Question

Hi, I have to dertermine the speed distribution of the fluid (vz(r)) in the same configuration of the exercice 4.88 of the book Fluid Mechanics of Frank M White. But instead of a fixed outside cylinder, the outside cylinder is moving to its left with a constant speed V. For what ratio value V/U, the shear force on the two walls of the cylinder will be equal?

Answer 1

flow is steady b 12 2 Tag 2 flow is fully axial ie Vecco e Vo=0 Vz Pure OL, SA ie Vz= f(01) only using スー momentum egy +t? 12 r de 20% V2 + 2 де dz² sl 34z + Ve BVZ + V DVZ + Vz09z) = -2+39ztu Ot de de nea Continuity & (V) zo There is a voi JZ ☆ on (1734 a V2 er © -O dz density at constant pressure & we get for Steady flow 2z =0 (steady How ot flow is Pune axial Nrz voro is constant pressure 을 so O+O + 4 a / 1er 212 2 (a doraz) - ediz idi dr de integratis. er du CU Saxzos Nz Cienrt (2 a ena+2 U B. Vzlasu Vz(b)zov a enb tc2 U- CE Utv (2= U+v) eng ene) il)

Nz = (U+V) enx + U - (U+v) en a V+ (U+V) in en 19 in un (9) r=b b Shear stress Trab) = u dvz u (U+V). I en 19) de luzb b Shear force ! FO TEXA: 2 Tb x) MCU+V) en a ot 2 itu (Utv) enla at r=a Shear Stress Terza)= ll av -- du luze u (U+V) de leza en ) a Shear force Tox Aa : ULU+V). 2019 FE a en (4) 204 (U+V) en la equal for any ř Ratio Shear force is always Any But fer shear stress b = u (u tw ) į Ta= ulu+v) ben (9) a en la they becomes equal no there is ř ratio fer which b = a Tb = Ta only if