An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a sink at a rate of $$50kW.$$ The entire work output of the heat engine is used to drive a reversible heat pump operating between a set of independent isothermal heat reservoirs at $${17^ \circ }C$$ and $${75^ \circ }C$$. The rate (in $$kW$$) at which the heat pump delivers heat to its high temperature sink is

The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential component of velocity at blade outlet is zero. The flow velocity remains constant throughout the blade passage and is equal to half of the blade velocity at runner inlet. The blade efficiency of the runner is

A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If $$N$$ is the $$RPM$$ of the full scale turbine, then the $$RPM$$ of the model will be

Match the items in columns $$I$$ and $$II$$.

Column $$I$$
$$P:$$ Centrifugal compressor
$$Q:$$ Centrifugal pump
$$R:$$ Pelton wheel
$$S:$$ Kaplan turbine

Column $$II$$
$$1:$$ Axial flow
$$2:$$ Surging
$$3:$$ Priming
$$4:$$ Pure impulse