4-6. A storage tank is \( 10 \mathrm{~m} \) high. At a particular time the liquid level is \( 5 \mathrm{~m} \) high within the tank. The tank is pressurized with nitrogen to 0.1 bar gauge to prevent a flammable atmosphere within the tank. The liquid in the tank has a density of \( 490 \mathrm{~kg} / \mathrm{m}^{3} \).
a. If a 10-mm hole forms \( 3 \mathrm{~m} \) above the ground, what is the initial mass discharge rate of liquid (in \( \mathrm{kg} / \mathrm{s} \) )?
b. Estimate the distance from the tank the stream of liquid will hit the ground. Determine whether this stream will be contained by a 1 -m-high dike located \( 1 \mathrm{~m} \) from the tank wall.
Hint: For a freely falling body the time to reach the ground is given by
\[
t=\sqrt{\frac{2 h}{g}},
\]
where \( t \) is the time, \( h \) is the initial height above the ground, and \( g \) is the acceleration due to gravity.
