Bob uses a computational fluid dynamics code to model steady flow of an incompressible fluid through a two dimensional sudden contraction as sketched in Fig. P9–119. Channel height changes from H₁ = 12.0 cm to H₂ = 4.6 cm. Uniform velocity

is to be specified on the left boundary of the computational domain. The CFD code uses a numerical scheme in which the stream function must be specified along all boundaries of the computational domain. As shown in Fig. P9–119, ψ is specified as zero along the entire bottom wall of the channel. 

(a) What value of ψ should Bob specify on the top wall of the channel? 

(b) How should Bob specify ψ on the left side of the computational domain?

(c) Discuss how Bob might specify ψ on the right side of the computational domain.

FIGURE P9–119

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V₁ = 18.57 m/s