A cylindrical tank having cross-sectional area `A = 0.5 m^(2)` is filled with two liquids of density `rho_(1)=900 kg m^(-3)` and `rho_(2)=600 kgm^(-3)`, to a height `h=60cm` each as shown in the figure. A small hole having area `a=5cm^(2)` is made in right vertical wall at a height `y = 20 cm` from the bottom. A horizontal force `F` is applied on the tank to keep it in static equilibrium. The tank is lying on a horizontal surface. Neglect mass of the cylindrical tank in comparison to mass of the liquids (Take g = 10 ms^(-2)`).

The velocity of efflux is

Options

A. `10ms^(-1)`
B. `20ms^(-1)`
C. `4ms^(-1)`
D. `35ms^(-1)`

Answer

C

Explanation

Since area of a hole is very small in comparison to base area `A` of the cylinder, velocity of liquid inside the cylinder is negligible.
Let velocity of effux be `v` and atmospheric pressure be `P_(0)`. Consider two points `A` (inside the cylinder) and `B` (just outside the hole) in the same horizontal line as shown in the figure in question.
Pressure at `A, P_(A)=P_(0)+hrho_(2)g+(h-y)rho_(1)g`
Pressure at `B, P_(B)=P_(0)`
According to Bernoulli's theorem
Pressuure energy at `A =` Pressure energy at `B +` Kinetic energy at `B`
`:.P_(A)=P_(B)+1/2rho_(1)v^(2)`
`:. v=4ms^(-1)`