Problem $6(10$ points$).$ A pump with a shaft power of $30kW$ and an efficiency of $70\%$ is used to pump water from the lower reservoir to a higher reservoir $($see the figure below$).$ If the head loss in the piping system is $3m,$ determine the discharge rate of water and the pressure difference across the pump. The density of water is $1000k\frac{g}{m^3}.$