Author(s): Tomio Ida
Abstract: New formulae for efficiency scaling-up from model to prototype of a hydraulic turbine are presented based on the theoretical analysis that considers the only friction losses through the turbine. Two formulae are presented; one is the precise conversion formula, and the other the simplified practical one. The former can precisely decide the prototype efficiency from the model performance considering the relative friction loss corresponding to the respective Reynolds number and surface roughness in the individual flow passages of the model and prototype turbines, respectively. The latter simplify the precise formula by using a relative total friction loss that can be assumed constant irrespective of type of machines and specific speed, instead of the individual friction losses through the turbine. The new formulae need not the classical loss distribution coefficient V. The prototype efficiency scaled up with the precise formula agrees closely with the theoretical value calculated for a model Francis turbine and a pump-turbine. The efficiency obtained from the practical formula agrees well with the theoretical values, and also with the efficiencies calculated from the formulae stipulated in the JSME Standard by using the accurate loss distribution coefficients obtained analytically with each model.