A steel pipeline conveys water (density 1000 kg/m3 , bulk modulus 2.05x109 N/m² ) from an upper to a lower reservoir the pipeline material is steel with Young’s modulus 210x109 N/m² . It is 611 m long, has an internal diameter 1.1m, wall thickness 25 mm and surface roughness 0.68 mm. The flow is controlled by a valve located at the entrance to the lower reservoir, 211 m below the surface level in the upper reservoir.

(a) Under steady flow conditions the valve is in the open position and the gauge pressure in the
    pipeline just before the valve is 1000 kN/m². Assuming rough turbulent flow and considering head
    losses due to friction along the pipe only, calculate the steady flow discharge. Confirm that the
    flow is indeed rough turbulent.