Question

A sniper shoots a bullet into a gasoline tank making a hole $53.0\text{m}$ below the surface of gasoline. The tank was sealed at $3.10\text{atm}$. The stored gasoline has a density of $660{\text{kg/m}}^3$. The velocity with which gasoline begins to come out of the hole is
($g=10{\text{m/s}}^2$)

• A. $27.8{\text{ms}}^{-1}$
• B. $41.0{\text{ms}}^{-1}$
• C. $9.6{\text{ms}}^{-1}$
• D. $19.7{\text{ms}}^{-1}$

Answer 1

The correct option is B $41.0{\text{ms}}^{-1}$


Using Bernoulli's theorem,
$P_B+h\rho g=P_A+\frac{1}{2}\rho v_A^2$
(Assuming $v_A>>v_B)$
$\Rightarrow 3.10P+53\times 660\times 10=P+\frac{1}{2}\times 660\times v_A^2$
$\Rightarrow 2.1\times 1.01\times {10}^5+3.498\times {10}^5=\frac{1}{2}\times 660\times v_A^2$
$\therefore v_A=\sqrt{\frac{2\times 5.619\times {10}^5}{660}}\approx 41\text{m/s}$