INSTITUTO TECNOLOGICO DEL ALTIPLANO DE TLAXCALA
5° “A”. INGENIERIA EN AGRONOMIA
MATERIA; HIDRAULICA
INVESTIGACION: HIDROSTÁTICA, PRINCIPIO DE PASCAL, DISTRIBUCION DE PRESION Y PRINCIPIO DE ARQUIMIDES.
Presenta:
MARCO ANTONIO TEHUACATL ALAMIHUA
“VIDA, TIERRA Y CIENCIA”
INDICE INTRODUCCION............. INTRODUCCION............................ ............................. ............................. .............................. ............................. ............................. ............................. ......................... ........... 3 1.4.1.4.- ESTUDIO Y APLICACIÓN DE LA HIDROSTÁ HIDROSTÁTICA........................... TICA......................................... ............................. ............................... ................ 4 1
1.5.- ECUACIÓN GENERAL DE LA HIDROSTÁTICA:............................................................................4 1.6.- PRINCIPIO DE PASCAL............................................................................................................. 7 1.7.- EMPUJE SOBRE SUPERICIES PLANAS Y CUR!AS:................................................................... " 1.".- PRINCIPIO DE AR#UIMIDES:.................................................................................................1$ CONCLUSION:............................................................................................................................... 14
$
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
3
1.4.- ESTUDIO Y APLICACIÓN DE LA HIDROSTATICA D&/+0+9/: L2 &'(<02 *& )+*,' &'()*+2 %2' 0,/*+0+,/&' *& &)+%+;+, *& %,' )+*,' &/ &8,', 0)2/*, '& (2(2 ',%, *& %>)+*,' '& *&/,+/2 +*,'(<02. D&'*& &% 8)/(, *& +'(2 *& +/=&/+&>2 0++% &' ' +8,(2/(& &% &'()*+, *& %,' %>)+*,' &/ &8,', )& *& %,' =2'&' 8, %, 0)2% 2)> '& 2 )/ 2, +/028+? &/ %,' %>)+*,' &/ 82<0)%2 &/ &% 2=)2. A8%+020+9/: 2 C2%0)%, *& %2' )&@2' 20()2/(&' 2% +/(&+, *&% )+*,. ; C2%0)%, *& %2' )&@2' 20()2/(&' ',;& ')8&0+&' ')&=+*2'. 0 C2%0)%, *& %2' )&@2' *& ,(20+9/.
1.5.- ECUACIÓN GENERAL DE LA HIDROSTÁTICA: S& 0,/'+*&2 +*&2%&/(& )/ &%&&/(, *& )+*, &/ ,2 ,(,?*+02 0,/ *+&/'+,/&' * * *@F *,/*& %2 *&/'+*2* &' ρ %2 8&'+9/ p. H2;+?/*,'& &%&=+*, )/ '+'(&2 *& 0,,*&/2*2' 0,/ &% && *&% '+'(&2 *& (2% 2/&2 )& %2 8&'+9/ '& +/0&&/(& &/ 2=/+()*&' *+&&/0+2%&' =&/&& %2' )&@2' )& '& ,;'&2/ &/ %2 =)2
S,;& %2' 022' *&% (+&*, ,8)&'(, %2' 8&'+,/&' '&/ &'8&0<2&/(&: 4
p +
∂ p ∂ x
p +
dx F
∂ p dy ∂ y F
p +
∂ p ∂ z
dz
H2;+?/*,'& *&'8&0+2*, +//+(?'+2' *& ,*&/ ')8&+, 2% 8+&,. S&2
F =¿ L2 R&')%(2/(& *& %2' )&@2' &(&+,&' , )&@2 T,(2% &(&/2 8, )/+*2* *& 2'2
)& ')8,/&,' 28%+02*2 &/ &% 0&/(, *& =2&*2* *& %2 2'2 * *&% &%&&/(, *+&&/0+2% ,(,?*+0, *& ,%)&/
d ∀= dxdydz .
E' *&0+
F = X i + Y j + Z k
:
(ξ)
D9/*&: )&@2 8, )/+*2* *& 2'2 *&;+*2 2 %2 +/&0+2 )& '& ,+=+/2 8, %2 20&%&20+9/ &(&/2 2% )+*,F &' )/2 )&@2 '+02. Y K ',/ ')' 0,8,/&/(&'. T2;+?/ '& %& *&/,+/2
20&%&20+9/ &(&/2
( ⃗a )
.
C,, &% &%&&/(, *+&&/0+2% *& )+*, '& &/0)&/(2 &/ &)+%+;+, '& &+02 &/ 02*2 &&
∑ F i =φ
0,,*&/2*,: C,/*+0+9/ *& &)+%+;+, E/ &% && Y:
(
pdxdz − p +
pdxdz − pdxdz −
)
∂p dy dxdz + Yρdxdydz= 0 ∂y
∂p dydxdz + Yρdxdydz= 0 ∂y
∂p dydxdz =Yρdxdydz ∂y
5
∂p = ρY ∂y E/ &% && :
(
pdydz − p +
)
∂p dx dydz + Xρdxdydz= 0 ∂x
pdydz − pdydz −
∂p dxdydz + Xρdxdydz =0 ∂x
∂p dxdydz = Xρdxdydz ∂x ∂p = ρX ∂x
E/ &% && K:
(
pdxdy − p +
)
∂p dz dxdy + Zρdxdydz =0 ∂z
pdxdy − pdxdy −
∂p dxdydz + Zρdxdydz =0 ∂z
∂p dxdydz = Zρdxdydz ∂z ∂p = ρZ ∂z
6
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
7
D&*)00+9/: E/)/0+2*, *&% 8+/0+8+,: %2 8&'+9/ )& '& &&0& ',;& %2 ')8&+0+& %+;& *& )/ %>)+*, '& (2/'+(& 8, &% +', &/ (,*2 *+&00+9/ '&/<*, +=)2 1. +=)2 1: &0+8+&/(& 0,/ 2+2' ;,02' 02*2 )/2 0,/ ') ?;,%, (,*2' *& *+'(2 ')8&+0+&.
+=)2 $: P&/'2 +*)%+02
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
1.7.- EMPUJE SOBRE SUPERFICIES PLANAS Y CURAS: S)8&0+&' P%2/2': A %2 )&@2 0,/ %2 )& &% 2=)2 20(Q2 ',;& %2' 82&*&' *&% &0+8+&/(& )& %2 0,/<&/& '& *&/,+/2 &8)& +*,'(<0,. E% EH &' +=)2% 2% 8,*)0(, *&% &2 *& %2 ')8&0+& 8, %2 8&'+9/ )/+(2+2 &/ ') 0&/(, *& =2&*2*. C&/(, *& 8&'+,/&':
"
EL CENTRO DE PRESIONES NO COINCIDE CON EL CENTROIDE UERKAS SOBRE SUPERICIES PLANAS
SUMERGIDAS
M2=/+()* *& %2 &')%(2/(&: ℎ
D,/*& &' %2 )&@2 &')%(2/(& *&% 8+'2 *& 8&'+,/&' A &% &2 *& %2 ')8&0+& (&'(2*2 %2 8,)/*+*2* &<02% *&% 0&/(,+*& *& %2 ')8&0+&. S+ '& *&/,+/2 PG 0,, %2 8&'+9/ &/ &% 0&/(,+*&:
PG PG A %2 )&@2 &')%(2/(& *& %2 8&'+9/ &&0+*2 ',;& )/2 ')8&0+& 8%2/2 &/ &% +/(&+, *& )/ %>)+*, &' &% 8,*)0(, *&% &2 8, %2 8&'+9/ &/ &% 0&/(,+*&.
yp =
I 0 + y Ay
D,/*&: Y8: &' %2 8,)/*+*2* *&% 0&/(, *& 8&'+,/&' I: &' &% ,&/(, *& +/&0+2 /&)(2 A: &' &% &2 *& %2 ')8&0+& Y: &' %2 8,)/*+*2* *&% 0&/(,+*& &/ %2 0,,*&/2*2 .
1
S)8&0+&' 0)2': E/ &% 02', *& ')8&0+&' 0)2' /, &' 8,'+;%& ,;(&/& *+&0(2&/(& %2 &')%(2/(&. E' /&0&'2+, ,;(&/& %2' 0,8,/&/(&' ,+@,/(2% &<02% *& %2 &')%(2/(&.
C,/'+*&2/*, &% *+2=22 *& 0)&8, %+;& *& %2 =)2: E/ %2 *+&00+9/ ,+@,/(2%.
E' *&0+: L2 0,8,/&/(& ,+@,/(2% *& %2 &')%(2/(& *& 8&'+,/&' *& 0)2%)+& ')8&0+& &' '+&8& +=)2% 2 %2 &')%(2/(& ',;& %2 8,&00+9/ &<02% *& %2 ')8&0+&. L2 &')%(2/(& &'(2 %,02%+@2*2 ',;& &% 0&/(, *& 8&'+,/&' *& %2 ')8&0+& 8,&0(2*2. E/ %2 *+&00+9/ &<02%:
11
L2 0,8,/&/(& &<02% *& %2 &')%(2/(& *& 8&'+,/&' &/ 0)2%)+& ')8&0+& +=)2% 2% 8&', *& %2 0,%)/2 *& 2=)2 ',;& %2 ')8&0+&. L2 &')%(2/(& &'(2 %,02%+@2*2 ',;& &% 0&/(,+*& *& %2 0,%)/2 *& 2=)2. L2 0,8,/&/(& ,+@,/(2% *& %2 )&@2 &')%(2/(& *& %2 8&'+9/ +*,'(<02 &' '+&8& +=)2% 2 %2 8&'+9/ (,(2% ',;& %2 8,&00+9/ &<02% 2 %2 8&'+9/ (,(2% ',;& %2 8,&00+9/ &<02% *& %2 ')8&0+&. L2 0,8,/&/(& ,+@,/(2% *& %2 )&@2 &')%(2/(& '& %,02%+@2 &/ &% 0&/(, *& 8&'+,/&' *& %2 8,&00+9/ *& %2 ')8&0+&. L2 0,8,/&/(& &<02% *& %2 )&@2 &')%(2/(& *& %2 8&'+9/ +*,'(<02 &' '+&8& +=)2% 2% 8&', *& %2 0,%)/2 *& 2=)2 ',;& %2 ')8&0+&. L2 0,8,/&/(& &<02% *& %2 )&@2 &')%(2/(& '& %,02%+@2 2 (2?' *&% 0&/(,+*& %2 0,%)/2.
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
1$
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
13
CONCLUSION: E% &'()*+, *& %2 +*,'(<02 &' ) +8,(2/(& 822 0,/,0& &% 0,8,(2+&/(, *& %,' )+*,' 2 ;2'& *& )& /, &'(/ &/ ,++&/(, 8&, &/ &'(& 02', %2' 8&'+,/&' )& &&0&/ ',/ '+=/+02<2' &/ &'(& (&2 &+'(&/ %&&' *& 0+&/X0,' )& '& 2/ *&*+02*, 2 (2% &'()*+, *& &'(,' )+*,'. C2;& &/0+,/2 )& %,' 2)(,&' %& *+&,/ '&=)++&/(, 2 %2 &0)20+9/ *& %2 +*,'(<02. E+'(& %2 2@9/ *& )& 2 2, 8,)/*+*2* 2, 8&'+9/. C,, %,' )+*,' /, '& &/0)&/(2/ &/ ,++&/(, &/(,/0&' &'(,' 0,/'&2/ )/ &)+%+;+, &/ (,*2' %2' *+&00+,/&'.
14
LITERATURA CITADA:
H+*)%+02 &%&&/(2% R. E*)2*, A(&2=2 T,2 C28+/=, M?+0,. H+*)%+02 G&/&2% N,(2' *&% 0)',. D. P,%+,8(, . M2X/&@ A)'(+2 UDLAP. 8':&'.'0+;*.0,*,0)&/($5157$15P+/0+8+,-*&-P2'02% 11--$16 8':&'.'0+;*.0,*,01"3$$E0)20+,/-)/*2&/(2%-*&-%2-H+*,'(2<02 11--$16
15