In order to have maximum power from a Pelton turbine, the bucket speed must be

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

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