(Solved): A pump as shown in the figure is operating at free delivery conditions as sho ...

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A pump as shown in the figure is operating at free delivery conditions as shown in the image. The pipe, both upstream and downstream of the pump, has an inner diameter of \( 2.0 \mathrm{~cm} \) with a rough pipe-roughness \( \varepsilon=0.12 \mathrm{~mm} \). The minor loss coefficient associated with the sharp inlet is \( 0.50 \), each valve has a minor loss coefficient of \( 2.4 \), and each of the three elbows has a minor loss coefficient of \( 0.90 \). The contraction at the exit reduces the diameter by a factor of \( 0.60 \) ( \( 60 \% \) of the pipe diameter), and the minor loss coefficient of the contraction is \( 0.15 \). This minor loss coefficient is based on the average exit velocity, not the average velocity through the pipe itself. The total length of pipe is \( 8.75 \mathrm{~m} \), and the elevation difference is \( \left(z_{1}-z_{2}\right)=4.6 \) m. By what percent does the flow rate decrease when compared to the flow rate of a pipe with zero roughness?