# 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) $$= 10 m/s^{2}$$