Question

A spherical tank of $1.2m$ radius is half filled with oil of relative density $0.8$. If the tank is given a horizontal acceleration of $10m/s^2$. Calculate the inclination of the oil surface to horizontal and maximum pressure on the tank.

Answer 1

The inclination will be

$\theta ={tan}^{-1}\frac{a}{g}={tan}^{-1}\frac{10}{10}={45}^0$

Also, the pressure will be, using resultant force in direction of the resultant acceleration,

$P=\frac{\rho \frac{2}{3}\pi r^3\sqrt{g^2+a^2}}{\pi r^2}=\frac{2}{3}\rho r\sqrt{g^2+a^2}=\frac{2}{3}\left(800\right)\left(1.2\right)\left(10\sqrt{2}\right)\approx 9600\sqrt{2}Pa$

Answer is ${45}^0$ and $9600\sqrt{2}Pa$.