Consider a variation of the fully developed Couette flow problem of Prob. 7-52-flow between two infinite parallel plates separated by distance
h
, with the top plate moving at speed
V top
and the bottom plate moving at speed
V bottom
as illustrated in Fig. P7-107. The flow is steady, incompressible, and two-dimensional in the
xy
-plane. Generate a dimensionless relationship for the
x
-component of fluid velocity
u
as a function of fluid viscosity
μ
, plate speeds
V top
and
V bottom
, distance
h
, fluid density
rho
, and distance
y
. (Hint: Think carefully about the list of parameters before rushing into the algebra.) FIGURE P7-107
