Fluids with a pinch of calculus!

Consider a hemispherical tank of radius \(R \)containing a non-viscous liquid of Density \(\rho\). A small hole is formed at the bottom of the tank and the area of cross section of the hole is \(a\). If the liquid starts dripping from the hole at time \(t = 0\) and if at time \(t = T\) the tank is empty find the sum of digits of

\(\bigg \lfloor T \bigg \rfloor\)

Given that:

\(\rho = 2.7 g/cm^3\)

\(R = 4 metres \)

\(a = 35 sq.centimetres \)

\(g \) (i.e. Acceleration due to gravity) \( = 10 m/s^{2}\)

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