At a place where the surroundings are at $$1$$ bar $${27^ \circ }C,$$ a closed rigid thermally insulated tank contains $$2$$ $$kg$$ air at $$2$$ bar, $${27^ \circ }C,$$ This air is then churned for a while, by a paddle wheel connected to an external motor. If it is given that the irreversibility of the process is $$100$$ $$kJ,$$ find the final temperature and the increase in availability of air. Assume for air $${C_v} = 0.718\,\,kJ/kg\,K$$

Kaplan turbine is

A water turbine delivering $$10$$ $$MW$$ power is to be tested with the help of a geometrically similar $$1:8$$ model, which runs at the same speed as the proto-type.

(a) Find the power developed by the model assuming the efficiencies of the model and the proto-type are equal.

(b) Find the ratio of the heads and the ratio of mass flow rates between the proto-type and the model.