Question

Navier-Stokes Equation:

RB RA

An incompressible Newtonian liquid is confined between two concentric cylinders of infinite length—a solid inner cylinder of radius RA and a hollow outer cylinder of radius RB. The inner cylinder rotates at angular velocity ω and the outer cylinder is stationary. The flow is steady, laminar, and two-dimensional in the r-θ plane. The flow is rotationally symmetric, meaning that nothing is a function of the coordinate θ. The flow is also circular so that ur=0 everywhere.

Found Uθ= Ra^2w/(Ra^2-Rb^2)*(r-[Rb^2/r])

a. Derive an expression for the wall shear stress on the inner rotating cylinder.

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Answer #1

Shean st asて is given by n-I Rb RA- RB 2 2. Shean stasslat innci cylinde): 2rRjusince Bhe cyindcxs anc infinitely ton), the end ch fects can cd 2 any poopes. RA e 22-D, con tinuity equtation in Paan coNdinsimplifying 옮[읗끓(ove))- la 15.function 아ㆆ ㎝l cnveit to ordinany diffee ntials 6 Constant Bundany conditions atたR61 2 RB 2RA 위

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