A new chemical plant requires a water flow rate of \(5.75 \mathrm{~m}^{3} / \mathrm{min}\). The gauge pressure in the water main, located in the street \(50 \mathrm{~m}\) from the plant, is \(800 \mathrm{kPa}\). The supply line will require installation of four elbows and one ball valve and will be \(65 \mathrm{~m}\) in total length. Each elbow adds an additional equivalent length/diameter \((L / d)\) of 30 to frictional losses and the ball valve adds another equivalent length/diameter \((L / d)\) of 50 . The gauge pressure supplied to the plant must be no lower than \(625 \mathrm{kPa}\). Pipe diameters of \(0.2 \mathrm{~m}, 0.175 \mathrm{~m}\), and \(0.15 \mathrm{~m}\) are available \((\varepsilon=0.0005)\). What is the smallest diameter that should be used and what would be the inlet pressure to the plant?