(Solved): Please show complete solution. Thank you. 1) Between two sections in a vessel, a fluid moves in a ...

Please show complete solution. Thank you.

1) Between two sections in a vessel, a fluid moves in a steady flow manner. At entrance: \( A_{1}=20 \mathrm{~m}^{2}, \rho_{1}=1300 \mathrm{~kg}_{\mathrm{m}} / \mathrm{m}^{3} \). At exit: \( \mathrm{A}_{2}=10 \mathrm{~m}^{2}, \mathrm{v}_{2}=0.00125 \) \( \mathrm{m}^{3} / \mathrm{kg}, \overline{\mathrm{U}}_{2}=3 \mathrm{~m} / \mathrm{min} \). Determine the following: a) \( \dot{m}_{1} \) in \( \mathrm{kg} / \mathrm{min} \) b) \( \bar{u}_{1} \) in \( \mathrm{m} / \mathrm{min} \) 2) A compressor draws in \( 0.5 \mathrm{~kg} / \mathrm{m} / \mathrm{s} \) of air with \( 7 \mathrm{~m} / \mathrm{s} \) speed, \( 100 \mathrm{kPa} \) pressure, and \( 0.95 \mathrm{~m}^{3} / \mathrm{kg}_{\mathrm{m}} \). The air leaves at \( 5 \mathrm{~m} / \mathrm{s}, 700 \mathrm{kPa} \) and \( 0.19 \) \( \mathrm{m}^{3} / \mathrm{kg}_{\mathrm{m}} \). The internal energy of the air leaving is \( 90 \mathrm{~kJ} / \mathrm{kg}_{\mathrm{m}} \) greater than that of the air entering which is \( 70 \mathrm{~kJ} / \mathrm{kg}_{\mathrm{m}} \). The coolant absorbs heat from the air at the rate of \( 58 \mathrm{~kW} \). Determine the work in \( \mathrm{kW} \).