Consider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with thetop plate moving and the bottom plate stationary as illustrated in Fig. P7-56. 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 xcomponent of fluid velocity u as a function of fluid viscosity μ, top plate speed V, distance h, fluid density rho, anddistance γ, Show all your work.

Question

Jaden Barnett

Engineering

4 June, 19:25

Consider fully developed Couette flow-flow between two infinite parallel plates separated by distance h, with thetop plate moving and the bottom plate stationary as illustrated in Fig. P7-56. 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 xcomponent of fluid velocity u as a function of fluid viscosity μ, top plate speed V, distance h, fluid density rho, anddistance γ, Show all your work.

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Clinton Bridges · Answer 1

The flow is two dimensional

So velocity = (dv/dx-du/dy) k

= (0-v/h) k

= (-v/h) k

Velocity is non-zero, so flow is rotational.

But velocity is z - direction is - v/h

Velocity is negative so fluid particles rotate in clockwise direction.