Question

A large tank is filled with water (density$={10}^{3}kg/m^3$). A small hole is made at a depth $10m$ below water surface. the range of water issuing out of the hole is R on ground. What extra pressure must be applied on the water surface so that the range becomes $2R$ ( take $1atm={10}^{5}Pa$ and $g=10m/s^2$)

• A. $9atm$
• B. $4atm$
• C. $5atm$
• D. $3atm$

Answer 1

The correct option is D $3atm$

Range will become twice, if the velocity of efflux becomes twice. Since velocity of efflux is $\sqrt{2gh}$, it will become twice, if $h$ becomes $4$ times, or $40m.$
Thus, an extra pressure equivalent to $30m$ of water should be applied.
$1atm=0.76\times 13.6$ m of water $=10.336m$ of water
$30m$ of water $\approx 3atm$