소방 유체 역학 강의노트 -...
TRANSCRIPT
-
- 1 -
( http://web3.gwangju.ac.kr/~tjyu/ )
-
- 1 -
1 ()
-
- ,
- (shearing force)
(deformation)
- (normal stress) , ()
,
(stress)= : ,
(shearing force) : () ,
.
A A
F1 :
F2 :
= =
-
(viscous fluid) : (=, )
(inviscous fluid) : (=, )
-
(incompressible fluid) : (p) (V), (, )
(compressible fluid) : (, ), (=V)
-
(ideal fluid), (perfect fluid): ,
constant,
(real fluid):
-(dimension):
175cm A, 70kgf B ?
()
3
- 3 MLT : (M), (L),(T) (SI ) SI : System International d'Unites
- 3 FLT : (F), (L), (T)
-
- 2 -
LMT LFT mks ()
(L)(A)(V)
LL2
L3
LL2
L3
mm2
m3
(T)(v)
(a)(,)
(Q)
TLT-1
LT-2
L2T-1
L3T-1
TLT-1
LT-2
L2T-1
L3T-1
sm/sm/s2
m2/sm3/s
(m)
(F)
()
(, )
(,)
(,)
(K)
,(p, ())
, (E)
(Power)
M
MLT-2
L-3M
ML-2T-2
ML-1T-1
MT-2
ML-2T-1
ML-1T-2
MLT-1
ML2T-2
ML2T-3
FL-1T2
F
FL-4T2
FL-3
FL-2T
FL-1
FL-2
FL-2
FT
FL
FLT-1
kgfs2/m
kgfkgfs
2/m4
kgf/m3
kgfs/m2
kgf/m
kgf/m2
kgf/m2
kgfs
kgfm
kgm/s
,
TL
[]=[/]=[LT ] []= MLT F
-(unit) :
: mm, cm, m. km...
: g, kg, ...
: sec, min, hr, day, ...
CGS : cm, g, s(=sec)
mks : m, kg, s(=sec)
,
-=(specific weight, , ) : (unit volume) (weight)
g :
L
F
http://blog.daum.net/kinhj4801/15960589 http://scale0114.tistory.com/91
: SI : Nm (N : Newton, N kgmsec) : m
kgf
(4) w Nm(SI ) kgfm(), 1kgf =1kg9.8m/sec2=9.8N
-
- 3 -
EX kgfsec . mkg?
kgfsm
sec sec
mkg
EX Nm, 13.55 , ?
VWV
mg , Nm msec
msec
Nsec
sec sec
- (density, , ): (Mass)
g
: L M ML
kgm(SI ) kgfsec()
w wg w g
wmsec
sec
[2] (specific volume, vS) : , vs m
V
, ( : [ ])
[4] (specific gravity, s) : ,
s
w
w
: (Dimensionless)
- ,
-
- 4 -
dp
V V-V
V
-
: or (compressibility)(/N /kgf )
( )
K : (bulk modulus of elasticity): (N/ kgf/ )
( )
mN EX . ?
(, cmkgf.)
dP
VV
cmkgf
kgfcm
EX , kgfcm m (K) ?
K
dpV
Vkgfcm
kgfcm
(Viscosity) http://www.youtube.com/watch?v=x0Y9XJvHwD0http://www.youtube.com/watch?v=7xb5i1SR-MQ https://www.youtube.com/watch?v=XX0JdlXZmWs
()
uA
uBy
- =
(): ([F/L2]) : ([L/T])
(): ([??]) : ([L])
: ([1/T])
-
- 5 -
-
dydu
L LTFL
FTL
F TL MLT TL MLT - : g/cmsec(=Poise), cP=centi Poise, Pasec(N sec/)
- : (kinematic viscosity, , )
: []=FL T FTL
L T ML MLT
L T - : cm2/sec =stokes, /sec
-
:
: (http://blog.naver.com/gangplank/40035350121)
EX , . ?
, stokes cmsec,
cmsec Ncm
Nseccm
cmsec Nseccm NseccmEX ( u ms y m) mm
. ( Pasec.) ,
m
sec
Pasec sec Pa
-
- 6 -
EX mm Pasec . ms .
Pa
(surface tension)
-
,
) , ,
- () : : Nm , kgf/m- :
R p
R
: R : : =
-
- 7 -
0.0756 0.0742 0.0728 0.0695 0.0644
0.0733 0.0720 0.0706 0.0675 0.0626
0.474 0.473 0.472 0.468 0.463
0.0240 0.0231 0.0223 0.0206 0.0182
- 0.0236 0.0228 0.0210 0.0183
http://www.youtube.com/watch?v=wOOY1szbcX4 http://www.youtube.com/watch?v=sLI_JKNYXVU
-
-
(cohesion)(adhesion)
(, )
>
(, )
(: , : )
- (capillary tube), (meniscus)
h
h h
(a) (b)
T=
d
T
h
- =
= =g d h
cos cos gh
d dcos
-
- 8 -
(, )
(, )
ALPHA NU
BETA XI(KS-EYE)
GAMMA OMICRON
DELTA PI (PIE)
EPSILON RHO (ROW)
ZETA SIGMA
ETA TAU(TAU) ,
cos
cos : , !!
: (d: )
: :
: : (theta)
EX 1mm ?(, Nm.)
cos
m
http://www.youtube.com/watch?v=Ks4VuXTTKmo
- (equilibrium state)
- (vapor pressure) .
- ( https://www.youtube.com/watch?v=NEhRSFmqsJU )
1.03kg/
0
time= 0 time=
6.6 12.7 35.5 100
(kgf/) 0.01 0.015 0.05 1.033
-
- 9 -
THETA UPSILON
IOTA PHI(FEE)
KAPPA CHI(K-EYE)
LAMBDA PSI (SIGH)
MU OMEGA
-
- 10 -
2 ()-:
- : ( )
- : , ,
(pressure)- :
- (SI : 1m2, 1)
Pa
-
SI : Pa(pascal)N/, MPa Pa Nm : kgf/, kgf/
mm Hg, cm Aq, m H2O
( atm) )
-
p
dz
p gdz
p gdxdx
pa:
pahdpgdzpa
phdp
hgdz
ph pa gh hph pah
: h
: (= ), 0 : ( : 1000kg/) g : : ( : 9,800N/, 1,000kgf/)
-
- 11 -
1atm=760mmHg =10.332m H2O(m Aq)= 101,325N/m2=101.3kPa=1013.3hPa=1.013bar=1013.3mbar
=1.0332kg/cm2=10,332kg/m2=1.013bar=101,300.8Pa(N/m2)
=101.3kPa(=kN/m2)=0.1013MPa(MN/m2)
1.0332kg/cm2=0.1013MPa(MN/m2) 1kg/cm2=0.098MPa0.1MPa(=106 N/m2)
(pa): http://www.youtube.com/watch?v=8vMSyQkCECw
(a) (b)
hm=76cmhw=10.332m
atm mm Hg m Aqpa h kgfm mkgfm kgf kgfcm kgfm kgf
kgmsec
sec
Nm Pa hPa bar m bar
1.0332kg/cm2=101,325N/=101.3kPa=0.1013MPa 10m H2O=1kgf/cm2=0.098MPa0.1MPa
EX kgfcm . p h kgfm kgfm
kgfcm kgfcm
p h Nm Nm Pa papa
Kpa Kpa
(absolute pressure) (gauge pressure)
- ( ) : ( 0 )
- ( ) : (=0)
6 (Six Principles of Fluid Pressure)
.
-
- 12 -
EX 2 ,
.
EX
( )
? ,
.
O Moment
.
(confined fluid)
. pascal (pascal's principle) .
P , h
.
, (Pascal )
P
A
p=P/A
h
:A1:A2
F1
F2
h
(h )
( ( )
. http://www.youtube.com/watch?v=A3ormYVZMXE
-
- 13 -
(open vessel) (liquid) .
(open vessel) . ,
.
EX
. ? (,
.)
p h kgfm m kgfm kgfcm
EX . .
: =
-
:
-
pghh
EX
,
. (
),
. ( 25 9,800N/
)
m m m mNm
-
- 14 -
h p
- (Bourdon)
, ()
.
- (manometer)- (Piezometer tube)
-p h- (manometer)-U
manometer
(gauge fluid) (manometer fluid)
pC pB
- (manometer)- (differential manometer)
U
pa pbpa pA hapb pB mhbhcpA pB mhb hc ha
-
- 15 -
EX U , ,
, ?
pA pagh gh pagh h msec m
kgmsec
EX , 120mm, 300mm . (
.)pA gh pB gh gh h
EX (pipe orifice) 0.81 .
?
p ppA pB
< >
- : p h- : :
O
a
b
c d
e
() : P pA hA hA : ()
-
- 16 -
p h
:
A
()
- :
- dA dP hdA - A
P dP A hdA AhdA hGA (= )hG : A hGA AhdA : dA 1 moment!!
O
dA
G
C
A
h
C
dP
P
hGhc :
EX 3m 2m2m .
2m
B
A
P
3mhc
-
- 17 -
O
G
C
dA
S
SG
SC y
x
S
z
x Od Acos c
za
b
Asin
P Pz
Px
dA
dP zdA Ssin A
P zdA sin sin , sin , P hGA (=)
P Px P sin sin ( )
P Pz P cos cos ( )
P Px Pz
Ax
S60
G
C
hGhC
P
4m
B
4m 3m
. AB
.
P hGA ton
- ()
-,
ABC
A
B
C
P
P
PH
PV
FH
FV
FBC
FAC
WABC
-
- 18 -
FH FBC PH - AB BC ( )
FV FAC WABC PV - AB ( )
(buoyancy) https://www.youtube.com/watch?v=ijj58xD5fDI
z
M
I
L
J
P2
K
N
N'M'
P1
P1
P2
B
W
- :
- (): MIN - MKN
= ( )
:
: ()
- W = W-B(Archimedes )
- : W()=B()
-
- 19 -
http://www.youtube.com/watch?v=KqqtOb30jWs&feature=related
http://www.youtube.com/watch?v=NplrDarMDF8&feature=related
http://www.youtube.com/watch?v=XOLl2KeDiOg&feature=related
3 ()
< > Reynolds
(laminar flow) (turbulent flow)
(laminar flow) (turbulent flow) >
(pressure drop) (loss head)
Reynolds (Number)
-
visceus for inertia for
Re : Reynolds () :
: : :
-
- 20 -
EX mm cms cms Re ?
, msmms
EX ms mm . .
( )
m ms
ms msec
m ms
- : Re ( 2320)- :
- : - (upper critical velocity) :
- (lower critical velocity) : (
Reynolds=2100)
- () (steady flow) : ,
- () : , https://www.youtube.com/watch?v=io87_tffZt4
- (): ,
- () : ,
- (path line):
- (stream line):
- (streamtube): http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/cvanalysis/node8.html
2 v ds
ds
dx
dy
dx uxdt dy vydt uxdx vy
dy dt ux : x vy : y
-
- 21 -
EX 2 V =-2xi +2yj (2,1) ?
udx v
dy xdx y
dy ydx xdy , xy xy C , xy C (2,1) C , xy
wz : z
3 uxdx vy
dy wz
dz dt ( )
(i, j, k x,y,z ) ,
(s) .
(dt) ( )
- : ( , total acceleration)
- : (, convective acceleration)
- : (temporal acceleration)
- : (uniform flow) - :
- : (steady flow) - :
1 (continuity equation) :
: A2: v2
ds2: dt
12
: A1: v1ds1: dt
ds1 ds2
1, 2
-
- 22 -
dtdsA dsA
AV AV
, VA VAM ([M/T], ), g gvA gvAvA vA G ([F/T], ) ( ) vA vA Q ([L3/T], ) () , .
EX 50cm 20cm 4KN/sec . (, .)
kNsec , kNm kgfm,
NmNsec
msec
msec,
msec
1 Euler , Bernoulli ( )
ds
p
psp ds
dAdz
s
W=g ds dAds : , dA: , p: , dV:
W : (dV) , z: , v:
http://www.youtube.com/watch?v=RRj_I9ckp-Y&feature=related
http://www.youtube.com/watch?v=gk6rNFVc1Gs
https://www.youtube.com/watch?v=oUd4WxjoHKY
http://www.youtube.com/watch?v=xcZckKUmD4w&feature=related
http://www.youtube.com/watch?v=fgHvC55AKig&feature=related
S
mdtdv dV vs
vtv pdA ps
p dsdAWsin, dV dAds, W gdsdA , sin ds
dz
-
- 23 -
dAdsvsvtv s
p dsdA gdsdAdsdz
(tv )
vdsdv ds
dp gds
dz vds
dvds
dp gds
dz
vdvdp gdz dg
v
dp dz (1 Euler )
gv
p z H
(Bernoulli )
gvp z
(, , ) .
Bernoulli
(ideal fluid):
( )
(steady flow, )
(stream line)
Bernoulli
H
z1 z2
p2/
p1/
v12/2g
v22/2g
EL: Energy Line
HGL: Hydraulic Grade Line
v1
v2
- (HGL: Hydraulic Grade Line)
()
- Energy (EL: Energy Line)
"HGL(+)+"
-
- 24 -
EX d1=40cm d2=80cm . 1
=4m/sec, p=98kPa 2 p ?
,
ms
kPa
EX P2, v2, .(, kgcm, ms, cm, cm.)
cm m, cm m, s
ms
, m, kgcm kgm
m kgm kgcm
Bernoulli -
(head loss)
h h1
h2
A B
gv
(h=0) E.L(Energy Line)
( ) E.L(Energy Line)
( ) HGL
pg
vz
pg
vz h m
: (loss head)
-
- 25 -
EX 100mm, 50mm . A, B 4.5kgf/ 4.0kgf/, 100mm 1m/sec. A-B ?(, 9.8m/sec2, .)
rP g
vA r
P g
vBH
m
EX 200mm 0.2m/sec 300kPa 100mm kPa?(, 2m.)
v dd
v
ms, rp g
v z r
p g
v z H , z z
, p
kPa Bernoulli - Torricelli
A, B Bernoulli
gvA
pA zA g
vB
pB zB ,
vA , pA pB (), zA zB h g h g
vB
, vB gh
Bernoulli - (venturi meter) :
gv
p z g
v
p z ,
p
p h , Av Av
v AAA gh ,
Bernoulli - (pitot-tube)
:
1 2
h
v a
gv
p z g
v
p z
-
- 26 -
z z p a p a h v
gv a z g
a h
zv v gh
EX (nozzle) ?
msec
msec
-
- 27 -
F
Fx
Fy
4
, nozzle
1
:
F :
F m a mtv mt
v v Ft m v v :
F :
Ft : ()mv :
:
- (
)
- (
)
2 :
Fxt mvcos cos cos cos Fyt mvsin sin sin sin
(2) :
: (momentum flux)
, :
:
F :
x : Fx pAcos pAcos Fx Q vx vx Q vcos cos Fx pAcos pAcos cos cos
y
Fy pAsin pAsin Fy Q vy vy Q vsin sin W : ( )
Fy Q vsin vsin sin pAsin : F Fx Fy
b'
ba'
a
v1
F
Fx
Fy
v2
-v
v2-v
p1
p2
-
- 28 -
(2) :
Fx Q Vx Vx Fy Q Vy Vy
,
: ()
:
: (
)
()
,
Q
max
max
max
max
max
max
max
max
max
max
max
EX h max
.
v
dy
yh
vmax
max
-
- 29 -
Nozzle
p1 v1 v2
F
A1 A2
p
EX 1m 90 3m/sec
.
100kpa .
.(, .)
m,
msx :
Fx pAcos pAcos Fx Q vcos cos Fx pAcos pAcos
cos
cos
cos
y : Fy pAsin pAsin FyQ vsin sin sin
sin sin sin
N kN
kN , sin
sin
-
Fx pAcos pAcos Fx Q vcos cos
Fx Acos Acos Fx Q vcos cos
F
-
- 30 -
-
EX 4-7 ms , mm ms () .
F Avu N
-
- 31 -
5 ()
h
h1
h2
A B
-
( 0)
:
: D(=2), :
: max : 0
:
-
, ()
r
,
,
( )
,
: r=0 () max : r= ()
-
- 32 -
-
umax
u
dr
rro
dr
r
r dQ
Hagen Poiseuille 4 , ,
-
max
max
- Hagen-Poiseuille
( ) - =
-
: , ,
( f: ) :
(Darcy-Weisbach )
-
- 33 -
EX 50mm, 1.2km min ? (, 0.92, 0.056 Pasec.)
msec
Reynolds
()
Pa kPa
`
h pN
kPa m ()=
40cm 8m/sec 1000
kPa? . 0.1Pasec.
3 ?
1/81
EX 2cm 30/sec 1m . sec)
Sol)
(!!)
,
-
- 34 -
- (, major head loss) :
- ( , minor head loss): , , ,
, , (cock),
(union), (Tee)
(major head loss) :
-
(Darcy-Weisbach ) : f Reynolds
h:
:
:
:
Re: Reynolds
-
(Darcy-Weisbach ):
(f : Re (De
) )
e( )D
D :
e :
:
- (Prandtl):
log
- (Nikuradse):
log
- (colebrook & White) :
log
- ( ) ( ):
-
- 35 -
-
- 36 -
(, minor loss)http://www.youtube.com/watch?v=TdFdhUYO47I&feature=related
(, , , , ), (minor head loss) : ()
-
: (), ( )
: - fitting()
- Darcy-Weisbach
-
()
( )
:
:
:
- : ,
- , Bernoulli
-
- 37 -
gg
gg
- Bernoulli h
g
,
(exit loss)
,
EX mm mm s ?
ms
ms
m JN
-
-
, ()
< >
-
- 38 -
< >
ge
,
: , :
-
,
()
, : , sin
sin
-
- 39 -
, :
(sluice valve)
>
(glove valve)- :
mm
(butterfly valve)- :
-
- 40 -
(flap valve)
30 mm, 0.022 ( k=10) (k=1.8)
(equivalent length) m?
< >
(S : wetted perimeter)
-
-
-
()
DH
B
(, Hydraulic radius)
-
-
-
- D
,
,
- H, B
, ,
-
- 41 -
V Lhfg D f
g D L
h ,
(Chezy )
, D : R : ()
f : C : I : (=)
Chezy Manning V n
R I , ( )
Williams-Hazen V CR I (, ) Manning
n n
,
()
()
0.01~0.012
0.01~0.013
0.01~0.013
0.012~0.014
0.014~0.018
()
()
0.012~0.014
0.013~0.015
0.012~0.013
0.014~0.016
0.011~0.014
mm ()
mm mm
mm ( )
mm ( )
mm mm ( ) mm mm mm ( ) mm mm ( ) mm ( ) mm mm mm mm ( )( ) mm
Hazen-Williams
, ,
-
- 42 -
, ,
, Q : (/sec) : (m) : (m)
C : : (m)
: : m, Q: L/min, : mm, : :
-
-
. 50mm 260L/min . 100m ()?
, 100
,
minsec
, ,
d, p
(), (min ), (mm) p(kg/)==> p(10000kg/), Q(/sec)100060==> Q(L/min), d(mm)==>d(1/1000m)
sec
min
( : )
( ), (min ), (mm)
-
- 43 -
EX 13mm 230kPa 10
?
(1) 230kPa=0.23Mpa
min minmin
(2) =
sec
=secminminsec
EX 40mm, 300L/min 4kg/ 30m
? (, 1m
C 120 )
kg kgfcm
(Parallal pipes)
-
-
-
-
(, series pipes)
-
-
-
- 44 -
- =
: , ,
,
H Q
EX , m Q . , (=0.5), (=1.129),
(=7.5), (f) 0.024.
g
g
g
g
g
() () () () ()
g
sec,
sec sec
-
- 45 -
EX . , Q , Q .(10)[] 1. .
P C D Q
= 1m (kg/) = (L/min) C : =120 = (mm) 2. 27mm3. 25mm (90) 0.9m.4. A D (Tee)
10m F
2m25mm
200L/
3m
6m
CB
E
D
7m
A
, , min , min
-
- 46 -
6 http://www.simerics.com/simulation_gallery_roto_pump
: ,
: ,
(fire pump):
(Impeller)
(Impeller)
- (centrifugal force) ,
- ,
.
- (casing)
- (Impeller)
- ,
- : , , (bearing), (packing and sealing)
-
47
-
(volute pump): .
(turbine pump): .
,
-
(single suction pump):
(double siction pump): .
-
(single stage pump) : 1
(multi stage pump) : 2
- ,
-
48
: 0 ()
: 0
: %
(: actual head): +
-
- (actual suction head):
- (actual discharge head):
( : total head)
- =+
:
- ,
: (=) , :
, : ,
y =
-
49
EX ?
(=)
= (0 )+ +
mmHgmmHg
m
kgfcmkgfcm
m
m m
EX 38m, 2m
. 40cm,
?
m , m (), m , , m
: :
: :
: : ( )
: :
: :
: :
() ()()
()
()
-
50
,
: m
: S
(Force): (: N=kgm/sec2)(Work): ( : J=Nm=kgm2/sec2)(Power)
( : W=Nm/sec=kgm2/sec3)
: W 1,000W = 1 kW
=1Ps=75kgf m/sec=735W =1HP=76kgf m/sec=746W
:
-
-
(1,000kg/m3)
(m3/sec)
(m/sec2)
(m)
secsec sec
Q min
1 =1HP=746W=0.746kW
:
: (3585%), (m3/sec)
(m)
, : (1.1~1.2)
-
51
1.1
1.15~1.2
EX (HP) .
HP : mmin, : m , :
40HP
EX sec, mAq, , Kw?
sec
(Specific speed) :
- ()
-
: (rpm) :(mmin ) : (m) :
1/2
1
,
EX 80m,, 15/min, 1800RPM . 1 2 ,
1 .
1
2
1
(Affinity law)
(Affinity)
( ), ( ) (), ( ), ( )
-
-
52
-
-
, : (rpm), : (mm)
EX m ms . , .
m
(water hammer) http://www.youtube.com/watch?v=E6NIA4LxPPw&feature=related
http://www.youtube.com/watch?v=M2tekIXcjkw&feature=related
http://www.youtube.com/watch?v=6hVUeNp3o3M http://www.youtube.com/watch?v=X9UbzcanuDk&feature=related
, ,
.
,
http://www.plumbingmart.com/water-hammer-in
formation.html
-
-
- , ,
-
- ,
- (, surge tank)
- water hammer cusion
-
- fly wheel .
http://ssbayup.blogspot.com/2010_09_01_archive.html
-
53
http://www.shock-guard.com
http://kotraseal.kotra.or.kr/
http://www.indiamart.com/
(, cavitation) https://www.youtube.com/watch?v=NEhRSFmqsJU
- ,
()
- () :10.33m
- : 6~7m
-
-
- (, , )
-: , , ( , )
-:
(NPSHav, available Net Positive Suction Head) (NPSHav)
- ( )
- ()
NPSHav- NPSHav : ,
-
54
NPSHav Hav PaHs hl
Pvp()
NPSHav Hav PaHs hl
Pvp()
Hav : (NPSHav)Pa : ( : kgcm)Hs : ( ), (), ()Pvp : (kgfcm ) : (kgfm)hl: (m), -NPSHav (), (, , )
NPSHav - .
- : ,
- , .
-
-
- ( )
- .
-
-
-
55
EX .
NPSHav .
kgfcm. min. kgfcm . kgfcm, gcm
.
NPSHav
: kgfcm kgfcm kgfm : kgfm kgfcm kgfm
: kgfm gcm kgfm : kgfm kgfcm kgfm : m m NPSHav
m
EX NPSHav . 20, 0.6m .
NPSHav
m