Consider the one-dimensional, incompressible flow through the circular channel shown. The velocity at section (1) is given by \(U=U_{0}+U_{1} \sin \omega t\), where \(U_{0}=20 \mathrm{~m} / \mathrm{s}, U_{1}=2 \mathrm{~m} / \mathrm{s}\), and \(\omega=0.3 \mathrm{rad} / \mathrm{s}\). The channel dimensions are \(L=1 \mathrm{~m}, R_{1}=0.2 \mathrm{~m}\), and \(R_{2}=0.1 \mathrm{~m}\). Determine the particle acceleration at the channel exit. Plot the results as a function of time over a complete cycle. On the same plot, show the acceleration at the channel exit if the channel is constant area, rather than convergent, and explain the difference between the curves.

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R1 x1 L- P5.48 12 R2