In the incompressible flow through the device shown, velocities may be considered uniform over the inlet and

Question:

In the incompressible flow through the device shown, velocities may be considered uniform over the inlet and outlet sections. The following conditions are known: \(A_{1}=0.1 \mathrm{~m}^{2}, A_{2}=0.2 \mathrm{~m}^{2}\), \(A_{3}=0.6 \mathrm{~m}^{2}, \quad V_{1}=10 e^{-t / 2} \mathrm{~m} / \mathrm{s}\), and \(V_{2}=2 \cos (2 \pi t) \mathrm{m} / \mathrm{s}(t\) in seconds). Obtain an expression for the velocity at section (3), and plot \(V_{3}\) as a function of time. At what instant does \(V_{3}\) first become zero? What is the total mean volumetric flow at section (3)?

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