Question

3.0, Radial Flow between Concentric Spheres Consider an isothermal, incompressible fluid flowing radially between two concentric porous spherical shells. (See Fig. 3.0.) Assume stecady laminar flow withu- ul) Direction of flow flow between concentric porous spheres. Fig. 10. Radial Note that here the velocity is not assumed zero at the solid surfaces. Show by use of the cquation of continuity that a. (3.0- where y is a constant. b. Show by use of the equations of motion that the pressure distribution in this sysiem is described by the relations 1 p rsin & a4 t 3.0-2) =Pe r a0 (3.0-3) -( A (3.0-4) c Show that the radial pressure distribution may be expressed in terms of the quantity Pas -9, 0.0-5) w

Answer 1

Please go through the explanation

CLASS Date Corrtn uity equeen sperica AN COordinates +(s T(0 3e dt Oufe Cucompretiis dlooing Coneentrie sphèútul iso tueiuial alially betweu fhelliU Ghe_flos oainas two and P constant radia o thase Com tant dt becomes (^Aq^d)e ar 2 Integrating_ Constant

Naviel- Stokes quatim 2 RV Au b + V.fvv P ナ = - 2七 En coupride S : Constant as - VP + at Sphericap Navies-Stokesuation fm COordinate variabkid7, o, ¢ component ngiod d¢ at 22/Y2 Vr an and V¢= 0 state No - low Sicsdiy at ue. P e e for e component'-- aVa Nr No + No avo Na eTle Sino)

and 7 -|ap for componenz ' + N V + pe ayt 2 + YeN Cot) AVr oto Ive Yrr V and P