(Solved): Water flows steadily through the horizontal piping system as shown in the figure below. The veloci ...

Water flows steadily through the horizontal piping system as shown in the figure below. The velocity is uniform at section (1), the mass flowrate is \( 10 \mathrm{slugs} / \mathrm{s} \) at section (2), and the velocity \( V \) is nonuniform at section (3). Figure 1: Problem 1 1. Determine the value of the quantity \( \frac{D}{D t} \int_{s y s} \rho V \), where the system is the water contained in the pipe bounded by sections (1), (2), and (3). 2. Determine the mean velocity at section (2) 3. Determine, if possible, the value of the integral \( \int_{(3)} \rho V \cdot \mathbf{n} d A \) over section (3). If it is not possible, explain what additional information is needed to do so.