Zastosowanie techniki pomiarowej typu in

Zastosowanie techniki pomiarowej typu in

2016, 61, nr 11–12
788
Zastosowanie techniki pomiarowej typu in-line do oceny
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DOI: dx.doi.org/10.14314/polimery.2016.788
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*:*$*)<"kqk#"XWXh"S,$9/"o,5$-9&)$,5("f.()$<9&.)"G-I"
#-+,&$%58.,*" +3*45,+*" AQ@RE" +/%.*5%-.*" %" +/0-$%/()*.,&9" $;+.*.,*" ,%-)&$9/" Q@RE" 1/3*" $;+.*" eEj" 92/g.
|$&'.,*"+,&60-4M"%,*$&."<J/)&7-"G*GH3 (djhDE"-%.*5%-.*"
:$%/"<J/5,<"*:*$*)<"o*()&$(,%&$"ehhh"S,$9/"o*6T&$."f.()$<9&.)("B)'IE"+/.-(,3*"eEYg"#m.
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#$-5&(" 8-9-7&.,%*5=," :-6,&)/6&.<" %" +>76*.&9" +*:.,*" :$%&:$-+*'%-.-" %" %*()-(-+*.,&9" 6*1-$*)-$/=.&="
6,.,," +/)3*5%*.,*" ?+/)3*5%*$0*" '+<46,9*0-+*" S,$9/"
O*9*0"o&$5*)-$E"9-'&6"@}VgIXCE"-"4$&'.,5/"46,9*0;+"
d"x"Vg"99","()-(<.0<"l/d"x"WhDI"r%/(0*.-"=&'.-6,)/"7$*.<6*)"0-9:-%/);+"%*+,&$*=_5/58"UE"VWE"XV"-$*%"XY"Z"9*(I"
.*:&3.,*5%*E"-%.*5%-./58"+"'*6(%&="5%>45,":$*5/"=*0-!"mUE"
mVWE"mXVE"mXYI"
N*4'9/1#(B#9#<
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-0$&46*.-"+"+*$<.0*58"-)-5%&.,*"?$23D"-$*%"+"+*$<.0*58":$%&)+;$()+*"?$p, TDI"K"-'.,&(,&.,<"'-"+(%/()0,58"
9*)&$,*3;+" +/%.*5%*.-" 58*$*0)&$/()/0," p-v-T w pro5&(,&" ,%-)&$9,5%.&7-" (:$>J*.,*" %*" :-9-5_" <$%_'%&.,*"
pvT"Vhh"S,$9/"qKH"#-6/9&$)&58.,0"u91}"?v,&95/DI"v*"
:-'()*+,&"%*6&J.-45,"p-v-T"-0$&46*.-"-1=>)-4M"+3*45,+_E"
*".*()>:.,&"7>()-4M"9*)&$,*3;+":-6,9&$-+/58"+"'*./58"
+*$<.0*58"5,4.,&.,*",")&9:&$*)<$/"?p, TDE"-':-+,*'*=_5/58" +*$<.0-9" :*.<=_5/9" :-'5%*(" :-9,*$;+" $&-6-7,5%./58")/:<"in-lineI"K/0-$%/()*._"9&)-'/0>"+/%.*5%*.,*"7>()-45,"(%5%&7;3-+-"-:,(*.-"+":<16,0*5=,"`XWaI"
d"H%.*5%*.,&"9*(-+&7-"+(0*N.,0*"(%/10-45,":3/.,>5,*"+/)+-$%-./58"0-9:-%/);+".*"-(.-+,&"#@ABC":$%&:$-+*'%-.-" %7-'.,&" %" .-$9_" #vA@v" fqH" VVeeAV!XhVVE"
9&)-'_"k"?Vih"zGE"XEVg"07DE"%*":-9-5_":6*()-9&)$<"-15,_J.,0-+&7-"S,$9/"C/.,(5-E"9-'&6"WhhWI"
d"G8*$*0)&$/()/0,"$&-6-7,5%.&"9*)&$,*3;+"1*'*+5%/58"
-0$&46*.-" %" %*()-(-+*.,&9" $&-9&)$<" +/)3*5%*$0-+&7-" )/:<" in-lineE" +" 0);$&7-" (03*'" +58-'%,3*" +/)3*5%*$0*"=&'.-46,9*0-+*"S,$9/"o5"v&,6"k0$-.E"9-'&6"t*,$&[E"
-"4$&'.,5/"46,9*0*"d"x"Xj"99","()-(<.0<"l/d = 24 oraz
$&-6-7,5%.*"73-+,5*":-9,*$-+*"%"+/9,&../9,"'/(%*9,"`XjaI"K/0-$%/()/+*.&"'/(%&"0-3-+&"-"$;J.&="'3<7-45,"
(LD","4$&'.,5/"0*.*3<"?DD"(58*$*0)&$/%-+*.-"+")*1&6,"VI"
#-9,*$/":$-+*'%-.-"+"-0$&46-./58"+*$<.0*58"+*$)-45,")&9:&$*)<$/"()$&S"7$%&=./58"+/)3*5%*$0,E"%7-'./58"
%"+*$<.0*9,"()-(-+*./9,"+":$%&)+;$()+,&":-6,&)/6&.<"
9*3&="7>()-45,I"R&9:&$*)<$*"()-:,-.&7-")+-$%/+*":$%&'"
+&=45,&9"'-"0*.*3<":$%&:3/+-+&7-"'/(%/"+"+/:*'0<"
1*'*./58"9*)&$,*3;+"+/.-(,3*"VUh"y"hEj"zGI"
H5&.*"+3*45,+-45,"$&-6-7,5%./58"+/)+-$%-./58"0-9:-%/);+":$%/"<J/5,<"$&-9&)$<"+/)3*5%*$0-+&7-"-:,&$*3*"(,>".*"%*6&J.-45,"-1=>)-45,-+&7-".*)>J&.,*":$%&:3/~ D","5*30-+,)&7-"(:*'0<"5,4.,&.,*"?%p D".*"'3<7-45,"
+<"?Q
c
0*.*3<"'/(%/":-9,*$-+&=I"H1=>)-45,-+&".*)>J&.,&":$%&:3/+<" +/%.*5%*.-" .*" :-'()*+,&" +*$)-45," 9*(-+&7-"
~ D" %" <+%76>'.,&.,&9" 7>()-45,"
.*)>J&.,*" :$%&:3/+<" ?M
1*'*.&7-"9*)&$,*3<":-6,9&$-+&7-E"-0$&46-.&=".*":-'()*+,&"+/0$&(;+"p-v-TI"q)&$-+*.,&"(%/10-45,_"-1$-)-+_"
46,9*0*"?v!D"<9-J6,+,*3-"+/+-3*.,&"-0$&46-.&7-":$%&:3/+<")+-$%/+*"+"<03*'%,&"<:6*()/5%.,*=_5/9"+/)3*5%*$0,"-$*%"+"0*.*6&"'/(%/":-9,*$-+&=E"*")*0J&"%9,*.>"
=&7-".*)>J&.,*I"O*()-(-+*.-"(%/10-4M"-1$-)-+_"46,9*0*"
%"%*0$&(<"hEVUdhEUg"(-1.
Q(#(B(*(+(#((RS((J/2&#)/(:4':'!#./%0(9/:-(3'2&#)'!/%0(
Q(#(B(+(*((RS((H&2*.:&'.:('>(2*#:6)&.,(.'--+*:(6:*9(&.(40*(:469/
C3<7-4M"'/(%/"L
mm
|$&'.,5*"'/(%/"D
mm
L/D
|$&'.,5*"'/(%/"D
mm
L/D
|$&'.,5*"'/(%/"D
mm
L/D
20
3
6,67
2
10
–
–
30
3
10,00
–
–
–
–
40
3
13,33
–
–
–
–
jh
3
16,67
–
–
j
10
#HBfo@Pp"XhVgE"61, nr 11–12
UiV
K":-(%5%&7;6./58":<.0)*58":-9,*$-+/58"-0$&46*.-"
+*$)-4M".*:$>J&.,*"()/5%.&7-"?&wDE"+7"+%-$<"`XgE"XUE"eia!"
τw =
∆pcR
2L
4Q
πR3
(2)
gdzie: γa"d"(%/10-4M"45,.*.,*":3/.<".&+)-.-+(0,&7-"
(nieskorygowana) (s-1), Q"d"-1=>)-45,-+&".*)>J&.,&":$%&:3/+<"?93/s).
c*0" +,*'-9-E" (%/10-4M" 45,.*.,*" +" +/:*'0<" :3/.<"
.,&.&+)-.-+(0,&7-"?1*'*.&"0-9:-%/)/"+/0*%<=_"5&58/"
:3/.;+".,&.&+)-.-+(0,58DE".,&"=&()"$;+.*"(%/10-45,"45,.*.,*"+"'*./9":<.05,&":3/.<".&+)-.-+(0,&7-I"H0$&46&.,&" )&7-" :*$*9&)$<" .*" :-'()*+,&" '-4+,*'5%*6./58"
+/.,0;+"=&()"9-J6,+&"'%,>0,":-:$*+5&"P*1,.-+,)(58*"
`WhaI"#-"=&="<+%76>'.,&.,<"$;+.*.,&"?XD"-:,(<=_5&"(%/10-4M" 45,.*.,*" :$%/" 45,*.5&" 0*:,6*$/E" -:*$)&" .*" 9-'&6<"
:-)>7-+/9"H()+*6'*A'&"K*&6&L*E":$%/1,&$*":-()*M"`XgE"
XUE"eiE"WVE"WXa!"
γw =
ηw =
(1)
gdzie: %pc"d"(:*'&0"5,4.,&.,*".*"'3<7-45,"0*.*3<"?#*DE"
R"d":$-9,&2"0*.*3<"?99DE"L"d"'3<7-4M"0*.*3<"?99DI"
K*$)-4M".,&(0-$/7-+*.&="(%/10-45,"45,.*.,*"+/%.*5%*.-"%"$;+.*.,*"`XgE"XUE"eia!"
γa =
()-(-+*.&"+"1*'*.,*58"'/(%&I"B&:0-4M"(0-$/7-+*._"-16,5%*.-"%"%*6&J.-45,!"
4Q  3n+1 


πR3  4n 
(3)
gdzie: γw"d"(%/10-4M"45,.*.,*":3/.<".,&.&+)-.-+(0,&7-E"%+*.*"(%/10-45,_"(0-$/7-+*._"?(-1), (3n + 1)/4n = Ra
d":-:$*+0*"P*1,.-+,)(58*E"n"d"+/03*'.,0":3/.,>5,*"?bD"
`XgE"eiE"WeE"WWaI"
K/03*'.,0" :3/.,>5,*" +/%.*5%*.-" %7-'.,&" %" :$-5&'<$_" -16,5%&.,-+_" -:,(*._" (%5%&7;3-+-" +" 6,)&$*)<$%&"
`XgE"eiaI"K"-'.,&(,&.,<"'-":-6,&)/6&.<"-$*%"0*J'&7-"+/)+-$%-.&7-"0-9:-%/)<"-0$&46*.-"+*$)-4M"+/03*'.,0*"
:3/.,>5,*",":-:$*+0,"P*1,.-+,)(58*E"*")*0J&":$%&1,&7,"
.,&(0-$/7-+*./58"-$*%"(0-$/7-+*./58"0$%/+/58":3/.,>5,*","6&:0-45,":-'5%*(":$%&:3/+<":$%&%"+(%/()0,&"%*-
τw
γw
(4)
K/0-$%/()*.,&"'/(%"-"$;J./9"()-(<.0<"L/D":-%+-6,3-"
.*"0-$&0)>".*:$>J&.,*"()/5%.&7-"'%,>0,"+:$-+*'%&.,<"
:-:$*+0,"Q*76&/*"?eBDI"K*$)-4M"eB"+/%.*5%*.-".*":-'()*+,&"+/.,0;+":-9,*$;+"+/0-.*./58":$%/"<J/5,<"'/(%"
-"()*3&="4$&'.,5/E")=I"D"x"e"99","%9,&..&="'3<7-45,"L = 20,
ehE"Wh"-$*%"jh"99E"%7-'.,&"%":$-5&'<$_":-9,*$-+-A-16,5%&.,-+_"-:,(*._"+"`XjE"eiaI"
JTMK;K(U8H8V(K(KCO(INWJKXMKX
K/%.*5%*.,&"58*$*0)&$/()/0,"$&-6-7,5%.&="+/)+-$%-./58" 0-9:-%/);+" +" :-9,*$*58" )/:<" in-line, poprze'%-.-"-5&._"+:3/+<"'-'*)0<"+>76*.<"+*:.,*".*":-'()*+-+&" +3*45,+-45," :$%&)+;$5%&" +/)+-$%-./58" .*"
-(.-+,&":-6,&)/6&.<"0-9:-%/);+!"7>()-4M"-$*%"9*(-+/"
+(0*N.,0"(%/10-45,":3/.,>5,*I"
Y7:4'$Z(1'23'-/45!(
C-'*)&0" +>76*.<" +*:.,*" (:-+-'-+*3" .*)<$*6.&"
%+,>0(%&.,&" 7>()-45," 0-9:-%/);+E" :$-:-$5=-.*6.,&" '-"
%*+*$)-45," .*:&3.,*5%*E" -'" hEiXW" 7b593 dla PE-LD, do
+*$)-45," VEYhU" 7b593" d" 0-9:-%/)<" mXYE" %*+,&$*=_5&7-"
XY"Z"9*(I"G*GH3.
O9,*./" 7>()-45,"+" +*$<.0*58"-)-5%&.,*" :$%&3-J/3/"
(,>"1&%:-4$&'.,-".*"%9,*./"=&="+*$)-45,"+"+*$<.0*58"
:$%&)+;$5%/58"?p, TDI"H0$&46&.,&"(%/10-45,"45,.*.,*"+/9*7*"%.*=-9-45,"-1=>)-45,-+&7-".*)>J&.,*":$%&:3/+<E"
~=M
~ b DI"c*0"+/<+%76>'.,*=_5&7-"%9,*./"7>()-45,"?Q
p, T
0*%*.-" +" :<16,0*5=," `XWa" :-9,*$/" $&-6-7,5%.&" :$-+*'%-.&":$%/"<J/5,<"<$%_'%&2".,&<+%76>'.,*=_5/58"45,46,+-45,"9*)&$,*3<":-6,9&$-+&7-"+/9*7*=_"+/%.*5%&.,*"
%9,*."7>()-45,"+"+*$<.0*58"$-%:*)$/+*.&7-":$%&:3/+<I"#-'5%*(":$%&:3/+<":$%&%"0*:,6*$>"$&-9&)$<"+/)3*-
Q(#(B(*(+(#(([S((D#1)*:/(-2&#./(%&$.&*.&#(&('93'!&#9#P\%*(&2(-2&#./(,7:4'$%&(!(3'2&#)#%0()*'+',&%-./%0(4/36(in-line
Q(#(B(+(*(([S((]#.,*:('>(3)*::6)*(%0#.,*:(#.9(%'))*:3'.9&.,(9*.:&4/(@#)&#4&'.:(&.(in-line()0*'+',&%#+(2*#:6)*2*.4:
K/9,*$/"
D, L, mm
mU
PE-LD
mVW
mXV
mXY
€pc
MPa
(p, T)
kg/m3
€pc
MPa
(p, T)
kg/m3
€pc
MPa
(p, T)
kg/m3
€pc
MPa
(p, T)
kg/m3
€pc
MPa
(p, T)
kg/m3
D=2
L = 20
jEgdiEX
UUhEidUUXEg
jEUdiEg
YeVEYdYeeEj
6,2–10,2
861,6–863,4
gEYdVhEi
ihWEidihUEV
7,7–11,8
iUWEidiUUEe
D=3
L = 20
2,3–4,2
UgiEWdUUhEX
2,1–4,2
830,2–831,1
XEjdWEj
860,0–860,8
XEU"djEh
ihXEgdiheEi
XEYdjEX
iUXEVdiUeEj
D=3
L = 30
eEVdjEg
UgiEUdUUhEi
eEjdgEh
YehEYdYeVEi
3,6 –6,4
860,4–861,7
4,0 – 7,0
iheEedihjEh
4,3–7,8
iUXEidiUWEi
D=3
L = 40
4,1–7,1
770,2–771,6
4,6–8,0
831,3–832,8
WEidYEj
861,0–862,6
jEediEX
ihWEhdihgEX
6,0–10,1
iUWEhdiUgEX
D=3
L"x"jh
4,7–8,1
UUhEjdUUXEV
jEUdiEW
YeVEYdYeeEj
jEYdVhEV
861,4–863,3
gEedVhEi
ihWEgdihUEV
gEidVXEV
iUWEWdiUUEW
D"x"j"
L"x"jh
VEgdXEi
UgiEhdUgiEU
VEideEh
830,1–830,6
2,0 –3,4
YjiEUdYghEW
2,0 –3,6
ihXEediheEV
2,2–4,1
iUVEYdiUXEY
UiX
#HBfo@Pp"XhVgE"61, nr 11–12
UEU"'-"VXEV"o#*"%9,*.*"7>()-45,"+/.-(,3*"eEh"07b93I"v*=9.,&=(%&"%9,*./"7>()-45,"1*'*./58"9*)&$,*3;+"%*<+*J-.-" +" 5%*(,&" ,58" :$%&:3/+<" :$%&%" '/(%>" -" '3<7-45,"
L"x"jh"99","4$&'.,5/"D"x"j"99E"5-"1/3-"0-.(&0+&.5=_"
+/()>:-+*.,*".*=9.,&=(%/58"%9,*."5,4.,&.,*"?%pc).
2,0
MFR(230 °C, 2,16 kg), g/cm3
1,9
1,8
1,7
N#:'!/(!:1#^.&1(:-/B1'$%&(3"/.&7%&#(_MFR)
1,6
P/(<.&0" V" :$%&'()*+,*" %9,*./" +*$)-45," 9*(-+&7-"
+(0*N.,0*"(%/10-45,":3/.,>5,*"+"S<.05=,"%*+*$)-45,"+>76*.<"+*:.,*I"O7-'.,&"%"'*./9,"6,)&$*)<$-+/9,"`VhE"Wja"
+*$)-4M"MFR"0-9:-%/);+"#@ABCbG*GH3"9*6&=&":$-:-$5=-.*6.,&"+$*%"%"%*+*$)-45,_"+>76*.<"+*:.,*I"C-'*)&0"
.*:&3.,*5%*" :-+-'<=&" :-7-$(%&.,&" :$%&)+*$%*6.-45,"
0-9:-%/);+" ?MFR"D" .*" (0<)&0" +%$-()<" 6&:0-45," ?'!),
*")/9"(*9/9"%+,>0(%&.,*"-:-$;+":$%&:3/+<"`UE"ViE"WgaI"
o*3&"+*$)-45,"13>';+"+":-9,*$*58"MFR"9-7_"4+,*'5%/M"-"'-1$&="8-9-7&.,%*5=,"+/)+-$%-./58"0-9:-%/5=,I"
1,5
1,4
0
5
10
15
20
25
30
Zawartość CaCO3 w kompozycie PE-LD, % mas.
]/:S(RS(D#+*`.'$Z(MFR('9(-#!#)4'$%&(C#CI3(!(!/4!')-'./%0(
1'23'-/4#%0(aXbLH(
c&,S(RS(H*3*.9*.%*('>(MFR('.(C#CI3 %'.4*.4(&.(3)'96%*9((aXbLH(
composites
C0#)#14*)/:4/1#(3)#%/()*'2*4)6(!/4"#%-#)1'!*,'(
5%*$0-+&7-"?+"+*$<.0*58"()*3&=")&9:&$*)<$/":-9,*$<D"
.*"7>()-4M"+:3/+*"+*$)-4M"(:*'0<"5,4.,&.,*"+*$<.0-+*.&7-"+/9,*$*9,"0*.*3<"'/(%/I"K")*1&6,"X"%&()*+,-.-" %*0$&(/" %9,*." 5*30-+,)&7-" (:*'0<" 5,4.,&.,*" ?%pc)
-$*%" -':-+,*'*=_5&" ,9" %9,*./" 7>()-45," :-'5%*(" :$%&:3/+<"*.*6,%-+*./58"9*)&$,*3;+":-6,9&$-+/58":$%&%"
%*()-(-+*.&"+"1*'*.,*58"'/(%&":-9,*$-+&I"v*=+,>0(%&"
+*$)-45,"%pc"%*-1(&$+-+*.-"+"5%*(,&":$%&:3/+<"<:6*()/5%.,-./58")+-$%/+":-6,9&$-+/58":$%&%"'/(%>"-"'3<7-45,"L"x"Xh"99","4$&'.,5/"D = 2 mm oraz L"x"jh"99"
i D"x"e"99E"5-"+:3/.>3-".*".*=+,>0(%&"%9,*./"7>()-45," %*$;+.-" 0-9:-%/);+E" =*0" ," :-6,&)/6&.<I" #$%/03*'-+-E" :-'5%*(" :$%&)+*$%*.,*" 0-9:-%/)<" mXY" ?'/(%*"
L = 20 mm i D" x" X" 99DE" :$%/" %9,&../9" 5,4.,&.,<" -'"
12
11,4
L = 20 mm
L = 30 mm
L = 40 mm
L = 50 mm
9,5
∆pc, MPa
∆pc, MPa
10
K" 5&6<" (58*$*0)&$/%-+*.,*" :$*5/" $&-9&)$<" +/)3*5%*$0-+&7-"-$*%"<%/(0*.,*"'*./58":-9,*$-+/58"(3<J_5/58" '-" -0$&46&.,*" +*$)-45," .*:$>J&.,*" ()/5%.&7-"
,"(%/10-45,"45,.*.,*E"+"-'.,&(,&.,<"'-"+(%/()0,58"1*'*./58")+-$%/+":-6,9&$-+/58"-$*%"%*()-(-+*./58"+":-9,*$*58"'/(%"+/%.*5%-.-"0$%/+&"%*6&J.-45,"$%&5%/+,()&7-"(:*'0<"5,4.,&.,*"-'"(%/10-45,"-1$-)-+&="46,9*0*"
`%pc = f(v!Da" -$*%" -1=>)-45,-+&7-" .*)>J&.,*" :$%&:3/+<"
~ = f(v DaI"P/(<+"S<.05=,"(%/10-45,"-1$-)-+&="46,9*0*"`Q
!"
.&0"X":$%&'()*+,*"%*6&J.-4M"%pc = f(v!D"0-9:-%/)<"mVW"
:-'5%*(":$%&:3/+<":$%&%"'/(%&"-"4$&'.,5/"D = 3 mm
,"'3<7-45,"L"x"XhE"ehE"Wh"-$*%"jh"99I"O":$%&1,&7<"0$%/+/58" +/.,0*E" J&" +*$)-4M" %pc" %+,>0(%*" (,>" %*$;+.-"
8
PE-LD
K7
K14
K21
K28
7,6
6
5,7
4
2
0,13
0,26
0,39
0,52
vś, s
0,65
0,78
-1
]/:S([S(J/1)*:(-#+*`.'$%&(%#"1'!&4*,'(:3#916(%&$.&*.&#(_dpc) od
:-/B1'$%&('B)'4'!*P($+&2#1#(_v!e(1'23'-/46(;Rf(3'9%-#:(3)-*b
3"/!6(3)-*-(9/:-*('(!/2&#)#%0(D = 3 mm i L(g([hi(jhi(fhi(kh(22(
c&,S([S(a+'4('>(4'4#+(3)*::6)*(9)'3(_dpce(@*):6:(4#.,*.4&#+(@*+'(%&4/(
'>(#(:%)*!(_v!e(>')(;Rf(%'23':&4*(6:&.,(.'--+*:('>(D = 3 mm and
L(g([hi(jhi(fh(#.9(kh(22
0,13
0,26
0,39
0,52
0,65
0,78
vś, s-1
]/:S(jS(J/1)*:(-#+*`.'$%&(%#"1'!&4*,'(:3#916(%&$.&*.&#(_dpc) od
:-/B1'$%&('B)'4'!*P($+&2#1#(_v!e(B#9#./%0(4!')-/!(3'+&2*)'b
!/%0(3'9%-#:(3)-*3"/!6(3)-*-(9/:-7('(!/2&#)#%0(D = 3 mm
i L(g(fh(22(
c&,S(jS(a+'4('>(4'4#+(3)*::6)*(9)'3(_dpce(@*):6:(4#.,*.4&#+(@*+'b
%&4/('>(#(:%)*!(_v!e(>')(4*:4*9(3'+/2*)(2#4*)&#+:(6:&.,(.'--+*('>(
D = 3 mm and L(g(fh(22
#HBfo@Pp"XhVgE"61, nr 11–12
1,2 · 10
6,0 · 10
3,0 · 10
Q(#(B(*(+(#((jS((l-/:1&!#.*(!#)4'$%&(.&*:1')/,'!#.*P(:-/B1'$%&(
$%&.#.&#(_γae(!(-#+*`.'$%&('9(!/2&#)5!(9/:-/(_D, L)
Q(#(B(+(*((jS((H*3*.9*.%*('>(6.%'))*%4*9(:0*#)()#4*(_γae('.(.'--+*(
9&2*.:&'.:(_D, L)
-6
-7
PE-LD
K7
K14
K21
K28
-7
C3<7-4M"
dyszy L, mm
|$&'.,5*"
dyszy D, mm
-7
0,0
0,13
0,26
0,39
0,52
vś, s-1
0,65
0,78
]/:S( fS( J/1)*:( -#+*`.'$%&( 'BP74'$%&'!*,'( .#47`*.&#( 3)-*3"/b
!6(_Qe('9(:-/B1'$%&('B)'4'!*P($+&2#1#(_v!e(B#9#./%0(4!')-/!(
3'+&2*)'!/%0( 3'9%-#:( 3)-*3"/!6( 3)-*-( 9/:-7( '( !/2&#)#%0(
D = 3 mm i L(g(kh(22(
c&,S(fS(a+'4('>(@'+62*(>+'!()#4*(_Qe(@*):6:(4#.,*.4&#+(@*+'%&4/('>(#(
:%)*!(_v!e(>')(4*:4*9(3'+/2*)(2#4*)&#+:(6:&.,(.'--+*('>(D = 3 mm
and L(g(kh(22(
%&" +%$-()&9" (%/10-45," -1$-)-+&=" 46,9*0*E" =*0" ," :$%/"
v!"x"5-.()I"%&"%+,>0(%*=_5_"(,>"'3<7-45,_"'/(%/I"R*0*"%*6&J.-4M"=&()"%+,_%*.*"%&"%9,&.,*=_5/9,"(,>"+"$;J./58"0*.*3*58"'/(%/"-:-$*9,":$%&:3/+<I
#-'-1.&" %*6&J.-45," <%/(0*.-" +" +/:*'0<" +(%/()0,58" 1*'*./58" 9*)&$,*3;+I" O+,>0(%&.,&" -:-$;+" :$%&:3/+<")+-$%/+*":-6,9&$-+&7-"+"73-+,5/"+/)3*5%*$(0,&=E"(:-+-'-+*./"'-'*)0,&9"'-"#@ABC".*:&3.,*5%*E"
%+,>0(%*")&J"&.&$7-583-..-4M":$-5&(<")&58.-6-7,5%.&7-E"=&'.-5%&4.,&"%+,>0(%*"=&7-"()*1,6.-4M","&S&0)/+.-4M"
`WUaI"v*"$/(I"e":$%&'()*+,-.-"%9,*./":$%&1,&7<"%*6&J.-45,"%pc = f(v!D"+/.,0*=_5&"%"'-'*)0<"G*GH3 do osno+/" "#@ABC" :-'5%*(" :$%&:3/+<" )+-$%/+*" :$%&%" '/(%>"
-"4$&'.,5/"D = 3 mm i L = 40 mm.
v,&"()+,&$'%-.-"+:3/+<"%+,>0(%*.,*"%*+*$)-45,"+>76*.<"+*:.,*".*"+*$)-45,"-1=>)-45,-+&7-".*)>J&.,*":$%&:3/+<" 0-9:-%/);+I" v,&" %*-1(&$+-+*.-" )&J" +:3/+<"
+/9,*$;+"0*.*3<"'/(%":-9,*$-+/58".*"+*$)-4M"QI"c*0"
+/.,0*"%":-3-J&.,*"0$%/+/58":$%&'()*+,-./58".*"$/(I"WE"
'-'*)&0"G*GH3":-+-'<=&"+%$-()"+*$)-45,"Q"+"()-(<.0<"
do Q".,&.*:&3.,-.&7-"#@ABCE".,&"-1(&$+<=&"(,>"=&'.*0"
:$-:-$5=-.*6./58":$%&(<.,>M"0$%/+/58"Q = f(v!) wraz ze
%+,>0(%*=_5_"(,>"%*+*$)-45,_"G*GH3I"K"-'.,&(,&.,<"'-"
-0$&46-./58E"()*3/58"(%/10-45,"-1$-)-+/58"46,9*0*E"+*$)-45,"Q"(_"%16,J-.&E".,&%*6&J.,&"-'"%*+*$)-45,".*:&3.,*5%*"
+"0-9:-%/5,&I
J"#$%&!'$%&()*'+',&%-.*
#-9,*$-+&"%*0$&(/"(%/10-45,"45,.*.,*"+"$&-9&)$*58"
0*:,6*$./58")/:<"off-line"(_"<+*$<.0-+*.&"+*$)-45,_"(,3/"
:$%&(<+<")3-0*"-$*%"+/9,*$*9,"%*()-(-+*./58"'/(%"`WYaI"
K"+/:*'0<"$&-9&)$;+")/:<"in-line o zakresie γa"$;+.,&J"
'&5/'<=&"58*$*0)&$/()/0*"'/(%E"*6&":$%&'&"+(%/()0,9"d"
+/'*=.-4M" ," (:&5/S,0*" '%,*3*.,*" <03*'<" <:6*()/5%.,*=_-
L/D
γa, s-1
20
3
6,67
YhdejU
30
3
10,00
83–367
40
3
13,33
82–381
jh
3
16,67
84–366
20
2
10,00
XgjdVXjh
jh
j
10,00
20–77
5&7-"`XgE"XUE"WiaI"K/0-$%/()*.,&"+"$&-9&)$%&"+/)3*5%*$0-+/9" )/:<" in-line" 73-+,5/" %" +/9,&../9," '/(%*9,"
:-%+-6,3-" .*" 58*$*0)&$/()/0>" $&-6-7,5%._" 0-9:-%/);+"
+"(%&$-0,9"%*0$&(,&"(,3"45,.*=_5/58I"K":$%/=>)/9"%*0$&(,&"(%/10-45,"-1$-)-+&="46,9*0*"?hEVUd"hEUg"(-1DE"+*$)-45,"γa
9,&45,3/"(,>"+":$%&'%,*6&"XhdVXjh"(-1I"K"+/:*'0<"0*J'&="
%"%*()-(-+*./58"'/(%"<%/(0*.-"$;J.&"+*$)-45,".,&(0-$/7-+*.&="(%/10-45,"45,.*.,*"?)*1&6*"eDI"v*=+,>0(%&"+*$)-45,"
.,&(0-$/7-+*.&="(%/10-45,"45,.*.,*"-1(&$+-+*.-":-'5%*(":$%&:3/+<"1*'*./58"9*)&$,*3;+":$%&%"'/(%>"-"4$&'.,5/"D"x"X"99","'3<7-45,"L"x"Xh"99E".*)-9,*()".*=9.,&=(%&"
d":-'5%*(":$%&:3/+<":$%&%"'/(%>"-"4$&'.,5/"D"x"j"99"
,"'3<7-45,"L"x"jh"99I"
J/1"#9.&1(3"/.&7%&#i(3'3)#!1#(]#B&.'!&4:%0#(
r+%76>'.,&.,&":-:$*+0,"P*1,.-+,)(58*"?Ra) wprowa'%*"0-$&0)>"+*$)-45,"(%/10-45,"45,.*.,*E"5-"<9-J6,+,*"
+"+*$<.0*58":$-+*'%-./58":-9,*$;+"$&-6-7,5%./58"
:$%&=45,&"+"-1(%*$"58*$*0)&$/()/0"5,&5%/".,&.&+)-.-+(0,58I"K"5&6<"-0$&46&.,*"+*$)-45,"Ra"+/%.*5%-.-":$%&12,2
12,0
ln τw, Pa
Q̇, m3/s
9,0 · 10
Uie
y = 0,389 x + 9,841
11,8
n = 0,389; k = 18 788
11,6
11,4
4,4
4,8
5,2
5,6
6,0
6,4
ln γ̇a, s-1
]/:S(kS(J/1)*:(-#+*`.'$%&(.#3)7`*.&#(:4/%-.*,'(_w) od nieskob
)/,'!#.*P( :-/B1'$%&( $%&.#.&#( _γaei( !( 3'9!5P.&*( +',#)/42&%-b
./2(61"#9-&*(!:35")-79./%0i(1'23'-/46(;[m(3'9%-#:(3)-*b
3"/!6(3)-*-(9/:-7('(!/2&#)#%0(D = 3 mm i L(g(jh(22(
c&,S(kS(a+'4('>(:0*#)(:4)*::(_we(@*):6:(6.%'))*%4*9(:0*#)()#4*(_γa)
&.(9'6B+*b+',#)&402&%(%'')9&.#4*(:/:4*2(>')(;[m(%'23':&4*(#.9(
.'--+*('>(9&#2*4*)(D(g(j(22(#.9(+*.,40(L(g(jh(22
UiW
#HBfo@Pp"XhVgE"61, nr 11–12
Q(#(B(*(+(#((fS((J#)4'$%&(!/1"#9.&1#(3"/.&7%&#(_ne(&(3'3)#!1&(]#B&.'!&4:%0#(_Rae(B#9#./%0(4!')-/!(3'+&2*)'!/%0
Q(#(B(+(*((fS(n#+6*:('>(3'!*)(+#!(&.9*o(_ne(#.9(]#B&.'!&4:%0(%'))*%4&'.(_Rae('>(4*:4*9(3'+/2*)(2#4*)&#+:
K/9,*$/"'/(%/
D, L, mm
mU
PE-LD
mVW
mXV
mXY
n
Ra
n
Ra
n
Ra
n
Ra
n
Ra
D=2
L = 20
0,334
VEWii
hEeei
1,487
0,344
1,477
0,323
VEjXW
hEXie
VEgji
D=3
L = 20
0,408
1,363
0,466
1,286
0,428
1,334
0,441
1,317
hEWjX
1,303
D=3
L = 30
hEeiW
VEeYj
0,378
1,411
hEeig
1,381
0,387
VEeig
hEeYi
VEeie
D=3
L = 40
0,388
VEeiW
0,362
1,441
0,382
VEeie
hEeUj
1,413
0,361
VEWei
D=3
L"x"jh
0,386
VEeiY
hEejV
1,462
0,373
1,420
hEegi
1,428
0,367
1,431
D"x"j"
L"x"jh
hEWhi
1,361
0,384
1,401
hEeiY
1,378
0,412
VEejU
0,416
VEejV
<%/(0*.-" +" +/.,0<" 1*'*2" :$-+*'%-./58" :$%/" <J/5,<"
$&-9&)$<"+/)3*5%*$0-+&7-")/:<"in-line":-6,&)/6&.<"9*3&="
7>()-45,E":-6,&)/6&.<"4$&'.,&="7>()-45,"-$*%",58"9,&(%*.,./"
?jhbjhD"`eaI"O9,*.>"+*$)-45,"+/03*'.,0*":3/.,>5,*"*<)-$%/"
)3<9*5%/6,"$;J./9,"+*$<.0*9,":$%&:3/+<":$%&%"'/(%&"
-"%9,&..&="58*$*0)&$/()/5&"L/DI"R-"%"0-6&,"+:3/+*".*"%9,*.>"%*0$&(;+"(%/10-45,"45,.*.,*","6&:0-45,E"*")/9"(*9/9".*"
%9,*.>":$%&1,&7<"0$%/+&="6&:0-45,"`eiE"WYE"jhaI"K".,.,&=(%&="
:$*5/"+/0*%*.-"%*6&J.-4M"+*$)-45,"+/03*'.,0*":3/.,>5,*"
1*'*.&7-"#@ABC","=&7-"0-9:-%/);+"-'"+/9,*$;+"0*.*3<"
'/(%/E"*"=&'.-5%&4.,&"1$*0"%*6&J.-45,"n"-'"'-'*)0<"G*GH3.
r+%76>'.,&.,&":-:$*+0,"P*1,.-+,)(58*"+"$;+.*.,<"
?eD"-0$&46*=_5/9"(%/10-4M"45,.*.,*"<9-J6,+,3-"+/%.*5%&.,&":$%&1,&7;+"0$%/+/58"6&:0-45,"(0-$/7-+*.&=I"K")*1&6,"j"%&()*+,-.-"+*$)-45,".,&(0-$/7-+*.&=""?γa) i skory7-+*.&="?γwD"(%/10-45,"45,.*.,*"-$*%"-':-+,*'*=_5&",9"
+*$)-45,".,&(0-$/7-+*.&="?'aD","(0-$/7-+*.&="?'w) lepko45,"1*'*./58"9*)&$,*3;+E"+/%.*5%-.&":-'5%*(":$%&:3/+;+":$%&%"%*()-(-+*.&"+"1*'*.,*58"'/(%&":-9,*$-+&I"
800
700
600
η, Pa · s
1,&7,"0$%/+/58":3/.,>5,*"+(%/()0,58"1*'*./58")+-$%/+"
:-6,9&$-+/58":-'5%*(",58":$%&:3/+<":$%&%"'/(%&"-"$;J./58" +/9,*$*58I" v*()>:.,&" %" :$%&1,&7;+" .,&(0-$/7-+*./58" 0$%/+/58" :3/.,>5,*E" %.*='<=_5/58" (,>" +" :-'+;=./9"<03*'%,&"6-7*$/)9,5%./9E"-0$&46-.-"+*$)-4M"
+/03*'.,0*":3/.,>5,*I"v*"$/(I"j":$%&'()*+,-.-":$%/03*'-+_" 0$%/+_" :3/.,>5,*" 0-9:-%/)<" mXYE" +/%.*5%-._"
:-'5%*(":$%&:3/+<":$%&%"'/(%>"-"4$&'.,5/" D = 3 mm
,"'3<7-45,"L"x"eh"99E"-$*%"-':-+,*'*=_5&"=&="$;+.*.,&"
$&7$&(=," 6,.,-+&=E" +/03*'.,0" :3/.,>5,*" ?nD" -$*%" +(:;35%/..,0"0-.(/()&.5=,"?kDI"K*$)-4M"+/03*'.,0*":3/.,>5,*E"
.*"0);$&7-":-'()*+,&"+/%.*5%-.-":-:$*+0>"P*1,.-+,)(58*E"-':-+,*'*"+(:;35%/..,0-+,"0,&$<.0-+&9<":$-()&="6."w = f ln(γaDI"v*)-9,*()"+(:;35%/..,0"0-.(/()&.5=,"
()*.-+,":<.0)":$%&5,>5,*":$-()&="%"-(,_"$%>'./58I"
K"0*J'/9"+/:*'0<"+*$)-4M"n"‚"VE"5-":-)+,&$'%*E"J&"
1*'*.&"<:6*()/5%.,-.&")+-$%/+*":-6,9&$-+&"%*6,5%*"(,>"
'-"5,&5%/".,&.&+)-.-+(0,58"$-%$%&'%*./58"45,.*.,&9I"
C-03*'.&"+*$)-45,"+/03*'.,0*":3/.,>5,*"-$*%"-':-+,*'*=_5&" ,9" +*$)-45," :-:$*+0," P*1,.-+,)(58*" 1*'*./58"
9*)&$,*3;+"%&()*+,-.-"+")*1&6,"WI"
K&'3<7" '*./58" 6,)&$*)<$-+/58" `eiE" Wia" +*$)-4M" +/03*'.,0*":3/.,>5,*")+-$%/+")&$9-:6*()/5%./58"9,&45,"
(,>" +" :$%&'%,*6&" hEVidhEYhE" +" )*0,58" 7$*.,5*58" 9,&(%5%_"(,>")&J"+/%.*5%-.&"+"1*'*.,*58"+*$)-45,I"C-'*)&0"
+>76*.<"+*:.,*"'-"-(.-+/":-6,&)/6&.-+&="+:3/._3".*"
%9,*.>"6&:0-45,"0-9:-%/)<"=&'.*0".,&"%9,&.,3"=&7-"58*$*0)&$<I"K/%.*5%-./"+(:;35%/..,0"0-.(/()&.5=,"1>'_5/"
9,*$_"6&:0-45,"9*)&$,*3<"`eiE"WYE"Wia"$;+.,&J"1/3"%7-'./"
%"'*./9,"6,)&$*)<$-+/9,"`eiE"WiaE"=&7-"+*$)-4M"9,&45,3*"
(,>"+":$%&'%,*6&"VEhYdiEeg"ƒ"Vh4"#*"ƒ"(n.
O":$%&'()*+,-./58"'*./58"+/.,0*"?)*1&6*"XDE"J&"+*$)-4M"
+/03*'.,0*":3/.,>5,*E"*"+"0-.(&0+&.5=,":-:$*+0,"P*1,.-+,)(58*"=&()"%*6&J.*"-'"+/9,*$;+"%*()-(-+*./58"'/(%I"
K"+/:*'0<"'/(%/"-"()*3&="4$&'.,5/"?D"x"e"99D","'3<7-45,"
L"x"XhE"ehE"Wh"6<1"jh"99"+*$)-4M"+/03*'.,0*"n"9*6&=&"+$*%"
%"$-(._5_"'3<7-45,_"'/(%/I"v*)-9,*()"+/03*'.,0":3/.,>5,*"1*'*./58"9*)&$,*3;+":-6,9&$-+/58":$%&:3/+*=_5/58"
:$%&%"'/(%&"-"()*3&="'3<7-45,"L","%9,&..&="4$&'.,5/"$-4.,&"
+$*%"%&"%+,>0(%*=_5_"(,>"4$&'.,5_I"R*0,&"(*9&"%*6&J.-45,"
500
400
300
ηa = f(γ̇a) · s-1
ηw = f(γ̇w) · s-1
200
100
100
γ̇w, s-1
1000
2000 3000
]/:S(pS(;)-/!#(+*31'$%&(.&*:1')/,'!#.*P(q a = f_γae(&(+*31'$%&(
:1')/,'!#.*P( q w = f_γwe( 1'23'-/46( ;[m( 3'9%-#:( 3)-*3"/!6(
3)-*-(9/:-7('(!/2&#)#%0(D(g([(22(&(L(g([h(22(
c&,S(pS(833#)*.4(@&:%':&4/(%6)@*(qa = f_γae(#.9(%'))*%4*9(@&:%':&b
4/(%6)@*(qw = f_γwe(>')(;[m(%'23':&4*(6:&.,(.'--+*('>(D(g([(22(
and L(g([h(22
#HBfo@Pp"XhVgE"61, nr 11–12
Uij
Q(#(B(*(+(#((kS((a#)#2*4)/()*'+',&%-.*r(γa, γw, „a, „w(B#9#./%0(4!')-/!(3'+&2*)'!/%0
Q(#(B(+(*((kS((]0*'+',&%#+(3#)#2*4*):r(γa, γw, „a, „w '>(4*:4*9(3'+/2*)(2#4*)&#+:
q/91-6":$;10,
PE-LD
mU
mVW
mXV
mXY
K/9,*$/"'/(%/E"99
D
L
γa, s-1
γw, s-1
'aE"#*"ƒ"(
'wE"#*"ƒ"(
2
20
264–1240
eigdVYjh
VYgdjXU
VXWdejX
3
20
iedeij
VXgdjei
eiWdiWX
XYidgiV
3
30
UWdejX
102–488
eijdVhWY
XYjdUjU
3
40
77–326
VhUdWjj
WVhdVhhi
XiWdUXW
3
jh
UVdXij
100–413
WVediiW
XigdUVV
j
jh
17–82
23–111
ihVdXeUi
ggXdVUjh
2
20
XgjdVXjh
eiedVYgh
ViXdjWh
VXidegW
3
20
YhdejU
102–460
WWWdiYX
eWjdUgW
3
30
83–367
VVUdjVY
WVhdVhWj
XihdUWh
3
40
82–381
VVUdjjh
eiVdVhgh
272–736
3
jh
84–366
VXXdjej
386–1014
XgWdgiW
j
jh
20–77
28–108
iYXdXeXX
701–1660
2
20
XUidVXWh
413–1840
Xhgdjje
VeideUW
3
20
ihdeji
VXhdWUi
470–1042
ejXdUYV
3
30
83–377
VVjdjXV
427–1078
ehidUYV
3
40
86–374
VXedjee
WXUdVhih
XiidUge
3
jh
82–372
VVgdjXY
WhidVhgg
XYYdUjV
j
jh
20–86
28–118
iiWdXWXY
722–1760
2
20
XiYdVXYh
WjWdVijh
XVWdjUe
140–376
3
20
VhhdWVj
VeXdjWU
WjWdiii
eWWdUjY
3
30
iXdWhU
VXYdjgY
430–1078
308–772
3
40
YideiX
VeVdjUi
441–1178
XiidUii
3
jh
87–386
VXWdjjV
WXjdVhiV
XiYdUgW
j
jh
20–88
27–120
VhhidXWYU
743–1830
2
20
XiXdVXYh
WgYdXhjh
231–660
144–412
3
20
ihdegi
117–481
jeedVVWY
WhidYYV
3
30
YgdWhi
VVidjUh
WUgdVXWi
eWXdYiU
3
40
ihdeUh
VeWdjje
jVhdVeVY
342–883
3
jh
81–384
VVgdjWi
472–1270
330–887
j
jh
XVdih
XidVXV
VVeVdXgWj
YeUdVigh
P/(<.&0"g":$%&'()*+,*":$%/03*'-+&"+%*=&9.&":-3-J&.,&"0$%/+&="6&:0-45,".,&(0-$/7-+*.&="„a = f(γa) oraz krzy+&="6&:0-45,"(0-$/7-+*.&="„w = f(γwD"0-9:-%/)<"mXY":$%&:3/+*=_5&7-":$%&%"'/(%>"-"'3<7-45,"L"x"Xh"99","4$&'.,5/"
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12
160
γ$a = 189 s-1
10
γ$a = 302 s-1
8
τw = f(γ$a )
140
τB = f(γ$a )
γ$a = 415 s-1
τ, kPa
Δpc · 106, Pa
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120
4
100
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30
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0
100
200
300
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400
500
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