(Solved): The rotor of a turbomachine rotates counter clockwise at a constant angular velocity of \( \omega= ...

The rotor of a turbomachine rotates counter clockwise at a constant angular velocity of \( \omega=15 \) \( \mathrm{rad} / \mathrm{s} \). At the inlet section of the rotor, water enters radially without any tangential component. Measurements indicate that \( r_{1}=40 \mathrm{~cm}, r_{2}=80 \mathrm{~cm} \), the absolute velocity at the inlet \( V_{1}=10 \) \( \mathrm{m} / \mathrm{s} \), and the angle between the blade velocity \( U_{2} \) and the relative velocity \( W_{2} \) is \( \beta_{2}=90^{\circ} \). (a) If the magnitudes of the relative velocities remain constant across the entire rotor, determine if this turbomachine extracts energy from a fluid or adds energy to a fluid. (b) Distinguish between a positive-displacement turbomachine and a dynamic turbomachine. Give THREE (3) examples for each of them. (c) Briefly discuss the working principle of an impulse turbine.