A condenser of a refrigeration system rejects heat at a rate of $$120$$ $$kW,$$ while its compressor consumes a power of $$30$$ $$kW.$$ The coefficient of performance of the system would be

A Hydro turbine is required to give $$25$$ $$MW$$ at $$50$$ $$m$$ head and $$90$$ $$rpm$$ runner speed. The laboratory facilities available, permit testing of $$20$$ $$kW$$ models at $$5$$ $$m$$ head. What should be the model runner speed and model to prototype scale ratio?