A boiling-water-type nuclear fission reactor has shut down, the backup pumps have failed and emergency cooling water must be pumped between fuel-rod assemblies in the reactor core at an average velocity of 0.5 m/s. Cold sea water with a density of 1026 kg/m3 will enter the reactor vessel and exit near-boiling at a density of 984 kg/m3. There are 400 fuel-rod assemblies of square cross-section 0.1 m x 0.1 m. The reactor vessel has a 3 m internal diameter.
The friction factor for flow between the fuel-rod assemblies is known to be 0.025 and a Darcy- Weisbach equation based on the gap D2 between the assemblies is known to apply. The cooling-water entry to the bottom of the reactor vessel is rounded with negligible head loss. The exit is to the atmosphere and also has negligible head loss. The reactor is 100 m from the sea, the bottom of the fuel-rod assemblies where the cooling water enters is 6 m above sea level and the top where the water exits is 10 m above sea level. Steel piping 0.5 m in diameter is available on site. Calculate:
a) the head the pump must supply;
b)the mechanical power the pump must deliver.