Consider an old Francis hydro-turbine that operated at a sea-level site with a gross hydraulic head of 150 m and combined major and minor penstock pressure losses of 490.5 kPa (4.905 bar). The ambient water temperature is 10C. This old Francis hydro-turbine was badly damaged due to a failure of the mechanical over-speed mechanism. There is an offer for a refurbished Francis hydro- turbine that had been manufactured to operate under the following design parameters: Net hydraulic head = 120 m Power output 1 MW Coefficient of runner entrance velocity = 0.6 Coefficient of runner exit velocity = 0.373 Ratio of distributor height to internal diameter = 0.02 Runner rotational speed = 750 rpin Thoma's cavitation coefficient = 0.0241 m Overall efficiency 90% According to the "similarity laws", a turbine manufactured to operate under certain design parameters, will exhibit different characteristics when operating under new parameters. Derive expressions for the "similarity laws" that may be used for a Francis hydro-turbine and hence determine the key performance parameters for the refurbished Francis turbine operating at the sea- level site. [Max. 1 answer book]