To solve this problem, we need to calculate the power generated by the turbine.$\\$Given:$\\$• Height $h = 60$ m$\\$• Mass flow rate $\dot{m} = 15$ kg/s$\\$• Gravitational acceleration $g = 10$ m/s$^2 \\$• Frictional losses are $10\%$ of the input energy$\\$First, calculate the potential energy per second (power input) due to the falling water:$\\ P_{input} = \dot{m} \cdot g \cdot h \\ P_{input} = 15 \cdot 10 \cdot 60 \\ P_{input} = 9000$ W$\\$Since $10\%$ of the input energy is lost due to friction, the effective power output is $90\%$ of the input power.$\\ P_{output} = 0.9 \cdot P_{input} \\ P_{output} = 0.9 \cdot 9000 \\ P_{output} = 8100$ W$\\$Convert the power output to kilowatts:$\\ P_{output} = \frac{8100}{1000}$ kW$\\ P_{output} = 8.1$ kW$\\$Therefore, the power generated by the turbine is $8.1$ kW, which corresponds to Option 2.