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Mecânica de Fluidos Ambiental 2015/2016
Pratical Lecture 3
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
A figura representa um reservatório pressurizado, com fluidos em repouso (Mercúrio com massa volúmica de 13.6 *103kg/m3 e água com 103kg/m3). Na parte superior do reservatório encontra-se ar à pressão absoluta de 180kPa. a) Quando o manómetro A indica uma pressão absoluta
de 350kPa, quanto vale h? (1 val)b) Nessas condições quanto vale a pressão relativa
indicada pelo manómetro B? (considere a pressão atmosférica igual a 1 bar) (1 val)
c) Quanto vale a força exercida sobre a placa que separa o mercúrio da água? (2 val)
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Mecânica de Fluidos Ambiental 2015/2016
a)
m.*.*
.*.**.*h
g.*gPP
h
h*g.*gPP
h*gPP.*gPP
OH
HgsupA
OHHgsupA
OHsuperfaceint
HgInterfaceA
4768910
80891061310180350
8080
80
3
332
2
2
b) Altura da coluna de água: 7.27m
2
333Re
/71.071.0)8.047.6(*8.9*1010*18010*180
)8.0(*2
cmkgbarPP
hgPP
B
B
OHlSupB
c)A força resulta da distribuição de pressão hidrostática. Se a placa tivesse água dos dois lados a resultante da força seria nula. A força é devida à diferença de densidade do mercúrio e por isso exerce-se na superfície de 80 cm de profundidade. A diferença de pressões entre os dois lados da placa à profundidade do centro de gravidade e a força sobre a placa são respectivamente:
m/N.*PF
m/N/.*.**.P
CG
CG
39514804939228089101613 23
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Mecânica de Fluidos Ambiental 2015/2016
BA
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Mecânica de Fluidos Ambiental 2015/2016
BA
Pap
inmin
rlbfNlbf
SFp
FLLFpp
A
A
AA
BB
BA
6
222
10*9.1
10*54.2*5.1*
45.4*200045.4**2000
NFinminPaSpF
B
BBB
989
10*54.2*5.0*10*9.1*2
26
NF
lbfkgLLFF
FLLF
B
BB
BB
989
142.61511*989
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
NFAPFPa
ghP
SG
mh
CG
oilCGCG
oilwater
oil
CG
3
4
4
3
º
10*4.378.0*2.1*10*9.3*
10*9.38.9*10*82.0*89.4**
1000*82.0
89.440sin22.114
Xcp= distance of the pressure center to the beginning of the inclined surface. Ycp is the distance to the gravity center.
mXcmmY
Y
AP
bL
Y
CP
CP
CP
CGCP
6.16.00.115015.0
10*8.3712
2.1*8.0
40sin*8.9*10*82.0
1240sin*8.9*10*82.0
3
3
3
3
3
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Mecânica de Fluidos Ambiental 2015/2016
The momentum of P must balance the momentum of the hydrostatic force.
CG
The hydrostatic force is applied on the Center of Pressure.
CPYCP
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Mecânica de Fluidos Ambiental 2015/2016
The momentum of P must balance the momentum of the hydrostatic force.
CG
The hydrostatic force is applied on the Center of Pressure.
CPYCP
LYbLPP
LYLbLPP
LPYLbLPbLPF
CPCG
CPCG
CPCG
CGHid
21***
2/****2/***
**
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
Fh
Fv
hBC
Fh opens the gate and Fv closes it. The movement of the gate will depend on the momentum.
Neglecting gate thickness:
6
2*2
12*2
**sin*
)2
(*
1.0**2.0*2
2*2*
1
3
BCcp
BCBC
BC
cgcp
cpBC
hh
vv
BCv
BCBCh
BC
hY
hhg
h
gAP
IxxgY
YhFM
FMghF
hghF
hh
mhmh
h
hhh
ghhhhgh
MM
BC
BC
BCBCBC
BCBCBCBC
BC
vh
35.135.0
1.0*2.06
1.0*2.0)62
(*2
1.0**2.0*2)62
(*2
*2*
2
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
Fv
FhP1
P2 The total momentum referred to point O is zero.We have 4 Forces: 2 hydrostatic and 2 weights.
RhbgP
bRgP
bRRgF
bRgF
OHh
OHv
*4
*
*2
*
4*
2
2
1
2
2
2
2
2
122
34
2
1
2
3
2
RL
LL
RbRg
bRgRL
RL
v
OH
OH
h
v
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Mecânica de Fluidos Ambiental 2015/2016
RbRg
bR
gRbRRg
RRhbgRbRg
LFLPLFPLFLFLPLP
water
waterwater
water
hhv
hhvv
2
12sin2
*2
*
2*
34*
4
0*
3
22211
2211
RhR
Rh
R
Rh
RR
RRhR
RhR
water
water
waterwater
3
6
2
32
36
3623
6*
2*
34*
4
Fv
Fh P1
P2
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
NF
FFF
NF
bRhRgF
NF
RhbgbRgF
hv
h
h
v
v
5
22522
53
53
2
10*5.14
6.99.10*10
10*6.93*462*8.9*10
*2
*
10*9.107212*8.9*10
*4
*
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Mecânica de Fluidos Ambiental 2015/2016
Tableshttps://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=fl&chap_sec=&page=&appendix=sections
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Mecânica de Fluidos Ambiental 2015/2016
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Mecânica de Fluidos Ambiental 2015/2016
Spar buoy- bóia de mastro, é uma vara flutuante com um pes na extremidade de forma a uma parte da vara flutuar
2 in = 50mm18 in = 450mm
Newtons de aço
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Mecânica de Fluidos Ambiental 2015/2016