Question

Lu LLLLLLLLLLLL FLUID-A cs = ( h Vo Tl (6=1.5€ FLUID-B A thin flat plate is moving with a constant horizontal velocity of Vo through a narrow channel with a height of "h" as shown in the figure. The upper side of the plate is filled with fluid A while the lower side is filled with fluid B. If both fluids are Newtonian and the viscosity of fluid A and B are given as uA = u and MB = 1.5j, find the total friction force acting to the moving flat plate. Assume that velocity profiles are linear. Take the area of the flat plate as A.

Answer 1

LLLL Ihre ㄴ Fluid A As the that plate moves along the fluids it faces frictional forces from both the fluids Huid A l Pluid Bi Fa frictional force due to fluid A h Vo IE2 Fluid B 1.5u 7777 Fo frictional force due to fluid 'B. According to Newton's Law of viscosity u du. For fluidA :- du > FI u A z = shear stress - dy za Force Area FI all A dy as; dwave change in uelocity. dy = had a thickness of layer. vo h-l => FI MAVO - hol for flid B : F2 A l 3) Fq -1.54L AVO Total frictional force; F= Fitfa a de Avo 1.SMAVO hal e MAVolt (he) Is MAVO l(he) a losu vo e + a u Avol tl.sh u Avo-1.5 M A Vol echre) IShMAVO-OIS MA Vol dlhoe)