Q$2.$ Vortex Flow:

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$($a$)$ A cylindrical container of base diameter $1\mathrm{.}2$m contains water at level of $5$m when stationary. It is rotated about a vertical axis through the centre of the circular base at a speed of $20$ R$.$P$.$M$,$ resulting in a Forced Vortex, with the water surface forming a parabolic profile, under steady state conditions. Determine the maximum and minimum heights reached by the water surface during rotation.

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