Question

2 > (25pts) In studying sand transport by ocean waves, it was postulated that the threshold wave-induced bottom shear stress t required to move particles depends on gravity g, particle size d, particle density Pp water viscosity and water density p. Find all the dimensionless, i.e., pi groups for this problem. Consider p, g, d as repeating variables. Write all the quantities in terms of the primary dimensions, i.e. M, L, T. For example, the dimension of viscosity u is MLT T=f(g, d, Pp, H, P)

Answer 1

T2 M 2°°= (M13)? (LT2)=(24 (M2'4") 0 = 92+1 > Q2 = -1 0 = -392+b2+9 -7 762 = -3/2 0=-262-1 → b2 = -2 -/ S" T₂ = g -3/24 Tz 쓰 f g² [2] An. Z = ME'T-2 g=LT-2 d=L Pp = ME 4=N['T f = ME3 T = f( Jid, Pp, M, 8 No. of it tarons nm I (2 g, d, Sp,14,8) = 0 = 6-3 - 3 Total number of Vaziables, n = 6 No. of bepeating variables, m = 3 equation is given by f ( Ty; Izr TT3) IT, = 8h god". Iz = ga gleda u 173 = pang 19.3 T = (ML)(LT)"! (..)" (MCT) N'L'R' = (M2).(L1")"(UCMUT) Z T3 M° 2°T°= (MC?)"? (27-2363(L)(M13) 0 = 0=Qit1 Ya=-1 0 = -39, +by+G-174--| 0 = -26, -2 => b=-1 Ti = f! g*d! e IT- 93+1 = ag=0-1 0 = -393 + b3 + -3 7 4 =0 O=-2b3 = b3=0 T3 Sp Ar. S 그 " Epbs Spe