44 %!"+,#&'+*&s ,&' "+ =%+!*+* !s(!,##,+ *!" #'!%+". Ejemplo Nº1:
S# (+%+ ')!s%& *#s!@& s! #!'! "&s s#=)#!'!s *+&s G%+!*+* !s(!,##,+ *!" #'!%+" *! s3"#*&s !' "+ (?"(+
2.2. 70.
T#!(& *! +,&'*#,#&'+#!'& +,&'*#,#&'+ #!'&
2 #')&s.
F+,&% *! +=#+,#3' E' "+s +$"+s /+""+&s (+%+ )'+ G.E. *!" #'!%+" *! 2. !s #=)+" + 0.05. Solucin:
h R!!("++'*& ,&' s)s +"&%!s !' "+ 3%)"+4 !" &")!' *! "+ ()"(+ s!% (+%+ 500 TMV s! !'*%. V 500 : : 2 : 0.05 V 758. 7 h C", C",)" )"&& *! "+ ,+(+ ,+(+,# ,#*+ *+** *!" *!" +'1 +'1)! )! *! +,&' +,&'*# *#,# ,#&' &'+* +*&% &% 1)! 1)! !s+ !s+ !' "+s "+s +$" +$"+s +s "+s "+s *#!'s#&'!s ,&' +(%&:#+,#&'!s. +(%&:#+,#&'!s. h )! (+%+ !" ,+s& !s *! "+s s#=)#!'!s *#!'s#&'!s U' +'1)! ,#%,)"+% ,#%,)"+% *! ] : ] / ] ; i ].
h C+",)"+'*& s) ,+(+,#*+* (+%+ !s+s *#!'s#&'!s Vc. =
2 x r x h
V,. 7.8 : 2 : V,. 02 7. h T+$#9' !" &")!' s! ()!*! *!!%#'+% ,&'&,#!'*& !" ")>& *! ()"(+ ,&' "+ &%)"+ s#=)#!'! G. ! " ft3 #ul#a $ ton ólido ólido eco = 32 32 x G. x (G#. %
")
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2
Vs: ; F x Tie'po de retenci0n
Vs. 25 7#'.: 5#'. Vs. 7Q57. Ejemplo Nº!<
D!!% D!!%#'+ #'+%% !" ++@ ++@&& *!" +1)# +1)#'+ '+ D!' D!'!% !% P+!' P+!'+* +*&4 &4 (+%+ (+%+ )' !:,!"! !:,!"!'! '! +=#+ +=#+*&% *&% ; +,&'*#,#&'+*&% +,&'*#,#&'+*&% 1)! %!1)#!%!' T&'!"+*+ *! s3"#*&s (&% 2 /&%+s
20
T#!(& *! +=#+,#3' !' #')&s
25
G%+!*+* *! S3"#*&s S(.
2.
P&%,!'+>! *! S3"#*&s (+%! *! s3"#*&s *! 2.77 (&% s&"),#3' *! (!s&.
70 Solucin<
. E' "+ +$"+ &$s!%+&s "+ G%+!*+* Es(!,##,+ *! 2. 2. E' !" *! s3"#*&s *! 70 &$s!%+&s 1)! #!'! )' +,&% *! +=#+,#3' *! 0.05 7. "se la frmula: &l 'olumen en ft 3 = (a tonelada #or 2* hora x minuto de agitación x el factor de agitación).
V&". 20 : 25.0 : 0.05 V&". 827.Q 7
7
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2.- 5!%*o Ro*a*o!o 9GOOD7 OLI3ER ..- M); )#"#+*&s (+%+ #"%+% ,&',!'%+*&s *! Z#',4 s&' #"%&s *! T+$&% %&+&%#&s4 s#!'*& !" s ,&?' ; *#)'*#*+ "+ +%,+ O"#!%. O"#!%. L+ ,+(+,#*+* (%&!*#& (%&!*#& !s *! 700 L$2 + 800 L$ 2 (&% 2 /&%+s4 +s)#!'*& !" (%&!*#& *! "+ ,+(+,#*+* 50 L$2. E>!("&s ,+",)"+% !" ++@& *! #"%& +$&% %&+&%#& (+%+ #"%+% 2Q.5 TC *! +"#!'+,#3' *! ,&',!'%+*& *! #', !' 2 /&%+s.
S&" Á%!+ #"%+'!
2Q.5TCx 24000 $b O TC 2
I50 $b O ft
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0
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08
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DEN3ER DISC 5ILTRES Mach!n $ X-S!#$ D!c D=a [ [ [ [ [ 8[ 8[ 8[ 8[ 8[ 8[ 8[
Ca)ac!* 5!%*$ Tn P$ 2/ Z$a h. S.5* N N 2 7 5 2 7 5 8 Q
7- 8- -2 2-8 5-20 Q- - 2-2 2-7 75- 2-80 -88
22 88 0 80 00 50 200 250 700 750
D!"$n!on L [0 5[2 8[ Q[8 [ [ 5[ Q[7 [Q [ [7 2[Q
: 5[7 5[7 5[7 5[7 5[7 5[7 Q[^ Q[^ Q[^ Q[^ Q[^ Q[^
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0
58-Q8 8-8 Q0-8
00 50 500
7[ 5[7 8[Q
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h F)"!%s & !+ *#+!!% +%! ++#"+$"!. B+s!* &' &(!%+#&' #/&)" /#,!'!%s +'* &% #"!%#'= 700 L$s P!% s1)+%! && #' 2 /&)%s. F&% (;%!#, =&"*. P;,#! & #', ,&',!'%+!s4 +ss)! 00 L$s L$s (!% s1)+ s1)+%! %!
&& && #/ #/ + /#,/! /#,/!'!% '!%44 ,+(+,# ,+(+,##!s #!s & 5080 50800 0
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TABLA DE CALCULOS PARA 5ILTROS DEN3ER DRUN V TIPO 5LUORSPAR Mach!n Ca)ac!* 5!%*o $ X-S!#$ Tn Po 2/ Z$a D!c h. S.5* D!?". L>*h 7[ [ 7[ 2[ 2-7 [ [ 2-7 [ 2[ 7-5 25 [ 7[ 5-8 7Q [ [ Q- 50 [ 5[ - 82 [ 8[ 0-7 Q5 8[ [ 0-7 Q5 8[ 5[ 5-22 5 8[ 8[ 20-70 7
D!"$n!on L [72 5[7 [5 [ 5[ 8[ Q[ [ [ [ [
: [ 5[ 8[0 8[0 8[0 8[0 8[0 8[0 [ [ [
H 7[0 7[0 [0 [0 [0 [0 [0 [0 8[0 8[0 8[0
H.P. :!*ho'* 3ac. E'!). X X 2 7 7
A))o<. Sh!) :* L6 B$%* Q00 2750 2850 200 7500 700 500 500 000 Q00 0700
F#"%&s )#"#+$"!s )#"#+$ "!s *! [ 4 0[ 4 2[ ; [ *! *#!%& B+s+*&s !' 700 L$s (&% s1. *! %!+ *!" #"%&. C+(+,#*+* 1)! ()!*! !'!% )' #',%!!'& *! Q5-00 ,)+'*& !s !s(!s+*& !s )s+*& *!"+'! *!" #"%&.
CAPITULO VI OTROS CLCULOS
0
Mo*o 00 2800 200 7000 7Q00 800 500 8200 700 000 0Q00
1.- TIEMPO DE RETENCIÓN EN MOLIENDA, P+%+ "& ,)+" s! &+% !' ,)!'+ -
&")!' &+" *!" &"#'& 5[ : 5[ 2.88 7
-
C+%=+ &"!*&%+ 5.58 TM
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*! &") &")! !'' &,) &,)(+ (+*& *& (&% (&% "+s "+s $&"+ $&"+ss & B+%% B+%%+s +s !" !s(+ !s(+,# ,#&& #'!%s#,#+"4 s! ,",)"& (&% "+ s#=)#!'! &%)"+ V&")!' 7 28 / O#
D&'*! / +")%+ !*#+ *! "+ s)(!%#,#! *! "+ ,+%=+ ,+%=+ &"!*&%+ +" +" &%%& s)(!%#&% *!" &"#'& 7.Q2h 7 28 F+,&%!s !*#*&s. D# D#!%& #'!%#&% *!" &"#'& 5.h V&")!' 7 28 7.Q25.0 7.Q2 5.0 7 Q2.5 0.05 -
V&")!' &,)(+*& (&% "+s $&"+s ; !" !s(+,#& #'!%s#,#+". 2.88 : 0.0 0.88 7
S+$#!'*& 1)! "+ *!'s#*+* *! "+s $&"+s *! #!%%& !s .0 TM 7 -
V&")!' '!& &,)(+*& (&% "+s $&"+s 5.58.0 0.8 7
-
V&")!' &,)(+*& (&% !" !s(+,#& #'!%s#,#+" 0.88 0.8 0.Q27 7
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V&")!' &,)(+*& (&% "+ ()"(+ s !" !s(+,#& #'!%s#,#+" 0.288 0.Q 27 0.7 7
S# "+ ,+%=+ 1)! (+s+ (&% !" &"#'& !s *! .Q TMS/4 "+ D!'s#*+* *! "+ ()"(+ !' !" &"#'& &"#'& !s *! 2.0 2.0 T7 -
E" ,+)*+" *! ()"(+ 1)! (+s+ !' 7/ s!% .Q2.0 2.7 7/
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2.- CLCULO DEL :OR INDE, Po $% M*odo Ta>>a* . X 0 Xc
B20 cB Xc Xf
f c
0
D&'*! D&'* !
K0 T++@& ++@& (%&!*#& (%&!*#& !' #,%&'!s4 #,%&'!s4 (&% *&'* *&'*!! (+s+ !" 0 +,))"+*& !' (!s& *! "+s (+%<,)"+s #'!%+"!s 1)! ()!*!' s!% K 3 K2.
K, 4 K A$!%)%+ *! "+s +""+s =%)!s+s ; #'+s ,&' %!"+,#3' +" (&%,!'+>! *! (!s& +,))"+*& +,))"+*& %!!'#*& !' )' 20. ,4 P&%,!'+>! *! (!s&s +,))"+*&s %!!'#*&s s&$%! K,4 K4 %!s(!,#+!'!. %!s(!,#+!'!.
+.- CLCULOS EN CICLONES, + V!"&,#*+* N!,!s+%#+
$ Á%!+ *! "+ s!,,#3' *! E'%+*+
V C, : % : = D&'*!
A! V D&'*!
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C, C&!#,#!'! ,!'%<)=& 5
C+)*+" 3 ,+'#*+* *! ()"(+ !' , 7s!=
= G%+!*+* 0 ,s!=
CONMINUCION, Es +1)!" +" 1)! s! *!#'! + "+ *#s#'),#3' *! %&,+s =%+'*!s + %+=!'&s (!1)!@&s (&% %&(##!'& *! )!%+s *! ,&/!s#3' &"!,)"+% $ 'n )oc$o
$n $% c'a% %a $n$>=a c!n*!ca[ "$c?n!ca d$ 'na "a'!na ' o6($*o $ *an&$!da a 'n "a*$!a% )od'c!$ndo $n $% &!cc!on$ !n*$na ca%o '$ o!>!nan ' ')*'a
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L+ ,&'#'),#3' %!1)#!%! *! !"!+*&s ,&'s)&s *! !'!%=<+ 1)! !' ),/&s ,+s& ,+s&ss %!(% %!(%!s !s!' !'+ + +s +s *!" *!" 80 80 *!" *!" ,&s ,&s&& *! &(!% &(!%+, +,#3 #3'' *! "+s "+s ("+' ("+'+ +ss ,&',!'%+*&%+s ,&',!'%+*&%+s *!(!'*#!'*& *! "+ *)%!+ *!" #'!%+"4 (+%+ %!*),#% =+s&s *! "+ !'!%=<+ !' !s+ &(!%+,#3' ; *#!'s#&'+% !1)#(&s %!"+,#&'+'*& +s< "+ !'!%=<+ ,&'s)#*+ ; !" ++@& *!" +!%#+" (%&*),#*& (+%+ +s< !'!% )' ++@& &(#& *! =%+'&4 (+%+ ,)+" !',#&'+%!&s +"=)'&s (&s)"+*&s +,!%,+ *! !s! (%&,!s&.
POSTULADO DE RITTINGER L+ !'!%=<+ %!1)!%#*+ (+%+ %!*),#% *! ++@& !s (%&(&%,#&'+" + "+ ')!+ s)(!%#,#!.
POSTULADO DE IC L+ !'!%=<+ (+%+ %#)%+% )' #'!%+" !s (%&(&%,#&'+" +" =%+*& *! %!*),,#3' !' &")!' *! "+s (+%<,)"+s.
POSTULADO DE BOND N#!" *! !'!%=<+ !'!%=<+ *! "&s (%&*),&s
N#!" *! !'!%=<+ !'!%=<+ *!" +"#!'&
/.- CLCULO DE LA CAPACIDAD DE UNA BOMBA
N#!" *! !'!%=<+ !'!%=<+ *! "+ ,&'#'),#3'
+ W
%P& B#( C Tx0.G8Q5
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D&'*!. T T&'!"+>! *! s3"#*&s s!,&s *!s,+%=+*&s !' "+ ()"(+ !' 2 /. !' (!s& *! +=)+ !' "+ ()"(+. R !' (!s& *! s3"#*&s s!,&s !' "+ ()"(+. G. !s(. =%+!*+* !s(!,<#,+ *! "&s s3"#*&s s!,&s.
$. C",)"& *!" C+)*+" "
HPx HPx550 x, AP
D&'*! C+)*+" (#!7s!= N R!'*##!'& *! "+ B&$+ HP P&!',#+ *!" &&% *! "+ $&$+. A( P9%*#*+ *! (%!s#3' &+" L$(#!2 550 E1)#+"! E1)#+"!'! '! *! HP !' L$-s! L$-s!==
0.- CLCULO DEL CONSUMO DE REACTI3OS, + P+%+ %!+,#&s "<1)#*&s $bn O ton
c'7 O #' tx%r .esp.del$27.ido x j Ldelasol.ci0n 7G.Q xTonx xTonx 2Ihoras
67 P+%+ %!+,#&s s3"#*&s $b O ton
%rs %r s O #' .to 7G.Q xTonx xTonx 2Ihoras
P+%+ %+'s&%+% + =&' s! )"#("#,+ (&% 0.5.
K.- CLCULO DEL DIMETRO 9D7 DE LA TUBER8A DE BOMBEO . D 5.Q75 V%
D&'*! V% !"&,#*+* !"&,#*+* %!,&!'*+*& %!,&!'*+*& (&% "&s +$%#,+'!s 7.0Q s!= F")>& &")9%#,& 7#'
J.- 3ELOCIDAD DE LA PULPA EN LAS TUBER8AS
2
V + D&'*! F")>& &")9%#,& 7s!= A Á%!+ *! "+ s!,. T%+'s. T%+'s. D! "+ )$!%<+ (# : *# 2
.- CLCULO DE 3ELOCIDAD CRITICA LINEAL 93c7 !' T%+'s(.. /#*%)"#,& xDi Vc 0.0QIG x1xdo x1xdo .
G O G22
p x a x a
0.QQ5
D&'*! = A,!"!%. G%+. . s!= 2 D( D#!%& !*#& *! "+ (+%<,)"+ 0-
D!'s#*+* *! ()"(+ = 7
D# D#!%& #'!%#&% *!" )$& U V#s,&s#*+* +$s&")+ =.s!= a
D!'s#*+* *! "+ (+%<,)"+ = 7
a
D!'s#*+* *!" +=)+ + 20\C = 7
V, V!"&,#*+* ,%<#,+ "#'!+" s!=
.- MODO 5ACIL DE CALCULAR EL TAMA\O DE LAS POLEAS Y LA 3ELOCIDAD DE LOS EES. + S# s! ,&'&,! ,&'&,! "+ !"&,#* !"&,#*+* +* ; !" *#!%& *#!%& *! "+ (&"!+ (&"!+ #()"s&% #()"s&%++ ; !" *#!%& *#!%& *! "+ #()"s+*&%+ ; s! 1)#!%! s+$!% "+ !"&,#*+* *! 9s+ ?"#+4 )"#("#1)! "+ !"&,#*+* *! "+ #()"s&%+ (&% s) *#!%& ; *##*+ (&% !" *#!%& *! "+ (&"!+ #()"s+*+. #()"s+*+. E>!("& U'+ (&"!+ *! 2 !' )' &&% =#%+ + 4Q50 %( (+%+ #()"s+% )'+ (&"!+ *! 7.5 gC)" s!% "+ !"&,#*+* *! 9s+ ?"#+W
7
S&"),#3' M)"#("#1)! 4Q50 (&% 2 ; !" %!s)"+*& *#<*+"& !'%! 7.5 *+'*& )' %!s)"+*& *! 4000 %.(.. $ S# s! ,&'&,! "+ !"&,#*+* ; !" *#!%& *! "+ (&"!+ #()"s&%+ ; "+ !"&,#*+* %!1)!%#*+ *! "+ (&"!+ #()"s+*+ ; s! 1)#!%! &$!'!% !" *#!%& *! 9s+ ?"#+4 )"#("#1)! "+ !"&,#*+* *! "+ #()"s&%+ (&% s) *#!%& ; *##*+ !" %!s)"+*& !'%! "+ !"&,#*+* %!1)!%#*+ *! "+ (&"!+ #()"s+*+. E>!("& U' ,&'%+!>! *!$! =#%+% + 4850 %( +" s!% &#*& (&% )'+ (&% )'+ (&"!+ *! 7 1)! 1)! =#%+ =#%+ + 2400 240000 %( %( *!s* *!s*!! )'+ )'+ 1) 1)#' #'++ ,&' ,&'%& %&"+ "+*+ *+ (&% (&% )' =&$!%'+*&% gC)" !s !" ++@& *! "+ (&"!+ 1)! s! '!,!s#+ !' !" ,&'%+!>!W S&"),#3' M)"#("#1)! 24200 (&% 7 ; *##*+ !" %!s)"+*& !'%! 4850 *+'*& )' %!s)"+*& *! . , S# s! ,&'& ,&'&,! ,! "+ !"& !"&,# ,#*+ *+** ; !" *#! *#!% %&& %!1) %!1)!% !%#* #*&s &s *! )'+ )'+ (&"! (&"!++ ; "+ !"&,#*+* *!" !>! #()"s&% ; s! *!s!+ ,&'&,!% !" *#!%& *! "+ (&"!+ 1)! s! '!,!s#+4 )"#("#1)! "+ !"&,#*+* %!1)!%#*+ *! "+ (&"!+ #()"s+*+ (&% s) *#!%& ; *##*+ "+ !"&,#*+* *!" #()"s&%. #()"s&%. E>!("& U'+ %)!*+ #'!%%)(&%+ 1)! *!$! =#%+% + 4000 %( #!'! s&$%! !" %$&" )'+ (&"!+ *! X gC)" !s !" ++@& *! "+ (&"!+ 1)! s! '!,!s#+ !' )' &&% 1)! =#%+ + 4Q50 %(W S&"),#3' M)"#("#1)! 4000 (&% X ; *##*+ !" %!s)"+*& (&% 4Q50 *+'*& )' %!s)"+*& *! . * S# s! ,&'&,! ,&'&,! !" *#!%& *#!%& *! +$+s +$+s (&"!+s (&"!+s ; "+ !"&,#* !"&,#*+* +* %!1)!%#*+ %!1)!%#*+ (+%+ (+%+ !" !>! 1)! /+; 1)! #()"s+% ; s! *!s!+ s+$!% "+ !"&,#*+* *!" !>! #()"s&%4
)"#("#1)! !" *#!%& *! "+ (&"!+ #()"s+*+ (&% "+ !"&,#*+* %!1)!%#*+ ; *##*+ (&% !" *#!%& *! "+ (&"!+ #()"s&%+. E>!("& U'+ 1)#'+ ,&' )'+ (&"!+ *! 7 *!$! #()"s+% )' !>! *! 74800 %(. E" !>! #!'! )'+ (&"!+ *! 2 gC)" !s "+ !"&,#*+* + 1)! *!$! =#%+% "+ 1)#'+W S&"),#3' M)"#("#1)! 74800 (&% 2 ; *##*+ !" %!s)"+*& (&% "+ %!s()!s+ !s 74000.
1.- ESTIMACIÓN DE LA ENERGIA NECESARIA PARA TRITURACIÓN Y MOLIENDA. E' !" 9&*& *! B&'* !" _'*#,! *! %+$+>& 1)! !' s# !:(%!s+ "+ %!s#s!',#+ *!" +!%#+ + s!% %#)%+*& & &"#*+4 !s "+ !'!%=<+ !:(%!s+*+ !' / (&% &'!"+*+ %!1)!%#*+ (+%+ %!*),#% !" +!%#+" *! )' ++@& *! +"#!'+,#3' !3%#,+ #'#'#+ + 0 !'&% + 00 #,%&'!s. C&'&,#*& !" <'*#,! *! T%+$+>& T%+$+>& ; ,&' +;)*+ *! "+ !,)+,#3' *! "+ T!%,!%+ T!%,!%+ T!&%<+ !&%<+ *! R!*),, R!*),,#3' #3'4 4 !s (&s#$ (&s#$"! "! ,+",) ,+",)"+% "+% "+ !'!%= !'!%=<+ <+ '!,!s '!,!s+%# +%#++ (+%+ (+%+ "+ %#)%+,#3' ; "+ &"#!'*+4 +"&% ,&' !" ,)+" ()!*! s!"!,,#&'+%s! !" !1)#(& +*!,)+*&. L+ !,)+,#3' !:(%!s+*+ !' HP (&% &'!"+*+ ,&%+ (&% #')& !s "+ s#=)#!'!
W G.I8Wi G O P G O F
D&'*! L+ !'!%=<+ '!,!s+%#+ HP (&% &'#' F L+ +""+ !' "+ 1)! !" 0 *!" +!%#+" *! +"#!'+,#3' ,&'s#);! !" s)$++@&4 (#!s.
5
P L+ +""+ !' "+ 1)! !" )0 *!" +!%#+" %!*),#*& ,&'s#);! !" s)$++@&4 (#!s. # E" <'*#,! *! T%+$+>& !:(%!s+*& !' HP #'&'. P+%+ +,#"#*+* *!" !("!& *!" &'&=%++ s)=!%#*& (&% Z+'!% s! )!s%+ "+s !s,+"+s *! +"#!'+,#3' ; (%&*),& %!*),#*& !' ()"=+*+s ; !' s)s !1)#+"!'!s *! +""+ T;"!%. T;"!%. P&% &%+ (+%! s! #',");! + ,&'#')+,#3' (%&!*#&s *! <'*#,!s <'*#,!s *! %+$+>& *! "&s "&s +!%#+"!s s )s)+"!s )s)+"!s !' ')!s%+ ')!s%+ #'*)s%#+.
E>!("& 50 T&'/&%+ *! )' +!%#+" ,&' )' <'*#,! *! T%+$+>& T%+$+>& *! 8.Q7 s! *!s!+ %!*),#% *! 7 + 0.05. C+",)"+% "+ !'!%=<+ %!1)!%#*+ T%++% T%++% )'+ "<'!+ (&% F 7 ; P 0.05. 0.05. E" ()'& *! #'!%s!,, #'!%s!,,#3' #3' &$!'#*& ,&' "+ "<'!+ *! %!!%!',#+ )'#% ,&' !" +"&% *! 8.Q7. L!!% 25 HP (&% &'#'. P+%+ 50 &'s/&%+ 0.77 &'#' s! #!'! 2 HP.
MATERIAL .- M!'+ *! C&$%+ 2.- M!'+ *! C%&& 7.- F!%%&s#"#,#& .- G+"!'+ 5.- M!'+ *! O%& 8.- G%+'#& Q.- M!'+ *! /#!%%& .- M!'+ *! P"&& .- M!'+ *! P$-Z' 0.- D#&%#+ .- A'*!s#+ 2.-C)+%,#+ 7.- M!'+ *! M+'=+'!s& .- R&,+ &s#,+ 5.- M!'+ *! (#%#+ 8.- S<"#,!
PROMEDIO PESO ESP. INDICE DE TRABAO 7.02 7.7 .08 .80 . 2.7 5.7 0. 2.8 .7 2.8 .7 7.8 5. 7. .0 7.7Q .75 2.Q .0 2. 22.7 2.Q 2. 7.Q 2.8 2.88 0.7 7. .0 2.Q 7.57
8
Q.- M!'+ *! P"++ .- Es,&%#+ .- M!'+ *! Es+@& 20.- M!'+ *! Z#', 2.- B+s+"& 22.- G+$%&
2.Q2 2.7 7. 7.8 2. 2.7
Q.70 5.Q8 0. 2.2 20. .5
TABLAS 1.- TABLAS DE CON3ERSIÓN MAS USADAS,
LINEALES, M!%&s + (#!s
7.2
P#!s + !%&s
0.70
M!%&s + ()"=+*+s
7.7Q
P)"=+*+s + !%&s
0.025
C!'<!%& + (#!s
0.072
P#!s + ,!'<!%&s
70.
C!'<!%&s + ()"=+*+s
0.77Q 0.77Q
P)"=+*+s + ,s.
2.5
SUPER5ICIE
M!%&2 + P#!2
0.Q85
P#! 2 + ,2
2.070
M!%&2 + ()"=+*+ 2
5.8Q
P)"=2 + ,2
8.58
C2 + (#!2
0.000Q85
P)"=2 + !%&2
0.00085
C2 + ()"=+*+ 2
0.550
P#!2 A C2
8.58
3OLMENES,
M!%&7 + (#!7
75.72
P#!7 + !%& 7
0.027Q
M!%&7 + ()"=+*+7
827.7
P)"=7 + ,7
8.7Q
C7 + (#!s7
0.0000757
P)"=7 + !%&7
0.00008
C7 + P)"=+*+7
0.08
P#!7 + ,7
278.5
G+"&'!s USA + P#! 7
0.77Q
P#!7 + G+"&'!s USA
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I3.I3.- METODOS M ETODOS DE D E ANLISIS QU8MICO QU 8MICO CUANTITATI3O CUANTITATI3O ANLISIS DE PLOMO M9& M9&**& *!" M&"# M&"#$$*+& *+& *! A&' A&'#& #&..- Es )' 9& 9&**& s s !:+, :+,& (+% "+ *!!%#'+,#3' *!" ("&&4 (+%+ "& ,)+" s! (%!,#(#+ +" !s+*& *! +,!+& ,&' )'+ s&"),#3' !s'*+% *! 0. N&%+" 0.N *! M&"#$*+& *! A&'#&4 "+ 1)! s! (%!(+%+ *#s&"#!'*& .28 =%. D! 9s+ s+" "#%&4 !s+'*+%#'*&s! !s+'*+%#'*&s! ,&' "+ %!"+,#3' *! =+s& (%,#,&=+s& !3%#,&4 ,+",)"+*& (+%+ 0.2 =%. *! P$ ()%& !"!,%&"<#,&. E" ()'& #'+" *! "+ %!+,,#3' s! *!!%#'+ !'s+;+'*& )'+ =&+ *! "+ s&"),#3' *! ("&& +@+*#*& =%+*)+"!'! =%+*)+"!'! + %+9s *! )'+ $)%!+ =%+*)+*+4 ,&' ,&' )' #'*#,+*&% *! 0.05 *! ,#*& '#,& %!,#9' (%!(+%+*& 3 ,"&%)%& 9%%#,&4 ,&' "+ ,)+" *+ )'+ ,&"&%+,#3' ++%#""+ ,&' !" <'#& !:,!s& *! &"#$*+&.
ANLISIS DE COBRE M*odo d$% Yod'o d$ Po*a!o .- Es )'& *! "&s 9&*&s *! +;&% !:+,#)* (+%+ "+ *!!%#'+,#3' *!" ,&$%!4 s! $+s+ !' 1)! s# s! %++ )'+ s&"),#3' *! s+" ,?(%#,+ '!)%+ 3 "#=!%+ ,#*+ ,&' s&"),#3' *! I&*)%& *! P&+s#& s! &%+ !" I&*)%& C)(%&s& ; !" Y&*& "#$%!4 "+ 1)! s! +"&%+ ,&' s&"),#3' !s'*+% *! T#&s)"+& *! s3"#*& "+ 1)! s! (%!(+%+ *#s&"#!'*& =%s" *! 9s+ s+"4 s! !s+'*+%#+% ,&' 042 =%s. D! ,&$%! !"!,%&"<#,&4 )#"#+'*& ,&& #'*#,+*&% #'!%'& )'+ s&"),#3' *! *! +"#*3'.
Poc$d!"!$n*o .- P!s+% 0.5 =%s. *! )!s%+ ()"!%#+*+4 %+s+s+% !' )' !'"!'!;!% *! 00 3 250 ".
2.- D#s=%!=+% +' #=)+" 1)! (+%+ !" ("&& ; s)"+#+%"+4 *#")#%"+4 !'%#+%"+. 7.- A=%!=+% 5 " *! s&"),#3' *! +=)+ *! $%&&4 /!%#%"+ (+%+ !"##'+% !" !:,!s& *! $%&& !" $%&& &:#*+ +" #!%%& + %#+"!'!. .- N!)%+"#+% "+ s&"),#3' +=%!=+'*& ,&' H#*%3:#*& *! A&'#& ,&',!'%+*&4 !"##'+% !" !:,!s& *! A&'#& (&% !$)""#,#3'. L)!=& +=%!=+% ,#*& +,9#,& ="+,#+"4 s!=)#% /#%#!'*& /+s+ !"##'+% !" !:,!s& *! +,9#,&4 s!=)#*+!'! +=%!=+% *! 7 + =%s. *! ")&%)%& *! s&*#& /+s+ !% )'+ s&"),#3' %+'s(+%!'! *! !%*&s& + ,!"!s! ,"+%&4 !'%#+% +" +$#!'!. 5.- E' %#3 +=%!=+% 2 + 7 =%s. *! I&*)%& *! P&+s#& (+%+ (%!,#(#+% "+ s+" ,)(%&s+ ; "#$!%+,#3' *! I&*& (( ; s&"),#3' +'+%+'>+*&. 8.- T#)"+% !' %#3 ,&' "+ s&"),#3' +"&%+*+ *! T#&s)"+&4 )s+'*& ,&& #'*#,+*&% #'!%'& *! +"#*3' ,&' "+ ,)+" !" I&*& "#$%! *+ ,&"&%+,#3' +)". Q.- E" ()'& #'+" *! "+ #)"+,#3' !s !" #'s+'! !' 1)! ,+$#+ !" +)" + #',&"&%& 3 $"+',& (+>+. .- H+,!% "&s ,",)"&s *!" (&%,!'+>! *! ,&$%! +' #=)+" 1)! (+%+ !" ("&&. S! ()!*! +$#9' )#"#+% "+ s&"),#3' #"%+*+ *!" ("&& (+%+ "+ *!!%#'+,#3' *!!%#'+,#3' *!" ,&$%! ; s!=)#% "&s #s&s (+s&s.
ANLISIS DE 5IERRO M*odo d$% P$"an>ana*o d$ Po*a!o .- Es! 9&*& s! )'*+ !' !" (+s& *! "+ s+" !%%&s+ + 9%%#,& (&% "+ +,,#3' &:#*+'! *!" (!%+'=+'+& !' !*#& ,#*& s)"?%#,&. P+%+ "& ,)+" !" #!%%& *!$! s!% !s(!,#+"!'! %!*),#*& ,&' ,"&%)%& *! !s+@ !s+@&. &. L+ s&"), s&"),#3' #3' !s' !s'*+% *+% !s (%!(+ (%!(+%+* %+*&& *#s&" *#s&"#!' #!'*& *& 5.88 5.88 =%s" =%s" *! s+" *! (!%+'=+'+& (!%+'=+'+& *! (&+s#&4 +,&%#+'*& ,&' )'+ s&"),#3' ,&'&,#*+ *! O:+"+& *! S&*#&4 3 *! #!%%& !"#,&. P%&,!*##!'& .- P!s+% 0.5 =%s. *! )!s%+ ()"!%#+*+4 *#s=%!=+% !' )' +s& 3 !%"!'!;!% *! 00 + 250 "s. S)"+#+%"+4 !'%#+%"+ +" ,&& (+%+ !" ("&&4 s! ()!*! )#"#+%
20
+$#9' (+%+ *!!%#'+% !" #!%&4 "+ s&"),#3' *!" #"%+*& *!" ("&& 1)! +$#9' ,&'#!'! + !s! !"!!'&. 2.- A=%!=+% A=%!=+% 20 "s. D! +=)+ *! $%&&4 /!%#% (+%+ !"##'+% !" !:,!s& *! B%. B%. 7.- A=%!=+% A=%!=+% *! 2 + 7 =%s. *! ,"&%)%& *! A&'#& ; (%!,#(#+% +" #!%%& ,&' /#*%3:#*& *! A&'#& /#*%3:#*& 9%%#,&4 /!%#% (+%+ !"##'+% !" !:,!s& *! A&'#& /+s+ '& &"!% !" +&'#+,&. .- F#"%+% !' ,+"#!'! ,&' (+(!" #"%& ,)+"#+#& N\ 74 "++% +%#+s !,!s !" (%!,#(#+*& ,&' )'+ )'+ s&"),#3' +&'#+,+" +&'#+,+" *! 0 ; +=)+ ,+"#!'!. ,+"#!'!. 5.- T%+s+s+% !" (%!,#(#+*& *! /#*%3:#*& 9%%#,& +" %!,#(#!'! &%#=#'+"4 (&% !*#& *! ,/&%%&s *! +=)+4 "++% $#!' !" #"%& + #' *! 1)! '& 1)!*! '+*+ *! (%!,#(#+*& ,&' ,#*& ,#*& ,"&%/<*%#,& +" 0. 8.- D#s&"!% !" (%!,#(#+*& ,&' ,#*& ,"&%/<*%#,& +" 0 /!%#%"+4 +@+*#% s&"),#3' *! ,"&%)%& *! !s+@& =&+ !' =&+ /+s+ +",+'+% )'+ s&"),#3' #',&"&%+. Q.- A@+*#% 0 "s. *! )'+ s&"),#3' s)"&&s3%#,+ ; +s s&"),#3' *! ,"&%)%& !%,?%#,& (+%+ '!)%+"#+% !" !:,!s& *! !s+@& 1)! /)$#!%+. .- A)!'+% A)!'+% +=)+ *!s#"+*+ /+s+ *#")#%"+ + 50 "s. /!%#% ; !'%#+%. .- T#)"+% !' %#3 ,&' "+ s&"),#3' !s'*+% *! (!%+'=+'+& *! (&+s#& /+s+ &$!'!% )'+ ,&"&%+,#3' #&"!+ "#=!%& (!%s#s!'!. 0.- C+",)"+% !" (&%,!'+>! *! #!%%&4 +" #=)+" 1)! (+%+ !" ("&&.
ANLISIS DE INC M*odo d$ 5$oc!an'o d$ Po*a!o .- S# s&$%! )'+ )'+ s&"),#3' s&"),#3' +,#*##,+*+ *! s+" *! #',4 s! /+,! !,/+% )'+ s&"),#3' !s'*+% *! !%%&,#+')%& *! (%!,#(#+ )'+ !,"+ *! !%%&,#+')%& *! #', ; (&+s#&4 !%%&,#+')%& #',#,&. T!%#'+*+ "+ %!+,,#3'4 !" <'#& !:,!s& *! !%%&,#+')%&4 ()!s& +" ,&'+,& ,&' )'+ s&"),#3' +" *! +,!+& *! )%+'#& & ,"&%)%& 9%%#,&. L+ s&"),#3' !s'*+% s! (%!(+%+ (!s+'*& 2240 =%s" *! s+" *! !%%&,#+')%& *! (&+s#& ; s! !s+'*+%#+ ,&' 0.2 =%s. *! #', !"!,%&"<#,&. P%&,!*##!'&
2
.- P!s+% 0.5 =%s. *! )!s%+ ()"!%#+*+4 *#s=%!=+% ,&' ,#*& ,"&%/<*%#,& ; '<%#,& ,&',!'%+*&4 s)"+#+%4 s)"+#+%4 !' )' +s& *! 00 3 250 "s4 !'%#+%"+. 2.- A=%!=+% A=%!=+% 20 "s. *! +=)+ *! $%&&4 /!%#% (+%+ !"##'+% !" !:,!s& *! B%. 7.- A@+*#% 2 + 7 =%s. *! ,"&%)%& *! A&'#& ; (%!,#(#+% +" #!%& ,&' /#*%3:#*& *! A&'#&. .- F#"%+% !' ,+"#!'! (+%+ !:%+!% !" #!%%& #'!%!%!'! (+%+ !" +'"#s#s *! #',. T+$#9' s! ()!*! )#"#+% "+ s&"),#3' 1)! 1)!*+ *!" +'"#s#s *! #!%%& s# /)$#!%+ #',. S# /)$!%+ M+'=+'!s& "+ )!s%+ +=%!=+% P!%s)"+& *! P&+s#& (+%+ (%!,#(#+% +" M+'=+'!s&. O +$#9' s# )#!%+ A%s9'#,& A%s9'#,& +@+*#% *)%+'! "+ *#s=%!=+,#3' ,"&%+& *! (&+s#& ; s $%&& !' "+ &:#*+,#3' ; s +)%! (+%+ (%!,#(#+% +" M'4 ; !+(&%+% +" As. E" M' %++*& ,&' !" (!%s)"+& *! (&+s#& s! "! +=%!=+ s s 5 =%s *! ,"&%)%& *! A&'#& ; 50 "s *! H#*%3:#*& H#*%3:#*& *! A&'#& ; s! (%!,#(#+ !' &%+ *! ,#*& +'=+'&s&. 5.- A,#*##,+% "+ s&"),#3' "#$%! *! F!4 M' ; As ,&' ,#*& ,"&%/<*%#,& ,&',!'%+*&4 +@+*#% +s 5 "s *! !:,!s& *! ,#*&4 +=%!=+% =%+'+""+s *! P$ (+%+ (%!,#(#+% +" ,&$%! 1)! !s)#!%+ (%!s!'! !' "+ s&"),#3' 1)! +$#9' #'!%#!%! (+%+ !" ,",)"& *! #',4 3 ,&& !*#& *! s!=)%#*+* *! ,)+"1)#!% #'!%!%!',#+ /+s+ &$!'!% )'+ s&"),#3' #',&"&%+. 8.- L+ s&"),#3' +s< (%!(+%+*+ #)"+% ,&' "+ s&"),#3' !s'*+% *! !%%&,#+')%& )s+'*& ,&& #'*#,+*&% !:!%'& !' &%+ *! =&+s !' )'+ +;3"#,+ $"+',+ !',! !',!%+ %+*+ *+ )'+ )'+ s&") s&"),# ,#3' 3' +" *! +,! +,!+ +&& *! )%+' )%+'#" #"&4 &4 /+s /+s++ &$! &$!'! '!%% )'+ )'+ ,&"&%+,#3' (+%*+ ,&' <'#& !:,!s& *! !%%&,#+')%&. Q.- C+",)"+% !" (&% ,#!'& *! #',4 +" #=)+" 1)! !" ("&&.
ANLISIS DE PLATA PLATA M*odo Ga4!"*!co d$ Eco!&!cac!n Eco!&!cac!n Co)$%ac!n Co)$%ac!n .- S! $+s+ !' &$!'!% "+ ("++ !"#,+ (&% )s#3' *! s)s ,&(&'!'!s +@+*#!'*& )'*!'!s ; &*##,+*&%!s *! !s,&%#+s !' %!,#(#!'!s *! +!%#+"!s %!%+,+%#&s ; +$s&%$!'!s *! /)!s& !' /&%'&s *! )"+.
22
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6.- Co)$%ac!n, .- S! ,+"#!'+ (%!#+!'! "+s ,&(!"+s !' "+ )"+ + 0\C4 /+s+ !"##'+% s) /)!*+* )'&s 20 #')&s.
27
2.- C&"&,+% "&s ,)$&s *! ("&&-("++ ,&' )' (#'+ +*!,)+*+ !' "+s %!s(!,#+s ,&(!"+s !')!%+*+s4 !')!%+*+s4 *!'%& *! "+ )"+. 7.- T+' (%&'&4 !%#'+'*& *! ,&"&,+% "&s ,)$&s4 ,!%%+% "+ ()!%+ *! "+ )"+ (+%+ !"!+% "+ !(!%+)%+ *!" /&%'& )'&s 5 #')&s (!%+'!,!% /+s+ 1)! s! /+;+ )'*#*& !" ,)$&4 +$%#% "+ ()!%+ ; "+s ,&()!%+s *! s+"#*+ *! /)&s *! "+ )"+ )"+44 (+%+ (+%+ +' +'!' !'!% !% "+ !( !(!% !%+ +)% )%++ ,&'s ,&'s+ +' '!! + 80\ 80\C C ; "+ +3 +3s s!% !%++ +*!,)+*+ (+%+ "+ !+(&%+,#3' *!" ("&& ; !#+% !'3!'&s *! s&"#*##,+,#3' *!" "#+%=#%#& ,&& s! '&+% !' ,#!%&s ,+s&s *! "+ (%,#,+ (%,#,+ s&$%! !" $&3' *! ("++. E" ("&& !' (+%! (+%! !s +$s&%$#*& (&% "+ ,&(!"+ ; !" !" %!s& s! &"+#"#+. &"+#"#+. .- L+ ,&(!"+,#3' !%#'+ ,)+'*& s! &$s!%+ !' "+ ,3(!"+ +' s&"& )' (!1)!@& ()'& s#' %!s("+'*&% %!s("+'*&% 1)! !s !" $&3' $&3' *! ("++ !"#,+. !"#,+. 5.- U'+ ! *!s+(+%!,#*& &*& !" ("&& ; s! #!'! )' ()'& s#' $%#""&4 s+,+% "+ ,&(!"+ *!" /&%'&4 *!>+% 1)! s! !'%+*+s *!" "#+%=#%#& +"%!*!*&% *!" $&3'. G!'!%+"!'! "+ ,&(!"+,#3' *)%+ X *! /&%+ ; (+%+ +,!"!%+% "+ ,&(!"+,#3' s! *!$! #'s)"+% +#%! !' !" /&=+% *!" /&%'& )"+. Q.- C+",)"+% !" ,&'!'#*& *! ("++ !' &'+s TCS. P+%+ "& ,)+" s! *!!%#'+ )' +,&% *! ,&'!%s#3' !' $+s! +" (!s& *! )!s%+ &+*+ ; !" (!s& *! $&3' *! ("++4 & s!+ !' =%s + &'+s-%&;TCS4 (+%+ 5 =%s *! )!s%+ )!s%+ !s #=)+" + 5.7 !" +,&% *! ,&'!%s#3'. E>!("& P!s& *! )!s%+ 5 =%s s! !',&'%3 )' $&3' *! 0.8Q5 =s4 "+ "!; *! ("++ !' "+ )!s%+ )!s%+ !s *! 82.2Q 82.2Q &TCS.
ANLISIS DE ORO
2
M*odo M*odo Ga4!"* Ga4!"*!co !co d$ Eco!&!c Eco!&!cac! ac!n-Co)$ n-Co)$%ac! %ac!n.n.- A" #=)+" 1)! (+%+ "+ *!!%#'+,#3' *! "+ ("++ s! %!+"#+ "&s #s&s (+s&s ,&' "+ *#!%!',#+ *! 1)! s! *!$! *! (!s+% +;&% ,+'#*+* *! )!s%+ ; !'#!'*& !" $&3' *#s&"!% 9s+ ,&' ,#*& '<%#,& *#")#*& (+%+ s!(+%+%"+ *! "+ ("++ 1)! "! +,&(+@+.
Poc$d!"!$n*o, .- P!s+% 0 + 00 =%s *! )!s%+ ()"!%#+*+4 %+s+s+% + ,%#s&"!s *! 0 3 00 =%s *! ,+(+,#*+* 3 +$#9' !' !s,&%##,+*&%!s *! 7 ()"=+*+s *! *#!%&. 2.- A=%!=+% "#+%=#%#& 3 =%+'+""+s *! ("&& !' +;&% ,+'#*+*4 )'*!'!s ,&& /+%#'+ *! %#=&4 ,+%$&'+& *! s&*#&4 '#%+& *! (&+s#& ; s+" *! $3%+:4 !,"+%"+ /+s+ &$!'!% /&&=9'!&. /&&=9'!&. 7.- Es,&%##,+% *&s 3 +s !,!s /+s+ "+ ,&("!+ !"##'+,#3' *! "+ !s,&%#+ ; "+ &$!',#3' *! )' ,)$& *! ("&& '&%+" (+% "+ ,&(!"+,#3'. .- C&(!"+% "&s ,)$&s *! ("&&-&%&-("++4 +" #=)+" 1)! (+%+ "+ ("++ + !(!%+)%+ (%&!*#& *! 80\C. 80\C. 5.- L#(#+%"+ L#(#+%"+ !" $&3' *! !s,&%#+s !s,&%#+s 1)! )#!%+ )#!%+ +*/!%#*+s +*/!%#*+s44 *#s&"!%" *#s&"!%"++ ,&' ,)#*+*& ,)#*+*& ,&' ,&' ,#* ,#*&& '<% '<%#, #,&& +" 0 0 s&$% s&$%!! )' ,%#s ,%#s&" &" *! (&%, (&%,!" !"+' +'++ "!' "!'+ +!' !'! ! + !( !(!% !%+ +)% )%++ s s 3 !'& !'&ss *! 0\C 0\C44 /+s /+s++ *#s& *#s&" "!% !% &*+ &*+ "+ ("+ ("+++ 1)! 1)! "! +,&(+@+ +" &%& !" &%& '& !s *#s)!"& (&% !" ,#*& '<%#,&. 8.- S!(+%+% (&% *!,+'+,#3' "+ s&"),#3' *! '#%+& *! ("++ s#' 1)! /+;+ (9%*#*+ *! "+ (+%! s3"#*+4 "++% +%#+s !,!s ,&' s&"),#3' +&'#+,+" ; +=)+ *!s#"+*+ ,+"#!'!. Q.- S!,+% !" ,%#s&" 1)! ,&'#!'! !" &%& !' )'+ !s)+ !"9,%#,+ *)%+'! 20 #')&s + 00\C. .- S+,+% !" ,%#s&" !'%#+%"+ *!'%& *! "+ !s)+ #s+ ; !" +$#!'! (!s+% "+ (+%! s3"#*+ 1)! !s !" &%& !"#,&. .- C+",)"+% !" ,&'!'#*& *! &%& !' &'+s %&;TCS.
E($")%o, S! (!s3 (+%+ !" +'"#s#s 0 =%s *! )!s%+ ; s! !',&'%3 0.7 =%s *! &%& ()%&. C)" s!% "+ "!; *! &%& !' &TCS
25
So%'c!n, L!; *! O%& F+,&% (+%+ 0 =%s *! )!s%+P!s& *! $&3' *! A) 2.Q0 : 0.7 0.Q &TCS.
ANLISIS DE INSOLUBLES M*odo Ga4!"*!co .- T+$#9' !s '!,!s+%#& *!!%#'+% !' )'+ )!s%+ *! #'!%+" "+ (+%! 1)! '& *#s)!"! 1)! =!'!%+"!'! !s' ,&()!s&s *! s<"#,! ; &%+s.
Poc$d!"!$n*o .- P!s+% 0.5 =%s *! )!s%+ ()"!%#+*+4 %+s+s+% + )' +s& *! 000 3 250 "s. 2.- A=%!=+% 5 "s *! ,#*& ,"&%/<*%#,& ,&',!'%+*&4 /!%#% !' )'+ !s)+ /+s+ *#s#')#% &")!'4 +@+*#% 5 "s *! ,#*& '<%#,& ,&',!'%+*&4 /!%#% /+s+ s!1)!*+*. 7.- E' %<& +=%!=+% 00 ". *! +=)+ *!s#"+*+ ; s ,#*& ,"&%/<*%#,&4 /!%#% *)%+'! 0 #')&s. .- F#"%+%4 "++% !" #"%+*& +%#+s !,!s ,&' +=)+ *!s#"+*+4 s!,+% !" #"%& *! ,!'#+ ,&'&,#*+ !' )'+ !s)+ !"9,%#,+. 5.- C+",#'+% !" (+(!" s!,& 1)! ,&'#!'! "&s #'s&")$"!s !' )' ,%#s&" *! (&%,!"+'+ + 00\C4 (&% !s(+,#& *! 70 #')&s !' )'+ )"+ !"9,%#,+. P&% *#!%!',#+ *! (!s&s !'%! !" ,%#s&" s#' "+ )!s%+ ; ,&' )!s%+ ,+",#'+*+ s! /+""+% !" (&%,!'+>! *! #'s&")$"!s. #'s&")$"!s.
E($")%o S# (+%+ 0.5 =%s. *! )!s%+ s! !',)!'%+ )'+ *#!%!',#+ *! (!s&s *! 0.05 0.0555 =%s. =%s. *! +!%# +!%#+" +" ,+",#' ,+",#'+*& +*&.. C+",) C+",)"+% "+% !" (&%,!' (&%,!'+> +>!! *! #'s&") #'s&")$"! $"!ss 1)! ,&'#!'! *#,/& #'!%+" S# (+%+ 0.5 =%s. -------------------- 0.055 =%s. 00.0
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28
3.- ANL ANLIS ISIS IS DE LOS LOS ELEM ELEMEN ENTO TOS S CO CONT NTAM AMIN INAN ANTE TES S DE LOS LOS CONCENTRADOS DE P6-C'-A>. E' !" !s)*#& !+"?%=#,& *! ,&',!'%+,#3' *! )' #'!%+" !s #(&%+'! s+$!% s# /+; /+; 3 '&4 ; !' 1)! (&%,! (&%,!'+ '+>! >! "&s !"!!' !"!!'&s &s ,&'+ ,&'+#' #'+' +'!s !s +s< +s< A'#& A'#&'#& '#&44 A%s9'#,&4 M!%,)%#& ; &%&s4 s# !s' !' s)s !'+s s#("!s s&"&s 3 !' ,&()!s&s +s&,#+*&s ,&' !"!!'&s +"#&s&s. S# !s' +s&,#+*&s ,&' !" !"!!'& *! #(&%+',#+ +" ,&',!'%+%s! !s+s s! #',%!!'+%'4 (&% !s& s) ,&'%&" !s #(%!s,#'*#$"!4 (+%+ '& &$!'!% (%&*),&s & ,&',!'%+*&s ,&' ,&'!'#*& 1)! !'=+' +;&%!s (&%,!'+>!s + "&s "<#!s *! ,&!%,#+"#+,#3'. As< #s& s# !s' (%!s!'!s !' s)s !'+s "#$%!s s&' *#<,#"!s *! !"##'+%"&s !' "&s %!"+!s4 (&%1)! #!'!' (%&(#!*+*!s /#*%&3$#,+s As< ,&& !" s)"&+'#&'#)%&4 s)"&+%s!'#)%& ; !" ,#'+$%#&.
ANLISIS DE ARS]NICO Y ANTIMONIO M*odo d$ Iod!"$*=a P$"an>ano"$*=a P$"an>ano"$*=a .- Es! 9&*& !s )s+*& (+%+ +%#&s #'!%+"!s ; (%&*),&s !+"?%=#,&s4 ,&'s#s! !' s!(+%+% (&% *!s#"+,#3' !" +%s9'#,& ,&& ,&& %#, %#,"& "&%) %)%& %& ; *!! *!!% %#' #'+% +% !" +'# +'#&' &'#& #& 1)! 1)! 1)!* 1)!*++ !' "+ s&") s&"),# ,#3' 3' (&% (&% (!%+'=+'&!%<+. (!%+'=+'&!%<+.
1.- ARS]NICO Poc$d!"!$n*o, .- P!s+% =%. *! #'!%+" ()"!%#+*+4 %+s+s+% !' )' !%"!'!;!% *! 500 ". *! ,+(+,#*+*. 2.- A=%!=+% 5 =%s. *! B#s)"#& *! (&+s#&4 2 =%s. *! s)"+& *! A&'#&4 5 "s *! ,#*& s)"?%#,& ,&',!'%+*& ; )'+ &,++ (+%! *! (+(!" #"%&. 7.- C+"!'+% !' )'+ !s)+ !"9,%#,+4 ,+s# "+ s!1)!*+*4 !#+'*& 1)! s! s!1)!4 s&"& !' !s+*& (+s&s&.
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.- E'%#+%4 +=%!=+% 25 ". *! +=)+ *!s#"+*+ ; 5 =s. *! s)"+& !%%&s& ; ,&'!,+% !" !%"!'!;!% +" s#s!+ *! *!s#"+,#3'. 5.- C!%%+% !" )$& *! #'=%!s& *! ,#*& ,"&%/<*%#,&4 (&'!% )' +s& *! 0 "s *! +=)+ *!s#"+*+4 s#!'*& 1)! !" )$& *! s+"#*+ *! =+s !'%#+*& *!$!% !s+% s)!%=#*+ *!'%& *!" +=)+ *!s#"+*+ + ". *! (%&)'*#*+*4 (+%+ !#+% "+ )=+ *!" =+s *! %#,"&%)%& *! +%s9'#,&. 8.- H!%#% #')& (+%+ !:()"s+% !" +#%! *!" %+s,& !%"!'!;!%. !%"!'!;!%. Q.- I'%&*),#% =%+*)+"!'! + %+9s *! )$& *! #'=%!s& *! ,#*&4 0 "s *! ,#*& ,"&%/<*%#,& ,&',!'%+*& ; ,!%%+% "+ ""+! *! #'=%!s&4 +)!'+% 0 "s *! ,#*&. E" %!,#(#!'! *! ,#*& *!$! ,&'!'!% +;&% &")!' *! ,#*& (+%+ #'!%!%#% "+ )=+ *! =+s. .- C+"!'+%4 ,)+'*& "+ s&"),#3' *!" %+s,& ,&#!'+ + /!%#%4 *!>+% ,+!% "&s 0 "s *! ,#*& =&+ + =&+4 !' "+ #s+ %+3' *! "+s =&+s *! *!s#"+*&4 + #' *! +'!'!% )' &")!' ,&'s+'! !' !" %+s,&. .- C)+'*& &*& !" ,#*& + !%#'+*& *! ,+!%4 s! #'+"#+ "+ *!s#"+,#3' ; s! s!(+%+ "+ ,&'!:#3' ,&' !" *!s#"+*&% %!s!%+% "+ s&"),#3' *!" %+s,& (+%+ !" +'"#s#s *! +'#&'#&. 0.- N!)%+"#+% !" *!s#"+*& ,&' s&"),#3' *! /#*%3:#*& *! s&*#& )s+'*& 7 =&+s *!" #'*#,+*&% !'&"+"!#'+. .- A=%!=+% (&% !*#& *! )'+ $)%!+ ,#*& ,"&%/<*%#,& /+s+ "+ *!s+(+%#,#3' *!" ,&"&% *!" #'*#,+*&%4 +@+*#% 2 =&+s s !' !:,!s&. 2.- E'%#+% ; +=%!=+% 5 =%s *! $#,+%$&'+& *! s&*#& ; 0 " *! s&"),#3' *! +"#*3'. 7.- T#)"+% T#)"+% ,&' "+ s&"),#3' !s'*+% *! #&*& 0. N4 /+s+ "+ +(+%#,#3' *! ,&"&% +)" *! "+ s&"),#3'. .- H+,!% "&s ,",)"&s *!" (&%,!'+>! *! +%s9'#,&
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2.- ANTIMONIO,
2
Poc$d!"!$n*o, .- T%+s+s+% T%+s+s+% "+ s&"),#3' *!" *!s#"+*& + )' +s& *! 00 "s ; *##*#% + 200 ". 2.2.- S)" S)"/< /<*% *%#, #,+4 +4 ,&' ,&' ,#* ,#*&& s)"/ s)"/<* <*%# %#,& ,& =+s! =+s!&s &s&& *)%+ *)%+' '!! 70 #') #')& &ss /+s /+s++ (%!,#(#+,#3' ,&("!+ ,&("!+ ; *!>+% !' %!(&s& %!(&s& /&%+s 3 /+s+ /+s+ !" *<+ s#=)#!'!. s#=)#!'!. 7.- F#"%+% + %+9s *! )' #"%& #'& ; "++% !" (%!,#(#+*& ,&' +=)+ s+)%+*& ,&' ,#*& s)"/<*%#,& *!&"!% !" (%!,#(#+*& +" +s& &%#=#'+"4 *!s,+%=+% !" #"%&. .- D#s&"!% !" (%!,#(#+*& !' )'+ s&"),#3' ,+"#!'! *! s)")%& *! s&*#&4 #"%+% ; %!,#$#% !" #"%+*& !' )' !%"!'!;!% *! 500 "s )s+% "+ #s+ ,+'#*+* *! /#*%3:#*& *! s&*#& ,!%,+ *! 5 "s. 5.- R!#"%+% + %+9s *!" #s& #"%& !' ,+s& *! 1)! /+;+ &%&s s)")%&s4 ,+"!'+% )'&s #')&s. 8.- L++% 7 !,!s !,!s ,&' +=)+ *!s#"+*+ *!s#"+*+ ,+"#!'!4 ,+"#!'!4 *!s,+%+% *!s,+%+% !" (%!,#(#+* (%!,#(#+*&& 1)! '& s! *#s)!"! *!" #"%&. Q.- A=%!=+% A=%!=+% 5 =%s. *! $#s)"#& *! (&+s#& ; 0 " *! ,#*& s)"?%#,&. .- E+(&%+% !' ""++ )!%! /+s+ ,+s# + s!1)!*+*. .- E'%#+% ; +=%!=+% 00 " *! +=)+ *!s#"+*+ ; 0 " *! ,#*& ,"&%/<*%#,&4 /!%#% 5 #')&s /+s+ &$!'!% )'+ s&"),#3' #',&"&%+ ; *!>+% !'%#+%. 0.- T#)"+% ,&' s&"),#3' !s'*+% *! (!%+'=+'+& (!%+'=+'+& *! (&+s#&. L As
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ANLISIS DE MERCURIO M*odo Ga4!"*!co .- D&'*! !" !%,)%#& s! %!,#$! !' &%+ *! +(&% s&$%! ("++ '+#+ 1)! &%+ )'+ ++"=++ ++"=++ *! A=-H=.
Poc$d!"!$n*o .- P!s+% 0 =%s. *! )!s%+ ()"!%#+*+ 1)! ,&'!'=+ !%,)%#&. 2.- M!,"+% ,&' ,+%$3' ; (&"& *! /#!%%& %!*),#*&4 ""!'+% !' )' %!,#(#!'! *! #!%%& ,&' +(+ /!%9#,+ 1)! !'=+ %!%#=!%+,#3'4 s! ,&"&,+ )'+ "#'+ *!
2
("++ !' "+ ,)+" s! ,&'*!'s+ !" !%,)%#&. P&'!% "+ +(+ ; +s!=)%+% /!%9#,+!'!. 7.- C+"!'+% !" %!,#(#!'! ,&' )' !,/!%& B)'s!' /+s+ %&>& &s,)%& *)%+'! 0 #')&s4 +$%#!'*& !" s#s!+ *! %!%#=!%+,#3'. .- D!>+% !'%#+% + "+ !(!%+)%+ +$#!'!4 s+,+% "+ "#'+ *! ("++. 5.- P!s+% "+ "#'+4 (%!#+!'!4 s+,+% "+ *#!%!',#+ *! (!s& ; !:(%!s+% "+ "!; *! !%,)%#& !' (+%! (&% #""3' ((.
3I.- ANLISIS DE REACTI3OS DE 5LOTACIÓN ANLISIS DE CIANURO DE SODIO M*odo d$ N!*a*o d$ P%a*a .- S! )#"#+ s&"),#3' 0.N *! '#%+& *! ("++ ; ,&& #'*#,+*&% ;&*)%& *! (&+s#&.
Poc$d!"!$n*o .- M!*#% 5 "s. *! )!s%+ *! s&"),#3' (%!(+%+*+ !' "+ ("+'+ ,&',!'%+*&%+. 2.- A@+*#% A@+*#% 5 "s. *! #&*)%& *! (&+s#& +" 2. 7.- T#)"+% ,&' s&"),#3' +"&%+*+ *! 0.N *! '#%+& *! ("++ *! .005 *! +,&%4 /+s+ )' "#=!%& !')%$!,##!'&. !')%$!,##!'&. .- C+",)"+% !" (&%,!'+>! *! ,#+')%& *! s&*#&. E>!("& S# s! =+s& +" #)"+% "s. *! '#%+& *! ("++ *! +,&% .0054 !" (&%,!'+>! s!% N+CN 0.200 .005 : .5
ANLISIS DE SUL5ATO DE COBRE S! *!!%#'+ +" #=)+" 1)! !" ,&$%! (&% !" 9&*& %(#*& *! I.
Poc$d!"!$n*o, .- M!*#% 2.5 ". *! s&"),#3' *! %!+,#& *! )'+ ("+'+ *! "&+,#3'.
70
2.- S! /+,!' "&s #s&s (+s&s (+%+ "+ *!!%#'+,#3' *!" ,&$%!4 (&%1)! ;+ s! #!'! !' &%+ *! s)"+&4 3 s!+ s! &:#*+ ,&' +=)+ *! $%&&4 +=%!=+% ,"&%)%& *! A&'#& ; /#*%3:#*& *! A&'#&4 '!)%+"#+% ,&' ,#*& +,9#,&4 +@+*#% FN+ ; !' %<& +@+*#% ; #)"+% ,&' #&s)"+& *! (&+s#&4 !s+'*+%#+*&. !s+'*+%#+*&. 7.- H+,!% "&s ,",)"&s *!" (&%,!'+>! *! s)"+& *! ,&$%!. C) 0.005 : ". D! #&s)"+& : +,&% *! s&"),#3'. P&% !s!1)#& !s!1)#&!%<+ !%<+ s! /+,!' /+,!' "&s "&s ,",) ,",)"&s "&s *! (&%,!'+>! (&%,!'+>! *! s)"+& s)"+& *! ,&$%! ,&$%! C)SO.5H2O.
ANLISIS DE SUL5ATO DE INC Es )' +=!'! *!(%!s&% *! "+ $"!'*+4 s! *!!%#'+ +" #=)+" 1)! (+%+ !" #', s&"&.
Poc$d!"!$n*o .- T&+% 2.5 "s. *! )!s%+ *! s&"),#3' *! )'+ ("+'+. 2.- E"##'+% "&s #'!%!%!'!s (+%+ !" +'"#s#s *! #',. 7.- C+",)"+% !" (&%,!'+>! *! #', ; ")!=& !" *! s)"+& *! #',. L +n 0.005 x'l .deTit.laci 0nxFactord e(ol.ci0n.
ANLISIS DE ANTATOS 9 V 117 D!$#*& + s) =%+' (&*!% ,&"!,&% ; s!"!,##*+* ; $+>& ,&s&4 s&' ); )#"#+*&s !' "+s ("+'+s *! ,&',!'%+,#3' ,&',!'%+,#3' (&% "&+,#3' Z- Z- 3 #s&(%&(<"#,& *! s&*#&
Poc$d!"!$n*o, .- M!*#% 5 ". *! s&"),#3' *! :+'+& !' )'+ ("+'+. 2.- M!*#% 5 " *! s&"),#3' *! +"#*3' +" . 7.- T#)"+% ,&' )'+ s&"),#3' !s'*+% *! 0.N *! I&*&4 /+s+ )'+ ,&"&%+,#3' +)" #'!'s&. .- H+,!% "&s ,",)"&s *!" (&%,!'+>! *! Z-.
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ANLISIS DE AERO5LOAT 9A-2/27 9 DITIO5OS5ATO7 Poc$d!"!$n*o, .- M!*#% 2 ". *! +!%&"&+ 22 2.- A@+*#% A@+*#% 0 " *! +"#*3' +" . 7.- T#)"+% ,&' )'+ s&"),#3' !s'*+% *! 0.N *! I&*&. .- S!=?' !" =+s& /+,!% !" ,",)"& *! (&%,!'+>! *! +!%&"&+ 22. L A 2I2 G.Q2 x'l .Tit.laci0n
ANLISIS DE CAL M*odo d$ O
Poc$d!"!$n*o, .- P!s+% 0.5 =%s. *! )!s%+ ()"!%#+*+4 %+s+s+% !' )' +s& *! 00 & 250 ". ; +=%!=+% 20 ". *! ,#*& ,"&%/<*%#,& ,&',!'%+*&4 /!%#%. /!%#%. 2.- A@+*#% !' ,+"#!'! 0 ". *! /#*%3:#*& *! A&'#&4 (+%+ (%!,#(#+% !" #!%%&4 +")#'#&4 s# !s' >)'&s4 ")!=& #"%+%"&s #"%+%"&s ; *!s!,/+%"&s. 7.- A "+ s&"),#3' s#' F!4 A" !' ,+"#!'! +@+*#% 0 ". *! ,#*& &:"#,& +" 0 ; +s 20 ". *! &:+"+& *! A&'#&4 s!=)#% /#%#!'*&. .- F#"%+% !' %<& ; "++% !" (%!,#(#+*& +%#+s !,!s ,&' +=)+ *!s#"+*+. 5.- T%+s+s+% T%+s+s+% !" (%!,#(#+*& *!" #"%& +" +s& &%#=#'+". 8.- L)!=& +=%!=+% 0 ". *! ,#*& s)"?%#,& ,&',!'%+*&.
72
Q.- T#)"+% !' %<& ,&' )'+ s&"),#3' !s'*+% *! (!%+'=+'+& *! (&+s#& /+s+ &$!'!% )'+ "#=!%+ ,&"&%+,#3' %&s+*+ *!" (!%+'=+'+&. .- C+",)"+% !" (&%,!'+>! *! &:#*& *! ,+",#&. LCa3
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