GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

A test is conducted on a one-fifth scale model of a Francis turbine under a head of $2\mathit{m}$ and volumetric flow rate of $1{\mathit{m}}^3/\mathit{s}$ at $450\mathit{r}\mathit{p}\mathit{m}$. Take the water density and the acceleration due to gravity as ${10}^3\mathit{k}\mathit{g}/{\mathit{m}}^3$ and $10\mathit{m}/{\mathit{s}}^2$, respectively. Assume no losses both in model and prototype turbines. The power (in MW) of a full sized turbine while working under a head of $30\mathit{m}$ is ____________ (correct to two decimal places).