HARDY CROSSfinal.xlsx

8/18/2019 HARDY CROSSfinal.xlsx

1/34

CLASE PRACTICA -HARDY CROSS- Melissa Gonzales Cuentas

material de la tuberia PC

ru!osidad absoluta "#$%E-%&

li'uido Trans(ortado a!ua

Densidad )* "%%% +!,m.is/osidad absoluta 0* "#"1E-% Pa#s

.is/osidad /inemati/a .* "#"1E-%& m2,s

/ir/uito Tuberia Caudal Caudal lon!itud Diametro Diametro elo/idad

3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -7%#%% -%#%7%% 278#78 28#&% %#28& "#7%1 8&9%$2#8: "$791%%#%%

2 -$8#2% -%#%$82 &:#$7 "$2#%% %#"$2 #"$2 12%92:7#8 "%"9#

$ -2#2% -%#%22 "2"#:& "%1#&% %#"%1& #818 197"7#&8 &:98#

$ 7 -#&% -%#%%& "7:#78 7$#&% %#%7$& %#&2& 1&9:8"#1$ $89%&&8

8 7 $#&% %#%$& 1%$#8: ":%#2% %#":%2 "#2$ 2%:9%18#: "2&97%%#%%

" 8 1$#&% %#%1$& 28#7& ":%#2% %#":%2 "#&%$ 2&898&7#$8 "2&97%%#%%

2

1 -2%#%% -%#%2%% 21$7 "#%% %#" "#11% "&89:$"#1% 779&&&8

1 & -&% -%#%%&& "$2#$& 8"#2% %#%8"2 "#&$7 "%9$%#8" 1891&&8

$ & "%#%% %#%"%% 2&2#7 7$#&% %#%7$& "#87 "%918& $89%&&8

$ 2#2% %#%22 "2"#:& "%1#&% %#"%1& #818 197"7#&8 &:98#

$ & -"%#%% -%#%"%% 2&2#7 7$#&% %#%7$& "#87 "%918& $89%&&8

& "% -7#&% -%#%%7& ":"#& 8"#2% %#%8"2 2#"&% "19:%#&& 1891&&8

: "% ""#1% %#%""1 ""#8$ "%1#&% %#"%1& "#28 "2"9821#&2 &:98#

7 : 28#%% %#%28% "$#%2 "#%% %#" "#:1 22&981#: 779&&&8

$ 7 #&% %#%%& "7:#:8 7$#&% %#%7$& %#&2& 1&9:8"#1$ $89%&&8

D,;


2/34


3/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -82#& -%#%82& 278#78 28#&% %#28& "#&7 1"912%#2$ "$791%%#%%

2 -1:#7 -%#%1:7 &:#$7 "$2#%% %#"$2 2#81& &&9"&2#2$ "%"9#

$ -22#8 -%#%221 "2"#:& "%1#&% %#"%1& 2#&%1 279:%:#%" &:98#

$ 7 "#& %#%%"1 "7:#78 7$#&% %#%7$& %#2& "898$2#%% $89%&&8

8 7 12#:8 %#%1% 1%$#8: ":%#2% %#":%2 "#$"2 2$29"%#8$ "2&97%%#%%

" 8 $2#:8 %#%$% 28#7& ":%#2% %#":%2 "#7&1 ""9%"#: "2&97%%#%%

2

1 -22#1& -%#%22$ 21$7 "#%% %#" "#&"& "779$7:#11 779&&&8

1 & -:#%& -%#%%:" "$2#$& 8"#2% %#%8"2 2#28$ "129%72#"" 1891&&8

$ & $#"1 %#%%$" 2&2#7 7$#&% %#%7$& %#7:2 &89%%1#%1 $89%&&8

$ 22#8 %#%221 "2"#:& "%1#&% %#"%1& 2#&%1 279:%:#%" &:98#

$ & -$#"1 -%#%%$" 2&2#7 7$#&% %#%7$& %#7:2 &89%%1#%1 $89%&&8

& "% -": -%#%%&2 ":"#& 8"#2% %#%8"2 "#$$$ :89"1$#8$ 1891&&8

: "% "#7" %#%"7 ""#8$ "%1#&% %#"%1& "#&%8 "18912$#:: &:98#

7 : 2:#1" %#%2:1 "$#%2 "#%% %#" 2#""8 21&9:18#&1 779&&&8

$ 7 -"#& -%#%%"1 "7:#:8 7$#&% %#%7$& %#2& "898$2#%% $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -8%#&% -%#%8%& 278#78 28#&% %#28& "#$:2 "97&%#8 "$791%%#%%

2 -18#7% -%#%187 &:#$7 "$2#%% %#"$2 2#&1 $"92":#2% "%"9#

$ -2"#8& -%#%2"7 "2"#:& "%1#&% %#"%1& 2#$2 2297#7& &:98#

D,;

D,;


4/34

$ 7 2#7: %#%%2: "7:#78 7$#&% %#%7$& %#$% 898&#17 $89%&&8

8 7 1$#%% %#%1$% 1%$#8: ":%#2% %#":%2 "#$71 2&192$2#&2 "2&97%%#%%

" 8 $$#%% %#%$$% 28#7& ":%#2% %#":%2 "#:& 229:8#7% "2&97%%#%%

2

1 -2"#%1 -%#%2"% 21$7 "#%% %#" "#$"1 "8&9&87#78 779&&&8

1 & -8#&1 -%#%%8& "$2#$& 8"#2% %#%8"2 "#:": "":97#1 1891&&8

$ & %$ %#%%&" 2&2#7 7$#&% %#%7$& "#%$2 879:78#% $89%&&8

$ 2"#8& %#%2"7 "2"#:& "%1#&% %#"%1& 2#$2 2297#7& &:98#

$ & -%$ -%#%%&" 2&2#7 7$#&% %#%7$& "#%$2 879:78#% $89%&&8

& "% -$#&: -%#%%$8 ":"#& 8"#2% %#%8"2 "#1% 7:9%#&% 1891&&8

: "% "1#" %#%"1 ""#8$ "%1#&% %#"%1& "#&&$ "$298&1#%$ &:98#

7 : 2:#:" %#%2:: "$#%2 "#%% %#" 2#"$ 2$"9"1$#7$ 779&&&8

$ 7 -2#7: -%#%%2: "7:#:8 7$#&% %#%7$& %#$% 898&#17 $89%&&8


5/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#:8 -%#%8%% 278#78 28#&% %#28& "#$87 279:%#&$ "$791%%#%%

2 -18#"8 -%#%182 &:#$7 "$2#%% %#"$2 2#$:: 1&9$:" "%"9#

$ -2"#&7 -%#%2"8 "2"#:& "%1#&% %#"%1& 2#$2 2"91:$#8" &:98#

$ 7 #%" %#%%% "7:#78 7$#&% %#%7$& %#$2 :92:$#:$ $89%&&8

8 7 1$#& %#%1$& 1%$#8: ":%#2% %#":%2 "#&%& 2&89:1&1 "2&97%%#%%

" 8 $$#& %#%$$& 28#7& ":%#2% %#":%2 "#:$7 2&9&&8#72 "2&97%%#%%

2

1 -2%#1: -%#%2%$ 21$7 "#%% %#" "#18$ "829%$:#2$ 779&&&8

1 & -8#%: -%#%%8" "$2#$& 8"#2% %#%8"2 "#87" """92%1#%: 1891&&8

$ & %: %#%%&" 2&2#7 7$#&% %#%7$& "#%$: 8:917:#2% $89%&&8

$ 2"#&7 %#%2"8 "2"#:& "%1#&% %#"%1& 2#$2 2"91:$#8" &:98#

$ & -%: -%#%%&" 2&2#7 7$#&% %#%7$& "#%$: 8:917:#2% $89%&&8

& "% -$#"7 -%#%%$2 ":"#& 8"#2% %#%8"2 "#%" 7"9288#:: 1891&&8

: "% "1#72 %#%"17 ""#8$ "%1#&% %#"%1& "#821 "$7922:: &:98#

7 : %#12 %#%%1 "$#%2 "#%% %#" 2#":% 2$$9112#28 779&&&8

$ 7 -#%" -%#%%% "7:#:8 7$#&% %#%7$& %#$2 :92:$#:$ $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -&:#&% -%#%&:& 278#78 28#&% %#28& "#$8% 289"$8#%: "$791%%#%%

2 -1% -%#%1&7 &:#$7 "$2#%% %#"$2 2#$8: 197&&8 "%"9#

$ -2"#$: -%#%2"& "2"#:& "%1#&% %#"%1& 2#$"2 2%91:%#:: &:98#

D,;

D,;


6/34

$ 7 #"2 %#%%" "7:#78 7$#&% %#%7$& %#$1 1%98$:#8 $89%&&8

8 7 1%% %#%1&% 1%$#8: ":%#2% %#":%2 "#&": 28%9"27#1& "2&97%%#%%

" 8 $%% %#%$&% 28#7& ":%#2% %#":%2 "#:8" 27971:#&1 "2&97%%#%%

2

1 -2%#2" -%#%2%2 21$7 "#%% %#" "#1$$ "&:982:#28 779&&&8

1 & -" -%#%%&7 "$2#$& 8"#2% %#%8"2 "#8"" "%&97$"#8 1891&&8

$ & "" %#%%&" 2&2#7 7$#&% %#%7$& "#%&2 8:9821#7: $89%&&8

$ 2"#$: %#%2"& "2"#:& "%1#&% %#"%1& 2#$"2 2%91:%#:: &:98#

$ & -"" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&2 8:9821#7: $89%&&8

& "% -1#:2 -%#%%1: ":"#& 8"#2% %#%8"2 "#2& 8892%7#:7 1891&&8

: "% "$#%7 %#%"$" ""#8$ "%1#&% %#"%1& "#8$$ "&%9::" &:98#

7 : %#&7 %#%%8 "$#%2 "#%% %#" 2#2%7 2$89&2%#$& 779&&&8

$ 7 -#"2 -%#%%" "7:#:8 7$#&% %#%7$& %#$1 1%98$:#8 $89%&&8


7/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#1% -%#%&:1 278#78 28#&% %#28& "#$&$ 2&9218#": "$791%%#%%

2 -1&% -%#%1&& &:#$7 "$2#%% %#"$2 2#$&7 129111#$ "%"9#

$ -2"#$1 -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%8 22:9::%$ &:98#

$ 7 #"7 %#%%2 "7:#78 7$#&% %#%7$& %#$$ 1"91:1#%$ $89%&&8

8 7 1% %#%1&2 1%$#8: ":%#2% %#":%2 "#&2& 28"92&$#"2 "2&97%%#%%

" 8 $% %#%$&2 28#7& ":%#2% %#":%2 "#:87 2:9:7% "2&97%%#%%

2

1 -2%#%& -%#%2%" 21$7 "#%% %#" "#111 "&791:#%" 779&&&8

1 & -&& -%#%%&8 "$2#$& 8"#2% %#%8"2 "#&81 "%19$12#1 1891&&8

$ & "2 %#%%&" 2&2#7 7$#&% %#%7$& "#%& 8:97$1#87 $89%&&8

$ 2"#$1 %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%8 22:9::%$ &:98#

$ & -"2 -%#%%&" 2&2#7 7$#&% %#%7$& "#%& 8:97$1#87 $89%&&8

& "% -1#87 -%#%%17 ":"#& 8"#2% %#%8"2 "#2%2 8$9%$$#71 1891&&8

: "% "$#22 %#%"$2 ""#8$ "%1#&% %#"%1& "#88" "&291&2# &:98#

7 : %#72 %#%%7 "$#%2 "#%% %#" 2#2"7 2$7988#22 779&&&8

$ 7 -#"7 -%#%%2 "7:#:8 7$#&% %#%7$& %#$$ 1"91:1#%$ $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#% -%#%&: 278#78 28#&% %#28& "#$& 2$98&2#:% "$791%%#%%

2 -1$% -%#%1&$ &:#$7 "$2#%% %#"$2 2#$& 1"9&78#2 "%"9#

$ -2"#$" -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%1 22:982#$" &:98#

$ 7 #2" %#%%2 "7:#78 7$#&% %#%7$& %#$$7 1"9778#%" $89%&&8

D,;

D,;


8/34

8 7 1% %#%1& 1%$#8: ":%#2% %#":%2 "#&% 28"978%#"% "2&97%%#%%

" 8 $% %#%$& 28#7& ":%#2% %#":%2 "#:7" %9$:"#27 "2&97%%#%%

2

1 -":#:: -%#%2%% 21$7 "#%% %#" "#1: "&89712#"7 779&&&8

1 & -$: -%#%%&& "$2#$& 8"#2% %#%8"2 "#&$1 "%92% 1891&&8

$ & "2 %#%%&" 2&2#7 7$#&% %#%7$& "#%&1 8:9:"1#8% $89%&&8

$ 2"#$" %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%1 22:982#$" &:98#

$ & -"2 -%#%%&" 2&2#7 7$#&% %#%7$& "#%&1 8:9:"1#8% $89%&&8

& "% -1#8" -%#%%18 ":"#& 8"#2% %#%8"2 "#"7 89:"2#"& 1891&&8

: "% "$#2: %#%"$ ""#8$ "%1#&% %#"%1& "#88: "&921%#7 &:98#

7 : %#7: %#%%: "$#%2 "#%% %#" 2#22 2$:97$#17 779&&&8

$ 7 -#2" -%#%%2 "7:#:8 7$#&% %#%7$& %#$$7 1"9778#%" $89%&&8


9/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#2$ -%#%&:2 278#78 28#&% %#28& "#$&2 2$9$%$#&: "$791%%#%%

2 -1$ -%#%1&1 &:#$7 "$2#%% %#"$2 2#$&% 1"927$#28 "%"9#

$ -2"#$% -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%2 22:9$87#21 &:98#

$ 7 #2 %#%%2 "7:#78 7$#&% %#%7$& %#$&" 129%:$#:" $89%&&8

8 7 1$ %#%1&1 1%$#8: ":%#2% %#":%2 "#&" 2829":"#1" "2&97%%#%%

" 8 $$ %#%$&1 28#7& ":%#2% %#":%2 "#:7 %9:"2#$7 "2&97%%#%%

2

1 -":#:$ -%#%":: 21$7 "#%% %#" "#1& "&891::1 779&&&8

1 & -$$ -%#%%&$ "$2#$& 8"#2% %#%8"2 "#&11 "%29&7"#7% 1891&&8

$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:1%: $89%&&8

$ 2"#$% %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%2 22:9$87#21 &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:1%: $89%&&8

& "% -1#&8 -%#%%18 ":"#& 8"#2% %#%8"2 "#"81 89%1#:7 1891&&8

: "% "$# %#%"$ ""#8$ "%1#&% %#"%1& "#871 "&9&$1#"2 &:98#

7 : %#: %#%%: "$#%2 "#%% %#" 2#22& 2$:98"%#$2 779&&&8

$ 7 -#2 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&" 129%:$#:" $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -&:#22 -%#%&:2 278#78 28#&% %#28& "#$&" 2$9&7#: "$791%%#%%

2 -1 -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$7 1"9%8"#1: "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:9$%%#$7 &:98#

D,;

D,;


10/34

$ 7 #2 %#%%2 "7:#78 7$#&% %#%7$& %#$&2 1292%8#%" $89%&&8

8 7 17 %#%1&1 1%$#8: ":%#2% %#":%2 "#&2 2829&2#2$ "2&97%%#%%

" 8 $7 %#%$&1 28#7& ":%#2% %#":%2 "#:71 "9%7#1 "2&97%%#%%

2

1 -":#:2 -%#%":: 21$7 "#%% %#" "#11 "&89"#&: 779&&&8

1 & -$2 -%#%%&$ "$2#$& 8"#2% %#%8"2 "#&: "%29:#1: 1891&&8

$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:&2#% $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:9$%%#$7 &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:&2#% $89%&&8

& "% -1#&$ -%#%%18 ":"#& 8"#2% %#%8"2 "#"&: 829:72#"& 1891&&8

: "% "$#$ %#%"$ ""#8$ "%1#&% %#"%1& "#87& "&978#7& &:98#

7 : %#:$ %#%%: "$#%2 "#%% %#" 2#227 2$:977#1 779&&&8

$ 7 -#2 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&2 1292%8#%" $89%&&8


11/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#2% -%#%&:2 278#78 28#&% %#28& "#$&" 2$92:": "$791%%#%%

2 -1% -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$8 1%9:$8#8: "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:91$:#2" &:98#

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$& 1292&"" $89%&&8

8 7 1% %#%1&1 1%$#8: ":%#2% %#":%2 "#& 28291$#"" "2&97%%#%%" 8 $% %#%$&1 28#7& ":%#2% %#":%2 "#:7$ "9"81#2: "2&97%%#%%

2

1 -":#:" -%#%":: 21$7 "#%% %#" "#1 "&892"% 779&&&8

1 & -$" -%#%%&$ "$2#$& 8"#2% %#%8"2 "#&& "%29"$8#$& 1891&&8

$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8%#71 $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:91$:#2" &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8%#71 $89%&&8

& "% -1#&1 -%#%%1& ":"#& 8"#2% %#%8"2 "#"&& 8297"%#$% 1891&&8

: "% "$#& %#%"$1 ""#8$ "%1#&% %#"%1& "#878 "&9::%#8" &:98#

7 : %#:& %#%"% "$#%2 "#%% %#" 2#227 2$:9:8$#2 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$& 1292&"" $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -&:#": -%#%&:2 278#78 28#&% %#28& "#$&" 2$92$8#$% "$791%%#%%

2 -1: -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$8 1%97:8#2 "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:918#"8 &:98#

D,;

D,;


12/34

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$& 1292:8#$& $89%&&8

8 7 1" %#%1&1 1%$#8: ":%#2% %#":%2 "#& 2829$%"#11 "2&97%%#%%

" 8 $" %#%$&1 28#7& ":%#2% %#":%2 "#:7$ "9222#&2 "2&97%%#%%

2

1 -":#:" -%#%":: 21$7 "#%% %#" "#1 "&89"&1#$" 779&&&8

1 & -$" -%#%%&$ "$2#$& 8"#2% %#%8"2 "#&1 "%29%&%#7 1891&&8$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8$#& $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%" 22:918#"8 &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8$#& $89%&&8

& "% -1#&1 -%#%%1& ":"#& 8"#2% %#%8"2 "#"&1 8298":#2% 1891&&8

: "% "$#& %#%"$1 ""#8$ "%1#&% %#"%1& "#877 "&19%$2#7& &:98#

7 : %#:& %#%"% "$#%2 "#%% %#" 2#22: 2&%9%21#"" 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$& 1292:8#$& $89%&&8


13/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#": -%#%&:2 278#78 28#&% %#28& "#$&% 2$92:2 "$791%%#%%

2 -1: -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$& 1%97&$#"1 "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:912$#11 &:98#

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$&1 129"1#27 $89%&&8

8 7 1" %#%1&1 1%$#8: ":%#2% %#":%2 "#& 2829$28#"$ "2&97%%#%%" 8 $" %#%$&1 28#7& ":%#2% %#":%2 "#:7$ "9217# "2&97%%#%%

2

1 -":#:% -%#%":: 21$7 "#%% %#" "#1 "&89":8 779&&&8

1 & -$% -%#%%&$ "$2#$& 8"#2% %#%8"2 "#& "%29%%:#7 1891&&8

$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:88#8$ $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:912$#11 &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:88#8$ $89%&&8

& "% -1#& -%#%%1& ":"#& 8"#2% %#%8"2 "#"&1 829&8%#& 1891&&8

: "% "$#8 %#%"$1 ""#8$ "%1#&% %#"%1& "#877 "&19%7$#:2 &:98#

7 : %#:8 %#%"% "$#%2 "#%% %#" 2#22: 2&%9%$%#"" 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&1 129"1#27 $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -&:#": -%#%&:2 278#78 28#&% %#28& "#$&% 2$922$#:8 "$791%%#%%

2 -1: -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$& 1%9717#% "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91":#2% &:98#

D,;

D,;


14/34

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$&1 1292#"7 $89%&&8

8 7 1" %#%1&1 1%$#8: ":%#2% %#":%2 "#&1 2829$1%#7 "2&97%%#%%

" 8 $" %#%$&1 28#7& ":%#2% %#":%2 "#:7$ "92&2#%" "2&97%%#%%

2

1 -":#:% -%#%":: 21$7 "#%% %#" "#12 "&89"22#2 779&&&8

1 & -$% -%#%%&$ "$2#$& 8"#2% %#%8"2 "#& "%"9:72#%" 1891&&8$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8:#%2 $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91":#2% &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8:#%2 $89%&&8

& "% -1#& -%#%%1& ":"#& 8"#2% %#%8"2 "#"& 829&11#8: 1891&&8

: "% "$#8 %#%"$1 ""#8$ "%1#&% %#"%1& "#87: "&19"%#$% &:98#

7 : %#:8 %#%"% "$#%2 "#%% %#" 2#22: 2&%9%&#:1 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&1 1292#"7 $89%&&8


15/34


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

"

" 2 -&:#": -%#%&:2 278#78 28#&% %#28& "#$&% 2$922%#"$ "$791%%#%%

2 -1: -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$& 1%977#: "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91"$#77 &:98#

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$&1 12928#:2 $89%&&8

8 7 1" %#%1&1 1%$#8: ":%#2% %#":%2 "#&1 2829$17#"" "2&97%%#%%" 8 $" %#%$&1 28#7& ":%#2% %#":%2 "#:7& "92&:#27 "2&97%%#%%

2

1 -":#:% -%#%":: 21$7 "#%% %#" "#12 "&89""1#$ 779&&&8

1 & -$% -%#%%&$ "$2#$& 8"#2% %#%8"2 "#& "%"9:&8#1& 1891&&8

$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8:#8% $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91"$#77 &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:8:#8% $89%&&8

& "% -1#& -%#%%1& ":"#& 8"#2% %#%8"2 "#"& 829&"#%$ 1891&&8

: "% "$#8 %#%"$1 ""#8$ "%1#&% %#"%1& "#87: "&19""2#7& &:98#

7 : %#:8 %#%"% "$#%2 "#%% %#" 2#22: 2&%9%8"#% 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&1 12928#:2 $89%&&8


3R3i 34 5l,s6 5m,s6 5m6 5mm6 5m6 5m,s6

" 2 -&:#": -%#%&:2 278#78 28#&% %#28& "#$&% 2$92"8#%$ "$791%%#%%

2 -1: -%#%1&1 &:#$7 "$2#%% %#"$2 2#$$& 1%971#%7 "%"9#

$ -2"#1: -%#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91"1#"" &:98#

D,;

D,;


16/34

$ 7 #21 %#%%2 "7:#78 7$#&% %#%7$& %#$&1 129%#11 $89%&&8

8 7 1" %#%1&1 1%$#8: ":%#2% %#":%2 "#&1 2829$$"#:7 "2&97%%#%%

" 8 $" %#%$&1 28#7& ":%#2% %#":%2 "#:7& "928#"$ "2&97%%#%%

2

1 -":#:% -%#%":: 21$7 "#%% %#" "#12 "&89""%#7 779&&&8

1 & -$% -%#%%&$ "$2#$& 8"#2% %#%8"2 "#& "%"9:$:#8" 1891&&8$ & " %#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:7%#%& $89%&&8

$ 2"#1: %#%2"$ "2"#:& "%1#&% %#"%1& 2#$%% 22:91"1#"" &:98#

$ & -" -%#%%&" 2&2#7 7$#&% %#%7$& "#%&$ 8:9:7%#%& $89%&&8

& "% -1#& -%#%%1& ":"#& 8"#2% %#%8"2 "#"& 829&2#81 1891&&8

: "% "$#8 %#%"$1 ""#8$ "%1#&% %#"%1& "#87: "&19""8#71 &:98#

7 : %#:8 %#%"% "$#%2 "#%% %#" 2#22: 2&%9%8$#22 779&&&8

$ 7 -#21 -%#%%2 "7:#:8 7$#&% %#%7$& %#$&1 129%#11 $89%&&8

3i 3< Pi zi z< zi-z< =l

" 2 2%#%% $%2#8 $%$#$ -2#7 2#"1

2 ":#1 $%$#$ $%$#1 %#" 2#"&

$ 2"#&% $%$#1 $%2#8 2#8 $#&8

$ 7 1#": $%2#8 1:8#8 $ %#87

8 7 -12%#%7 :18#8 1:8#8 1$% 1#28

" 8 2%#%% $%2#8 :18#8 -11$ 1#:2


17/34

1 2"#&% $%$#1 $%1#& %#7 #7%

1 & 2% $%1#& 1:: $#& $#22

$ & &:#:1 $%2#8 1:: #8 #1

$ 2"#&% $%$#1 $%2#8 2#8 $#&8

$ & &:#:1 $%2#8 1:: #8 #1& "% 8#%" 1:: 1&8#2 "#7 #$&

: "% &:#" 1&8#" 1&8#2 -%#" #1

7 : 1#": 1:8#8 1&8#" %#& 1#1

$ 7 1#": $%2#8 1:8#8 $ %#87


18/34

< =< Le,D


19/34

%#%%8&7

@2* -%#%%21$7

@* %#%%21%8

@"*


20/34

< =< Le,D


21/34

%#%222% %#& %#&172 2":#$

%#%"17" 1#%1 1#%:12 7:#8&2

%#%"128 1#8% 1#&::&$ 7$#11&

?* -%#: 81%#1$

%#%"&%" #18 7 %#%%72"8 %#%&& %#81 -1#2%:"" 2%%#%$:

%#%"8$ :8 -:81:1 :"#%$%#%"778 #28 #2&87" $:#8::

%#%"$2 $#7% $#7%12% 2&̫

?* -2#"" ":":#&1

%#%"778 #28 -#2&87" $:#8::

%#%"71" $#"& -$#"$&77 :%$#72

%#%"&1: 2#: 2#:1:7 2%$#"1

%#%"1:7 1#%8 1#%8"71 ""$%

%#%222% %#&1 -%#&$"$ 2":#1$%

?* -2#%$ 2%%&

%#%%%&2:

@2* %#%%%$$%

@* %#%%%$"2

@"*


22/34

< =< Le,D


23/34

%#%2"7" %#8 %#82&8% 22#&2&

%#%"18$ 1#2% 1#2%:1 :"#7&

%#%"12 1#7& 1#7$&7 7"7

?* -%#2: 8$#82

%#%"&" #2 7 %#%%72"8 %#%&& %#&7 -#:%:7 ":#12"

%#%"88$ $#&8 -$#&812: 7#%":%#%"77 #2 #22&1 $1#888

%#%"$2$ $#82 $#82%&8 2&$#%"

?* -%#$1 "7$#2

%#%"77 #2 -#22&1 $1#888

%#%"7:7 #:8 -#:821 7%8#21%

%#%"& #2 #22&7% 2"1#%%7

%#%"1:" 1#2& 1#2&118 ":#%%7

%#%2"7" %#8 -%#828%7 22#817

?* -%#$ ":W

%#%%%":1

@2* %#%%%"18

@* %#%%%"8

@"*


24/34

< =< Le,D


25/34

%#%"18 1#2$ 1#2$27 :"#7&&

%#%"12" 1#:% 1#:%27 78#%:1

?* -%#%7 8$7#1&

%#%"&"8 #"& 7 %#%%72"8 %#%&& %#&8 -#72:8& ":"#&"

%#%"878 $#1 -$#12"& 7""#%"&

%#%"772 #1 #&72 $11#7%%%#%"$2& $#&: $#&7&"1 2&1#2:

?* -%#"$ "7""#82

%#%"772 #1 -#&72 $11#7%%

%#%":"$ #&8 -#&8172 88:#:""

%#%"&27 #" #%7$2 2"""

%#%"1:% 1#2 1#"8&: ":#87$

%#%2"&7 %#8& -%#8&"" 28#8%$

?* -%#"$ ":"7#&"

%#%%%%$$

@2* %#%%%%1"

@* %#%%%%:

@"*


26/34

< =< Le,D


27/34

%#%2"&1 %#88 %#88%8 27#:7"

%#%"18 1#28 1#2&828 :2#%%2

%#%"12" 1#:2 1#:"&$8 78#2%"

?* -%#%2 8$:#8:

%#%"&"7 #"1 7 %#%%72"8 %#%&& %#&& -#7%8&% ":"#"%&

%#%"8:" $#2$ -$#2$%88 7%1#72%#%"772 #1 #1%8 $1$#%$&

%#%"$28 $#&7 $#&8&" 2&1#%71

?* -%#%1 "7%$#%7

%#%"772 #1 -#1%8 $1$#%$&

%#%":2" #$: -#$:2$ 882#"&

%#%"&28 # #"81 2"8#%77

%#%"17: 1# 1#28$ "1%#%%1

%#%2"&1 %#88 -%#8818 2:#"%8

?* -%#%1 ":"#12

%#%%%%"$

@2* %#%%%%"2

@* %#%%%%""

@"*


28/34

< =< Le,D


29/34

%#%2"& %#87 %#88&%" 2:#88

%#%"182 1#28 1#28"2 :2#%1%

%#%"12" 1#:2 1#:2%1 78#2"

?* -%#%" 8&%#"8

%#%"&"7 #"1 7 %#%%72"8 %#%&& %#&& -#7%"& ":%#:&

%#%"8:2 $#2 -$#22$"% 7%#%71%#%"772 #1 #1"$ $1$#"28

%#%"$28 $#&8 $#&827 2&1#%21

?* -%#%" "7%#2%

%#%"772 #1 -#1"$ $1$#"28

%#%":22 #$8 -#$&:1" 8&:#:&:

%#%"&28 #1 #72 2"8#28:

%#%"17: 1#1 1#8%2 "1%#%&&

%#%2"& %#87 -%#88&12 2:#$%

?* -%#%" ":""#:1

%#%%%%%1

@2* %#%%%%%

@* %#%%%%%

@"*


30/34

< =< Le,D


31/34

%#%2"& %#87 %#88&71 2:#17:

%#%"182 1#28 1#282$ :2#%$"

%#%"12" 1#:2 1#:2"1% 78#2:

?* %#%% 8&%#27

%#%"&"7 #"1 7 %#%%72"8 %#%&& %#&& -#8::$: ":%#:22

%#%"8:2 $#22 -$#2"87$ 7%2#$7:%#%"772 #1 #1"&2 $1$#"1&

%#%"$28 $#&8 $#&8217 2&1#%%7

?* %#%% "7%2#&8

%#%"772 #1 -#1"&2 $1$#"1&

%#%":2 #$& -#$&27: 8&:#17

%#%"&28 #1 #1%": 2"8#

%#%"17: 1#1 1#72 "1%#%7

%#%2"& %#87 -%#8882$ 2:#&"$

?* %#%% ":""#$

%#%%%%%"

@2* %#%%%%%"

@* %#%%%%%"

@"*


32/34

< =< Le,D


33/34

%#%2"& %#87 %#888%7 2:#$2" -#&%

%#%"182 1#28 1#282&& :2#%$1 $#&%

%#%"12" 1#:2 1#:2"8% 78#212 1$#&%

?* %#%% 8&%#"

%#%"&"7 #"1 7 %#%%72"8 %#%&& %#&& -#8::%: ":%#:"" -2%#%%

%#%"8:2 $#22 -$#2"$7% 7%2#1$% -&%%#%"772 #1 #1"8% $1$#"$2 "%#%%

%#%"$28 $#&8 $#&822$ 2&1#%% 2#2%

?* %#%% "7%2#$"

%#%"772 #1 -#1"8% $1$#"$2 -"%#%%

%#%":2 #$& -#$&"%1 8&:#"82 -7#&%

%#%"&28 #1 #1%8" 2"8#1: ""#1%

%#%"17: 1#1 1#7$8 "1%#%77 28#%%

%#%2"& %#87 -%#8881: 2:#&18 #&%

?* %#%% ":""#1"

%#%%%%%%

@2* %#%%%%%%

@* %#%%%%%%

P


34/34

2%

8#%"

8::

2:#:8

8::

82#7

82#8

&:#"

:#:8

Documents

HARDY CROSSfinal.xlsx