In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and exits at a pressure of $$15$$ $$kPa.$$ Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is $$90\% $$. The thermodynamic states of water and steam are given in the table.

$$h$$ is specific enthalpy, $$s$$ is specific entropy and $$v$$ the specific volume; subscripts $$f$$ and $$g$$ denote saturated liquid state and saturated vapour state.

Heat supplied $$(kJ/kg)$$ to the cycle is

A phenomenon is modeled using $$n$$ dimensional variables with $$k$$ primary dimensions. The number of non-dimensional variables is

A hydraulic turbine develops $$1000$$ $$kW$$ power for a head of $$40$$ $$m.$$ If the head is reduced to $$20$$ $$m,$$ the power developed (in $$kW$$) is