PHAN TCH TH NGUYEN VA ONG DANG Phn tch th nguyn1.1 Khi nim1.2 Phng php phn tch th nguyn - nh lut (Buckingham) 1.3 Cc v d p dngQuy lut ng dng2.1 Khi nim2.2 Cc tiu chun ng dng2.3 ng dng khng hon ho v th nghim m hnh

1. Phn tch th nguyn1.1 Khi nim - ai lng co th nguyen : gia tr bang so cua no phu thuoc vao tng he n v o lng.V du chieu dai L(m), van toc V(m/s)- ai lng vo th nguyen: gia tr bang so cua no khong phu thuoc vao bat ky he n v o lng nao. V du Re, Mach, Froude, , he so co hep - ai lng c ban: la nhng ai lng th nguyen n gian nhat, co 1 n v o lng c ban. V du trong he SI co cac ai lng c ban nh khoi lng (M), chieu dai (L), thi gian (T)- ai lng dan xuat: La nhng ai lng th nguyen c dien ta di dang la bieu thc cua nhng th nguyen c ban. V du : V(m/s), F(N = kgm/s2)- Th nguyen cua mot ai lng nao o c bieu dien trong trong dau [ ] bieu dien n v dan suat qua cac n v c ban.V du : Van toc [V] = L/T, [F] = MLT-2 , ..

Xt 1 hin tng vt l ph thuc vo n bin s f(a1,a2,a3,a4an) = 0 trong c k n v th nguyn c bn (L, M, T hay L, F, T)Hin tng ny c th c din t theo hm s ca m = n-k i lng v th nguyn 1, 2,3...m theo mi lin h :(1, 2,3...m )=0

1.2 Phng php phn tch th nguyn - nh lut (Buckingham)

Trong o a1, a2, . . . ak la nhng ai lng oc lap, 1, 2, 3. . . k la nhng hang soCac th nguyen oc lap thng :Chieu dai (L) Khoi lng (M)Thi gian (S)Cac bien gan vi L,M,SKhong chon bien au tienKhong chon bien anh hng trong mot pham vi nho1.2 Phng php phn tch th nguyn - nh lut (Buckingham)

V du: Tm cong thc ng suat ma sat trn b mt ong dn lu cht: = f(D, ,V, , )n = 6k = 3 (D,V,) => S cc i lng v th nguyn : n-k = 31 = g(2, 3)L0 M0 L0 = L-a-b+3c-1 M-c+1 T-2+b-a-b+3c-1 = 0a = 0-c+1 = 0=> c = 1-2+b=0b = 21.2 Phng php phn tch th nguyn - nh lut D : ng knh ng: kch thc m nhm ca b mt: khi lng ring ca lu cht : nht lu cht

1.2 Phng php phn tch th nguyn - nh lut

2. Quy lut ng dng2.1 Khi nimHai hin tng vt l gi l ng dng nu nh tt c cc i lng c trng ca chng ng dng : ti im tng ng, ti thi im tng ng, i lng c hng phi ng dng hnh hc, i lng v hng tng ng t l c tnh ca cc loi m hnh my thy kh (bm, qut, my nn..), tu thuyn, my bay ch c p dng trn m hnh thc khi chng tho mn cc iu kin v ng dng :ng dng hnh hcng dng ng hcng dng ng lc hc

a) ong dang hnh hoc:Chieu dai : aL = Lm/Lt Dien tch : aA = Am/At = (LM/LT)2 = aL2, The tch : a = m/t = aL3Cac t so ong dang hnh hoc thng c xac nh khi che tao mo hnh2. Quy lut ng dng

2. Quy lut ng dngng dng hnh hc ca (a) m hnh tht (protoype) v (b) m hnh thu nh vi t l 1/10

2. Quy lut ng dngTha mn ng dng hnh hc ca (a) m hnh tht (prototype) v (b) m hnh thu nh vi t l 1/10 khi:Bn knh ti u mi theo ng t l 1/10 nhm b mt trn m hnh thu nh theo ng t l 1/10Nu m hnh tht c b dy lp bin l 5mm ti v tr cch mi 1.5mm m hnh thu nh phi c b dy lp bin l 0.5mm ti v tr cch mi 0.15mm

Chuyn ng trong hai h thng c xem l ng dng nu nh cc phn t lu cht tng ng ti nhng v tr tng ng v ti nhng thi im tng ng nhaub) ong dang ong hoc: Thi gian: aT = Tm/Tt Van toc : aV = Vm/Vt = aL/aT Gia toc : aa = am/at = aL/(aT )2 Lu lng : aQ = Qm/Qt = (aL)3/aT . . . . .Cac t so ong dang ong lc hoc xac nh c neu biet ong dang ve thi gian 2. Quy lut ng dng

c) ong dang ong lc hoc: Trong trng hp tong quat tai mot iem co the co cac lc tac dung sau : trong lc G, ap lc P, lc ma sat T, lc cang be mat Fc va tong cac lc nay can bang vi lc quan tnh I = ma. Mot mo hnh c goi la ong dang ong lc hoc khi co c mot t so ong dang aF cho tat ca loai lc tren2. Quy lut ng dng

c) ong dang ong lc hoc: The forces acting on the flow element are due togravity FG, pressure Fp, viscosity FV, surface tension FT (when the prototype model is on the boundary of water and air), inertia FI, and elasticity FE.The forces can be expressed as shown below.2. Quy lut ng dng

Trong thc te khi che to mo hnh khong the co c t so ong dang aF cho tat ca cac lc, do o phai chap nhan mot s ong dang khong hoan hao a en cac loai mo hnh sau.2.2 Cc tiu chun v ng dng2.2.1 M hnh ReynoldsKhi nh hng ca tnh nn c l khng ng kKhi khng c nh hng ca mt thongnh hng ca lc ma st v trng lc l ng kV d: dng chuyn ng trong ng, chuyn ng tu ngm, hay chuyn ng ca my bay trong khng kh vn tc thp

2. Quy lut ng dng

2. Quy lut ng dngwhich defines the Reynolds number Re,Re = LV/v2.2 Cc tiu chun v ng dng2.2.1 M hnh Reynolds

2.2.1 M hnh Reynolds : khi xem anh hng cua ma sat la quan trong

2.2 Cc tiu chun v ng dng2.2.2 Tiu chun FroudeKhi kho st nh hng ca lc cn sng ln chuyn ng ca tu thuyn, t l gia lc qun tnh v trng lc c nh hng quan trng:2. Quy lut ng dng

tng ng vi trng hp s Reynolds (Re c bc 1 theo vn tc V). S Froude c nh ngha bng (u2/gL)0.5 Froude number Fr, ng dng Froude cho php tnh ton lc cn sng trn vt th tht t m hnh. Nu tnh ton lc cn ton th, cn xc nh thm lc cn ma st Mo hnh Froude dung cho : Dong chay qua ap tran Lc can do song (len tau thuyen, cong trnh bien ) Dong chay trong may thuy lc (bm, tuabin )2. Quy lut ng dng2.2 Cc tiu chun v ng dng2.2.2 Tiu chun Froude

Tiu chun Froude

2. Quy lut ng dng2.2 Cc tiu chun v ng dng2.2.3 Tiu chun Mach

1 kn =1.689ft/s