-
Bi ton l tngDng dng 1D khng nht, khng nn
Phng trnh lin tc:
Phng trnh BT ng lng:
Gii chnh xc bng l thuyt
0t
=
( ),0,0V u=
0 onstc =
0ux
=
0px
=
-
Bi ton thc n gin
Dng 1D nht, khng nn
Phng trnh lin tc:
Phng trnh BT ng lng:
Gii chnh xc bng l thuyt
2
21u p u
t x x
= +
0ux
=
0t
( ),0,0V u=
0 onstc =
-
Bi ton thcDng 3D nht, khng nn
Phng trnh lin tc:
Phng trnh bo ton ng lng:
Gii chnh xc bng l thuyt ???
0t
( ), ,V u v w=
0 onstc =w 0u v
x y z
+ + =
( ) 1V V V gradp Vt
+ = +
-
Bi ton thc
Phng php l thuyt
Phng php thc nghim
Him
Ph bin
PP m hnh ha
Thay th vic nghin cu hin tng ca mt i tngtrn nguyn mu bng vic
nghin cu hin tng tng ttrn m hnh c kch thc b hn hay ln hn
Quy lut Nhng tiu chun tng t
-
Bi ton thc
Phn loi cc hin tng nghin cu:
Nhng hin tng v cc qu trnh c th c m tbng cc phng trnh (vd: phng
trnh vi phnchuyn ng ca cht lng trong ng, trong khe hp, )
Tiu chun tng t
Nhng hin tng v cc qu trnh cha c m tbng cc phng trnh.
L thuyt th nguyn
Tiu chun tng tCc h s ca PT dngkhng th nguyn
-
II. Tng t v gii tch thnguyn
2.1. Dng tng t2.2. nh l ca Vaschy-Bukinhgham
-
L thuyt th nguynnh ngha
i lng c th nguyn l i lng m cc gi trbng s ca n ph thuc vo h n v o
lng do ta chn
i lng khng th nguyn l i lng m ccgi tr bng s ca n khng ph thuc vo
h n vo lng do ta chn
V d: Chiu di, thi gian, khi lng, vn tc,
V d: S Reynolds, s Mach,
-
L thuyt th nguynPhn bit n v v th nguyn
Th nguyn: l mt khi nim nh tnh hay l mt tngtru tng. K hiu [..]V
d: [chiu di] = khong cch gia hai imn v: l mt khi nim nh lng. Ch r
quy tc nh lng. V d: n v ca chiu di l m hay mile
: Th nguyn ca x m v x miles l nh nhau[x m] [x miles]: x miles v
x m c chiu di khng bng nhaux m x miles: i lng x miles c th nguyn ca
chiu dix miles [L]: i lng x m c th nguyn ca chiu dix m [L]
V d
-
L thuyt th nguyn
K hay C[]Nhit s[T]Thi gianm[L]Chiu dikg[M]Khi lng
n vTh nguyn
n v c bn n v dn xut (VD: vn tc,
Cc i lng c bn
-
L thuyt th nguynCc i lng c bn
V d: Tm th nguyn v n v
Vn tc (V) Lc (F)
Th nguyn: [L.T-1]n v: m.s-1
Th nguyn: [M.L.T-2]n v: kg.m.s-2 hay N
Khong cch dch chuyntrong mt n v thi gian
nh lut th hai ca Newton:Lc = Khi lng * gia tc
Gia tc: vn tc trn mt n v thi gian
-
L thuyt th nguynCc i lng c bn
Trng hp: cc n v c bn l qu ln hoc qu nh
Thm cc tin t trc cc n v c bn n v miPhn s v bi s
10-6p (micro)10-3mm (milli)103k (kilo)106M (Mega)
Biu thTin t V d: 1 MW = 106 W1 mm = 10-3 m1 pm = 10-3 mm
1 mm2 = 10-6 m2
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2.1. Dng tng t
Hai dng khc nhau c gi l tng t nu davo cc c trng ca hin tng ny c
th suy racc c trng ca hin tng kia bng mt php bini c bn
Cc tiu chun tng t phi bng nhau
iu kin
n: nguyn mum: m hnh
Ren=RemMn=Mm
nh ngha
-
2.1. Dng tng t
iu kin - dng tng t Tng t hnh hc kL: T l tng t hnh hc
Tng t ng hc Tng t hnh hc (kL) v tngt thi gian (kT) (Vn tc, p
sut, )
Tng t ng lc hc Tng t ng hc v tngt khi lng k
( )2n nL Lm m
L Sk kL S
= =
11
1n n n n
T L Tm m m m
T v L Tk k kT v L T
= = =
Ne: Tiu chun tng t Newton hay s Newton
43 2
3 2 2 onstLn n n n n n
m m m m m m T
k kF L L Tk Ne cF L L T k
= = = = =
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2.1. Dng tng t
V d - Tng t hai chuyn ng phng Phng trnh lin tc:
Phng trnh Navier-Stokes:
iu kin hai dng chuyn ng phng l tng t?
0divv =
( )* * * * * *21 1Re evSt v v Eugradp V ft F + = + +
Phng trnh bo ton nng lng
-
2.1. Dng tng t
V d - Tng t hai chuyn ng phngHai dng chy tng t khi:
Qu trnh khng dng
Lc trng trng
Lc nht
p lc
0 0
LSt idemTV
= =
0VFr idemLg
= =
0
0
Re V L idem
= =
02
0 0
pEu idemV
= =
-
2.1. Dng tng t
V d - Tng t hai chuyn ng phng
Phng trnh nng lng:
: S Prandtl - t s gia nhit lng ctruyn bng dn nhit v i lu
: S Grashop - t s gia lc Acsimet vlc nht
-H s dn nhit; -H s n th tch; - chnh nhit
M=idem v k=idem
20
2 2 20 0 0
1 1 1p a pEu a kV k v k M
= = = = k: ch s on nhit
Cht lng nn c:
Pr pC
idem
= =3
2g L TGr idem
= =
-
2.2. nh l Vaschy-Buckinhgham
nh l Pi (): Biu thc bt k gia cc i lng cth nguyn c th biu din nh
biu thc gia cc i lng khng th nguyn
a1, a2,,ak, ak+1, , an: i lng c lp vi nhau cth nguyn
( )1 2 1, , ,k k na f a a a a a+=
-
2.2. nh l Vaschy-Buckinhgham
Nu k n l s cc i lng c th nguyn c bn (n+1-k) t hp khng th nguyn
Pi:
1 21 2
11 1 2
1 2
1 21 2
m m mkk
kp p pk
k
nn k q q qk
k
a
a a a
a
a a a
a
a a a
pi
pi
pi
+
=
=
=
-
2.2. nh l Vaschy-Buckinhgham
Nu k n l s cc i lng c th nguyn c bn (n+1-k) t hp khng th nguyn
Pi:
( )1 2 1, , ,k k na f a a a a a+=
C (n-k) t hp khng th nguynHay c =n-k tiu chun tng t
( )11,2 , , n kf kpi pi pi =
-
2.2. nh l Vaschy-BuckinhghamTng hp
Lp biu thc ph thuc(n+1) i lng a. Ghi thnguyn ca chng. Chn k i
lng c bn (thng thng k=3). Vit cngthc th nguyn ca cc i lng vt l. C
n+1-k shng S hng u tin (tch ca k i lng c s m chabit vi mt i lng khc
c s m bit (=1) k i lng c bn, chn mt trong nhng i lngtip theo lp s
hng . Lp lin tip cho cc s sau h k phng trnh i s s m ca mi s hng
-
2.2. nh l Vaschy-BuckinhghamBi tp 1
p dng nh l Pi lp biu thc tnh cng sut N cabm. Bit N ph thuc vo lu
lng Q, ct p H vtrng lng ring Gii: n = 4 v k = 3 (thy kh ng lc) =
1
Vit di dng th nguyn:
( ), , x y zNf Q H N Q H pi = =
[ ]1 3 1 3x y zFLT LT FL L = 1x y z = = =N N k QHQ Hpi = =
-
2.2. nh l Vaschy-BuckinhghamBi tp 2
p dng nh l Pi lp biu thc tnh lc cn Cx cacnh vo cc thng s dng
chy.Gii: Gi s Cx ph thuc vo khi lng ring , nht , vn tc v v chiu di
ca cnh.
Cng thc th nguyn:( ), , ,xC f v L =
[ ] [ ] [ ] [ ] [ ] 1b c d nxC v L = =
[ ] [ ] [ ] [ ] [ ]3 1 1 1ML ML T v LT L L = = = =
-
2.2. nh l Vaschy-BuckinhghamBi tp 2
Cx ph thuc vo s Reynold. S m n c th tm bngthc nghim hoc t cc iu
kin ph v sc cn cacnh
: 0: 3 0: 0
M b db c n
L b d c nd n
T d c
+ = = =
+ + = =
=
( )Ren
n
x
vlC f f
= =
