Question

Consider a cylindrical tank of radius $1 \,m$ is filled with water. The top surface of water is at $15 \,m$ from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of $5\, m$ from the bottom. A force of $5 \times 10^5 N$ is applied an the top surface of water using a piston. The speed of efflux from the hole will be : (given atmospheric pressure $P _{ A }=1.01 \times 10^5 Pa$, density of water $\rho_{ w }=1000\, kg / m ^3$ and gravitational acceleration $g=10 \,m / s ^2$ )

• A. $11.6 \,m / s$
• B. $10.8\, m / s$
• C. $17.8 \,m / s$
• D. $14.4 \,m / s$

Answer 1

Answer: (C)

Apply Bernoulli's theorem between Piston and hole
$P _{ A }+\rho gh = P _0+\frac{1}{2} \rho v_{ e }^2$
Assuming there is no atmospheric pressure on piston
$ \frac{5 \times 10^5}{\pi}+10^3 \times 10 \times 10=1.01 \times 10^5+\frac{1}{2} \times 10^3 \times v _{ e }^2$
$ v _{ e }=17.8 \,m / s$