UNIVERSIDAD PRIVADA DE TACNA FACULTAD DE INGENIERIA ESCUELA PROFESIONAL DE INGENIERIA CIVIL
::::::::::::::::::::::::::::: ::::::::::::::: :::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::: :::::::::::::::::::::::::::: :::::::::::: ::::::::::::::::: TALLER Nº3 HIDRODINAMICA ::::::::::::::::::::::::::::: ::::::::::::::: :::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::: :::::::::::::::::::::::::::: :::::::::::: ::::::::::::::::: CURSO: FISICA II
DOCENTE
ING. JENNY GABRIELA HUAYTA CURO
INTEGRANTES
CHINO YUPANQUI, JESSERIN AGUILAR ALE, ASTRID MAMANI TUYO, JESUS
GRUPO
A FECHA DE ENTREGA
22/05/2017
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
1. U' $#+'& $#+'&$' $' -!## 20 '+#$ '+#$% % (!$('$#% (!$('$#% ( ( $'&! #% &# 1.00. 1.00. ' $#+'&#$' #%-3 (#(-'&' ' -4 &# 0.0 (. &# $'&!. S! ' $'6!&# &# '+' # # -4 #% &# 8.0/%, 9C # $'6!&# %'&$3&# % '+#$% '+#$% &# ' $#+'&#$'; Datos : r 1=1.00 mm =0.001 r 2=0.80 mm =0.008 v 1= 3 m / s
v 2 =?
Solución: Q 1 =Q 2 v 1∗ A 1= v2∗ A 2 3∗ (3.14 ) ( 0.008 )
2
= v 2∗( 3.14 ) ( 0.001 )2 ( 20 )
0.000192 = v 2∗0.00002 0.000192 = v 2 0.00002
v 2= 9.6 m / s
2. E ('&' &# <!& # (!$(' 6$ ' -4#$=' #% &# 1 !-$%/%#+&. L' "#(!&'&, # /% &# <!& # 6- # # # ' %#((!> -$'%"#$%' #% &# 200( 2 #%: S(!: Datos : 3
Q=18000 cm / s 2
A = 200 cm
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
2
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
Solución:
Q =V . A 3
cm =V ( ( 200 cm2) 18000 s 90 cm / s = V V =0.9 m / s
8. U -@# -@# &# '+' -!## -!## ' %#((!> %#((!> -$'%" -$'%"#$% #$%' ' (!$( (!$('$ '$ # %# '($-' &#%&# &!3#-$ &# 8. '%-' ' %#((!> &# 6$#4', ( &!3#-$ #% &# 1.2 . S! ' "#(!&'& &# '+' #% &# 8 /% # ' -4 -4#$ #$=' =' &# ' ' $$ &!3 &!3##-$ $,, &# &#-#$ -#$! !'$ '$ ' "# "#( (!&' !&'& & &# <!& # ' %#((!> &# 6$#4'. S(!: A 1=1.8 m A 2=0.6 m
V 1 =3.6 m / s 1 = A 2 V 2 2 A 1 V 1
2= V 2
1 A 1 V 1 A 2 2
V 2 2 =
π R ( 3.6 ) πR
2
2
2= V 2
π 1.8 ( 3.6 ) 2
π 0.6
2=32.4 m / s V 2
. L' "#( "#(!&' !&'& & &# '+' # ' -4#$ -4#$=' =' $! $!-' -' #% &# (. &# &!3#-$, #% &# /% ' 6$#%!> &# 1.5 '-. S! # &!3#-$ %#
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
8
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
$#&(# ' ' !-'&, ('(# ' 6$#%!> '- # #%-# 6-. S(!: '-. S! # &!3#-$ %# $#&(# ' ' !-'&, ('(# ' 6$#%!> '- # #%-# 6-. D'-%: D1= 6 cm= 0.06 m D2= 3 cm= 0.03 m V 1= 4 m / s g=10 m / s
2
P1=1.5 atm
P2=? atm
C"#$%!#%: P1=1.5
atm∗101325 pa =151987.5 pa =151987.5 N / / m2 1 atm
Q 1 =Q 2 A 1∗V 1 A2
=V 2
0.06 m
¿ ¿ ¿2 ¿ ¿ 4∗4 m / s ¿ 0.03 m
¿ ¿ ¿2 π ¿ ¿ V 2=¿
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
0.06 m
¿ ¿
¿ 2∗ 4 m / s ¿ 0.03 m
¿ ¿ ¿ V 2=¿
V 2=16 m / s
P1+
1 1 2 2 ρ∗V 1 + ρgh= P2 + ρ ∗V 2+ ρgh 2 2 4 m/ s
¿ ¿
16 m / s
¿ ¿ / m2 + 1 ∗1000 kg / m3∗¿ 151987.5 N / 2
4 m/ s
¿ ¿
16 m / s
¿ ¿ 1 / m2 + ∗1000 kg / m3∗¿ 151987.5 N / 2
P2=31987.5 N / m P2=31987.5
2
pa∗1 atm =0.32 atm 101325 pa
5. D# #F-!+!& #F-!+!&$ $ (-$' (-$' !(#&!% !(#&!% %'# %'# '+' 4' 6$#%!> 6$#%!> &# '!$#, ( ( %# #%-$' # ' +$' 9Q# -'-' 6$#%!> &# '!$# '-$!(' '$$!4' &# ' '-%$!(' %# $#!#$# 6'$' # # ($$ &# '+' -#+' ' "#(!&'& &# 80 /% ('& # !"# &# '+' #%-3 ' 0.50 ' &# ' 4!'; S(!:
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
5
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
P1+
1 1 p v1 + pgh= p 2+ p v 2 + pgh 2 2
P1= P2 +
1 ( 1000 ) ( 30 )2 +( 1000 )( 9.8 )( 0.5 ) 2
P1=450000 + 4900 P 1=454900 P1=454.9 KPa
. E ' -4#$=' -4#$=' $! $!-' -' < <# # '+' ( ' "#(!& "#(!&'& '& &# 2 /% 4' 4' ' 6$#%!> &# 2,8 F 10 5 N/. L' -4#$=' %# #%-$#(' '%-' ' !-'&, &# % &!3#-$. 9C3 #% ' 6$#%!>, # P', &# '+' # %-# ('%; S(!: A 1= 4 A 2 2 ( 4 A 2) =v 2 ( A2 ) Q 1= Q 2 v 1 . A 1= v 2 . A 2 v 2= 8 m / s 1
2
1
2
P e + ρ . v e = P s + ρ. ρ . v s 2
Ps= 200000 Pa
2
5
2.3 x 10 N 1 1 + x 1000 x 22= P s+ x 1000 x 82 2 2 m
Ps= 200 kPa
7. U -4 &# *#-$! *#-$! -!## 1 ( &# $'&! # % 6'$-# #%-$#( #%-$#(' ' 2( # % 6'$-# '('. L' "#(!&'& &# '+' # ' 6'$-# '(' #% 0,1 /%. H''$ ' ('=&' &# 6$#%!> # # -4.
Solución: A 1 V 1= A 2 V 2
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
( 3.14 ) ( 0.02 )2 ( 0.1 )=(3.14 ) ( 0.01 )2 V 2
( 0.0004 ) ( 0.1 )= 0.0001 V 2 V =0.4 m / s
Bernully: p + pgh+
1 1 pv = p 2+ pg h2 + p v 2 2 2
p− p2=
1 1 p v2 − p v 1 2 2 2
2
∆ p=500 ( 0.4 − 0.1 ) ∆ p= 75 Pa
> 6>%! %!- - &# +$ +$' ' %# %#(( ((!> !> %%-$' $'& & &# &#%( %('$ '$+' +' '+ '+' ' . E &# !4$##-# # ' '->%#$' 6$ # 6- 8, &# ' -4#$=' $!-'. S! A2 K 10 (2 , A8 K 5 (2 # ('&' &# %'!&' #% &# 10,5 !-$%/%. C'(# # "'$ &#: ' L' 6$#%!> # # 6- 2 4 L' '-$' H.
S(!: Caudal : Q3= A3 V 3 3
1m
=1000 ! −3
10.5 10
=5 10−4 V 3
V 3=21 m / s 1 1 2 2 P1+ ρ V 1 + ρg h1= P 2+ ρ V 2 + ρg h2 2 2
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
7
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
E 1 2: 1 2 Patm+ 0 + ρg h1= P2 + ρ V 2+ 0 2
E 1 8: 1
2
Patm + 0 + ρg h1= Patm + ρV ρ V 2 + 0 2
1 2 10 h1= 21 2
h1=22.05 m
CONTINUIDAD A 3 V 3= A 2 V 2 5 21=10 V 2
V 2=
5
10
10.5 m s
+ 1000 10 22.05 = P 2+ 500 10.52 5
P2=2.65 10 Pa
. P$ ' -4 -4#$= #$=' ' $! $!-' ' &# 20 (2 &# %# %#((! ((!> > -$'%"# -$'%"#$%' $%' # ' 6'$-# 6'$-# '(' 10 (2 # ' 6'$-# &#+'&', (!$(' '+'. S! ' '-$' &# '+' # % -4% "#$-!('#% A B, '4!#$-% ' ' '->%#$' % AK 15 ( B K 10 (. E(#-$#: ' L'% "#(!&'&#% &# =!& # '% 6'$-#% '(' &#+'&' 4 E ('&'
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
Solución: A 1 V 1= A 2 V 2
Q =V . A
V =( 1.14 )( 0.001 )( 3.14 )
( 0.002 ) V 1 =(0.001 ) V 2 2 V 1=V 2
P1= P A + P" P1= Pgh + P0 P1=( 1000 ) ( 9.8 ) ( 15∗10 )+ 1000 P1=101470
P2= P# + P 0 P2= Pgh + P0 P2=( 1000 ) ( 9.8 ) ( 0.1 ) + 1000 P2 =100980
P1+ pg h 1+
1 1 p v 1= p 2+ pg h2 + p v 2 2 2
101470 + 500 v 1 2
500 V 1
2
=100980 + 500 ( 2 V 1 )2
+500 ( 4 V 12 )= 490 2
1500 V 1
V 1=
=490
490 1500
V =0.57 V =1.14
)ISI )ISICA CA II ? HIDR HIDROD ODIN INAM AMIC ICA A
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL −3
V =3.579 ∗10
10.E '+' # -!## (-##&$ &# -#( '4!#$- (!=&$!(, $!-' ( ' !(!'(!> &# 58, # ' %6#$(!# #F-#$' %# $#'!' ' '6#$-$' &# 6## '+#$. C'('$ ' L' '-$' 3F!' &# '+' # ##$+#$3 4 E '+' #"' 3F! '('(# $!-'
S(! : v =√ 2 x 1021.25
v=
5m s
2
t =0.8 s
2
v $ = v 0− 2. g . h 0 =4
2
2
g . t h =v 0 . t + 2
0.8=
( 4 +0 ) 2
−2 x 10 xh
20 h=16
.t
t =0.4 s
t t =0.4 + 0.8
t t = 1.2 s
x max= v . t
h =0.8 m
% hmax =0.8 + 2.4 hmax =3.20 m
x max=3 x 1.2
)ISICA II ? HIDRODINAMICA
1 0
U!"#$%!&'& P$!"'&' &# T'(' ESCUELA PRO)ESIONAL DE INGENIERIA CI*IL
x max=3.6 m
)ISICA II ? HIDRODINAMICA
1 1
&scr'(a a)u* la ecuac'+,. ecuac'+, .
11.E ' -4#$=' $!-' # &!3#-$ &# ' %#((!> -$'%"#$%' 3% '(' #% &# ,0 ( &# ' 3% #%-$#(' #% &# 2,0 (. P$ ' -4#$=' <# +'% ' ' 6$#%!> &# 1,0 '- &#%&# A '(!' C, # -!## ' &#%!&'& &#% !&'& &# 1,8 +/8 #%('6' ' ' '-> '->%#$ %#$' ' # C. ρH+ K 18, F 108+/8 . L' '-$' &# #$($! # # '>#-$ D #% &# 1 (. D#-#$!'$: ' L' 6$#%!> &# +'% # ' 6'$-# #%-$#(' &# ' -4#$='. 4 L' "#(!&'& # ' 6'$-# '(' &# ' -4#$='. ( E ('&' +'%- # ' -4#$='.
D'-: PA PA = P 0 ( pres'o, atmos$er'ca ) P=60 cm -g
ρ=1.36
g dm
=1.36 3
kg m
2
S(!: ' P=h∗ ρ -g∗g P= 0.6∗13.6 x 10
3
∗9.8
P=79968 5
P= 0.79∗10 Pa
4 P$!(!6! P$!(!6! &# B#$ B#$! ! # A B } +ρgh 1 1 2 ¿ P A + ρ V A + ρgh = P 0+ ρ V 0 2 2 1 1 2 2 P A + ρ V A = P 0+ ρ V 0 .. ( 1 ) 2 2
P$!(!6! &# (-!!&'& A A∗V A = A 0∗V 0 2
2
D D π V A = π V 0 4 4 V 0= 9 V A
ρ -g=1.36
kg 2
m
12.P 12 .P$ $ # -' -' # # '4 '4!# !#$$- # # %# #% #%-$ -$' ' # ' + +$ $' ' < <# # '+ '+' ' (-!'#-#. E 3$#' -$'%"#$%' # # 6- 2 #% &# 0,00 2 # # 6- 8 #% &# 0,0102. E 3$#' &# -'# #% +$'&# # (6'$'(!> ( # 3$#' -$'%"#$%' &# -4. D#-#$!'$: ' L' 6$#%!> '-$!(' # # 6- 2. 4 E +'%- ('&'. R6-': ' ,F10 P' 4 0,200 8/%
' S(!> 1 2 1 2 P2+ v ρ 2+ ρgh ρg h 2= P3+ v ρ3+ ρgh ρg h 3 2 2
1 2 2 P2− P3= ρ ( v 3− v 2) 2
P2− P3=
1000 2 ( v 3− v 22) 2 4
P2− P3= 6.9∗10 Pa
4 S(!> v 3= √ 2∗g∗h v 3= √ 2∗9.81∗2
v 3= 4 √ g m / s
C'&' Q3= 4 √ g∗0.0160 3
Q3=0.200 m / s
v 3= 4 √ g m / s v 2=
Q 0.200 = A 0.0480
v 2= 4.17 m / s
18.U +$' -'# &# ''(#'!#-, '4!#$- # ' 6'$-# %6#$!$ # ( '+', # % (%-'& # 6- ' 1 '4' &# !"# &# '+' %# #'4$' $!(! 6##. L' $#'(!> &# < ' ('%' &# ' +' #% &# 2.50 F 10 ?8 8/!. D#-#$!#: ' L' $'6!&# ' ' # # '+' %'# &# $!(! 4 E &!3#-$ &# $!(!. S(!: 1 17.89 m −5 = A ( 17.89 ) 2.5 x 10 x v= Q= v . A v =√ 2 x 10 x 16 60 s
−6
2
A = 2.143 x 10 m
A = 2.143 mm
2
1.U' "!' '-!## +$' -'# ( ' 6'$-# %6#$!$ '4!#$-', # (-!## '+' 6'$' ##$+#(!'%. E '+' 6#&# &$#'$ &# -'# ' -$'"% &# ' '+#$' &# .0 ( &# &!3#-$. L' '+#$' -#$!' ( ' 4!' &# 2.20 ( &# &!3#-$. E ' 4!' %# !%#$-' -'6> &# +'. E !"# &# '+' # # -'# %# '-!## ' 7.50
%4$# ' 4!'. C'(#: ' L' #$' &# $!((!> # ' 4!' ##$(# %4$# # -'6>, 4 9Q '%' &# '+' <# &# ' 4!' # 2.00 %! %# !-' # -'6>; ( C'(# ' 6$#%!> '-$!(' &# '+' # (!$(' # ' '+#$' %- &#-$3% &# ' 4!' ' L 6$!#$ 6$!#$ # # ' # ('('$ ('('$ #% ' #$' %4$# %4$# # -'6> -'6> !& ' ' 6$#%!>, #%-' #$', '(!' '4', # %#$ &# !+' >& # ' #$' # ' 4!' $#(# 6$ $!((!> %4$# # -'6>, (%!&#$'& ' %-# &# 6#% &#%6$#(!'4# $#-# ' '% #$'% #(!'&'%. P= $uer/a $uer/a hac'aa(a0o hac'aa(a0o de('daa de('daa la pres'+ pres'+, , so(r so(re el tap+, tap+,
SOLUCION:
π d P= p A = ρ g h 4
2
do,de : d =2,20 cm =0,022 m 2
d d π = π ( ) ²= π r ²= 1readel 1readel tap+, tap+, 4 2 ρ=1000 kg / m ³ g=10 m / s ²
h =7,50 m P=1000 kg / m ³ 10 m / s ² 7,50 m 3,1416 0,022² m ² / 4 =28,51 N
P es hac'a a(a0o 2 se e)u'l'(ra co, 3
¿ 3 ∨¿∨ P ∨¿ 3 =28,51 N 4 29 N
4 C ' '-$' #% (%-'-# ' 6$#%!> ' ' %'!&' -'4! #%, # ('&' ('&' %'!# %'!#-# -# %# '-!# '-!## # (%-' (%-'-# -# #$(#& #$(#& ' ' *% "#( "#(!&' !&'& & &# %'!&' (%-'-#. Vs= √ ( 2 g h ) =
√(
2 10
m 2
s
7,5 m
)
2
=12,25 2
m s
2
E ('&' &# %'!&' #%:
0,022 m m =0,0047 m Qs=Vs A =12,25 π 4 s s
3
V =Qs.t =0,0046 m ³ / s 3600 s =16,92 m ³ Como%Q = = ¿ V = t m=masa =Vol de,s'dad de,s'dad= 16,92 m ³ 1000 kg / m ³=16920 kg deagua deagua
( S! %# (%!&#$' 6$&!&'% # =!&% $#'#% -#&$='% -#&$='% ' 6$&!&' ' ' #-$ #-$'& '&' ' &# ' '+ '+# #$' $' &# %'! %'!&' &',, (' ('! !' '&' &',, -$' -$' ' '$+ '$+ &# ' '+#$' 6$ ' $!((!>, &!%-$!4!&', -$' # ' 4!', ('!'&' ' 6$#%!> &# %'!&' #% 0, %#' ' '-%$!(' $#6!- # '4'% &# 6$#%!> $#'$#'-!"' !"' ' ' ' '->% '->%#$ #$' '.. E ##(##(-, , %! 6'-# 6'-#' '% % B#$ B#$! ! #-$# #-$# ' %6#$(!# !4$# 1 &# -'# ' %'!&' 2 %- '-#% &# ' 4!', ( %# 6!&# 2
2
p 1 V 1 p 2 V 2 1 + = / 2 + + / 1 + ρ g ( 2 g ) ( ρ g ) (2 g )
1 #% ' ' '-$' +#-$!(' &# ' %6#$(!# !4$# # # -'# -'& ( $##$#(!' ' '-$' &&# #%-3 ' -'6>. 61 #% ' 6$#%!> $#'-!"' # #%# 6-, %#' 0 ' '-%$!(', 6#$ $#'-!"' ' %= !%'. *1 #% ' "#(!&'& # ' %6#$(!# !4$# &# -'#, '6$F!'&'#-# ', 0. 2 #% ' '-$' +#-$!(' &# -'6> , ( %# %'(', &# &&# #%-'4' %-#. 62 #% ' 6$#%!> $#'-!"' # #%# 6- 6#$ '-#% &# ' %'!&', ( # '+' <#&, %#' %- '-#% &# ' 4!'. *2 #% ' "#(!&'& # # (&(- &# %'!&', %- '-#% &# ' 4!'. 2
2
1 p 1 V 1 p 2 V 2 + = / 2 + + / 1 + ρ g ( 2 g ) ( ρ g ) (2 g )
2
2
0 0 12,25 p2 + =0 + + 7,5 + ( ρ g ) ( 2 g ) ( 1000 ∗10 ) 2∗10
D&# % "'$#% $##6''&% #%-3 # # S.I. 7,5=
p2 1000∗10
2
+
12,25
2∗10
2
12,25 ) 9800 =0 Pa p 2 =(7,5 − 19.6
15.A -$'"% &# ' '+#$' (-$' !(#&!% &# .85 ( &# &!3#-$ (!$(' '+' ' ' $#'(!> &# 0.0120 8 /%. L' '+#$' -#$!' # ' 4!' &# 2.20 ( &# &!3#-$ !-#$!$. 9C3 #% ' $'6!&# ( ' # # '+' %'# &# ' 4!'; D'-%:
Q=0.0120 m 3 / s d =2.20 cm%r =1.10 cm=0.011 m
H''$ # 3$#': A = π r
2
A = π ∗( 0.011 )
2
−4
A =3.8∗10 m
2
H'' ' "#(!&'&: Q= A∗V V =
Q A 3
m 0.0120 s V = −4 2 3.8∗10 m V =31.57 m / s
1.A -$'"% &# ' -4#$=' (%-$#!&' ( %# #%-$' # ' )!+$' , %# #"# '+' # < !&#' #%-'4#. E 6-, &&# ' 6$#%!> #% 2.50 F 10 P', # &!3#-$ #% &# .00 (. E -$ 6- 0.500 3% '-, ' 6$#%!> #% !+' ' 1.50 F 10 P' # &!3#-$ #% &# .00 (. E(#-$# ' $'6!&# &# < #: ' ' %#((!> !#$!$, 4 # ' %#((!> %6#$!$ ( #(#-$# ' $#'(!> &# < &# "# ' -$'"% &# ' -4#$='.
L3#% 6- 1 ' &# ( &# 6- 2 # &# ( &# &!3#-$. C $##$#(!' -#% ' 6- &% # # $!+# 2K0 6$ -'- # 6- #%-'$' 0.5 6$ ' 1K0.5 &# ' #((! &# 4#$! 1 P 1 + D ∗g∗ / 1 +(1 / 2 )∗ D ∗V 1
2
2 = P 2 + D∗g∗ / 2 +(1 /2 )∗ D∗V 2 2
&&# P1 P2 % '% 6$#%!#% # # 6- 1 2 $#%6#(-!"'#-#
1 Y 2 ' 6$&!&'& *1 Y *2 #% ' "#(!&'& &# <!& D #% ' &#%!&'& 6'$' # '+' 1000 +/ 8 + #% ' +$'"#&'& %%-!-#& 2.5 F 10 1000.0.5 1/21000*12 K 1.5 F 10 1000.0 1/21000*22 200 500 *12 K 15000 500 *22 ...... #('(! 1
P$ -$ '& &# ' #('(! &# +'%- (-!!&'& %'4#% # ' ('-!&'& &# '+' # 6'%' 6$ # 6- 1 #% ' !%' # 6'%' 6$ # 6- 2 A1*1 K A2*2 &&# A1 A2 % '% '$#'% %%-!-#& 8.110.02 *1 K 8.110.022 *2 &#%6#'& *2 -##% # *2K 8.110.02 *1 / 8.110.022 *2K *1 ..... #('(!> 2 %%-!-#& *2 # ' #('(!> 1 200 500 *12 K 15000 500 *22 200 500 *12 K 15000 500 *12 &#%6#'& *1 200 500 *12 K 15000 000 *12 200 ? 15000 K 000 *12 ? 500 *12 100 K 7500 *12 *1K $'! 100 / 7500 *1K 1. /% A ' "#(!&'& # ' %#((! !#$!$ #% &# 1. /% 4 %%-!-#& ' *1 # ' #('(! 2 *2K *1 *2K 1. *2K 5. /% ' "#(!&'& # ' %#((! %6#$!$ #% &# 5. /% ( &# ' #(!( &# +'%-', 6'$' # 6- !#$!$ -##% < &# "# &#
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ρmar=1030 kg / m d'ametro =1.20 cm
%(! A
( )
0.012 3 so(resu dedo = &mpu0e = ρ - "mar ∗g ( 2 ) π 2 2
3 so(resudedo=1030∗9.8∗3.1416∗2
(
0.012 2
3 so(resudedo=2.28 N
SOLUCION B P$ T$$!(#! v √ 2 g ( 0.3)= 2.44 m / s
P$ (-!!&'& A∗V =
v t
( 0.012)2
π
2
( =
∗2.44 π
0.012 2
2
)∗( t
0.3043 )
)
2
2
t =0.125 s
1.E -4 &# *#-$! (%!%-# # ' -4#$=' $!-' (%-$#!&', -' ( %# #%-$' # ' %# %' 6'$' #&!$ ' $'6!&# &# < &# <!& !(6$#%!4#. D#-#$!#: ' ' $'6!&# &# < # # 6- 2 &# &!(' +$' 4 ' $#'(!> &# < &# <!& # #-$% (@4!(% 6$ %#+& %! %# ((# ' &!#$#(!' &# 6$#%!> P1 ? P2K 21.0 VPA % $'&!% % &# 1.00 ( # # -4 &# %'!&' %'!&' 2.00 ( # # &# #-$'&' #-$'&' (%!&#$# (%!&#$# # # <!& #% +'%!' &# &#%!&'& 700 +/ 8. S(!>: Q 1= Q 2
S# %'4#: A 1 V 1= A 2 V 2
( 0.02 )2 π V 1=( 0.01 )2 π V 2 V 1 ( 0.01 )2 = V 2 ( 0.02 )2 V 1 V 2
1 4
= =
1 K 4 K
U%'% B#$! ( !"# &# $##$#(!' # (#-$ &# -4 # (' '-$'"!#%' # 6- 1 2 # # +$3(: 2
P 1+ ρ 1 h 1 g +
V 1 ρ 1 2
2
= P2 + ρ2 h2 g +
2
P1+ ρ1 h 1 g +
V 1 ρ1 2
2
P 1− P2=
V 2 ρ2 2
2 2
= P2 + ρ2 h2 g + 2
−
V 2 ρ 2
V 1 ρ 1 2
ρ 2 2 P 1− P2= ( V 2−V 1 ) 2
V 2 ρ2 2
21000 =
700 ( 16 K 2−1 K 2) 2 2
60=15 K
K =2
R##6''%: V 1 V 2
1
1 K
4
4 K
= =
V 1=2
m m 2 V 2= 8 s s
E-(#%:
2 −3 m Q1=2 ( 0.02 ) π =2.51 10
3
s
1.U -'# (#$$'& (#$$'& # (-!## (-!## =!& =!& &# &#% &#%!&'& !&'& -!## $!(! # % (%-'& ' ' &!%-'(!' 1 &#%&# # & &# -'# ( %# #%-$' # ' )!+$' 10. E $!(! #%-3 '4!#$- ' ' '- '->% >%#$ #$' ' % &!3 &!3# #-$ -$ #% ( ( # #$ $ # # &!3 &!3##-$ $ %6#$!$ &# -'#. E '!$# %4$# # =!& %# '-!## ' ' 6$#%!> P. D#-#$!#: ' ' $'6!&# &# =!& # %'# &# $!(! ('& # !"# &# =!& #%-3 ' ' &!%-'(!' %4$# # $!(!, 4 ' $'6!&# &# =!& # %'# &# $!(! ('& # -'# #%-3 '4!#$- ' ' '->%#$' L# &# T$$!(#!.
S(!> : 1 1 ρ . g . h + ρ . v ( P + P ) + ρ . g . h + 2 ρ . v = P + ρ. 2 2
'
0
P + ρ . g . h=
4
0
1 2 ρ. v1 2
v 1= √ 2 x 10 xh
0
2
2 P + 20 ρ . h = ρ. ρ . v 1
v 1= 4.47 √ h
2 1
v=
1 2 P + ρ . g . h= ρ. ρ . g . h + ρ . v 1 2
√
ρ . h 2 P + 20 ρ. ρ
20.U %!> &# &!3#-$ !$# %# %' 6'$' &$#'$ '+' &# -'# ( %# !%-$' # ' )!+$' 11. S6+' < #%-'4# %! $!((!>. ' S! K 1.00 , #(#-$# ' $'6!&# &# < &# %'!&' # # #F-$# &# %!> 4 9Q 6'%'$=' %!; 9C3 #% ' !!-'(!> # ' '-$' &# ' 6'$-# %6#$!$ &# %!> %4$# ' %6#$(!# &# '+'; 6'$' # # < &# =!& %#' (-!, ' 6$#%!> # ('#$ ' &# ' 6$#%!> &# "'6$ &# =!&. h =1 m
5 =?
g=10
A6!('% ' #('(! &# B#$! B#$! ' % 6-% 1 2. P1= P2= Patm 2 1=h1 =h 6 2 2=0 % ,'vel ,'vel dere de re$er $ere,c' e,c'a a v 1= 0 v 2= v P1+
1 1 2 2 ρ∗ v 1+ ρg 2 1= P2 + ρ ∗v 2 + ρg 2 2 2 2
v =√ 2 g h1 v =4.47 m / s
