Consider a variation of the fully developed Couette flow problem of Prob. 7–55—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. P7–106. 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 ρ, and distance y.

FIGURE P7–106

Data from Problem 7–55

Consider fully developed Couette flow—flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary as illustrated in Fig. P7–55. The flow is steady, incompressible, and two-dimensional in the xy-plane. Use the method of repeating variables to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed V, distance h, fluid density ρ, and distance y. Show all your work.

FIGURE P7–55

Transcribed Image Text:

h ρ μ y Vbottom u V top X