First slide

Fluid dynamics

Question

A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm^–3. The velocity with which gasoline begins to shoot out of the hole is

Moderate

A

$27 .8 {ms}^{- 1}$
B

$41 .0 {ms}^{- 1}$
C

$9 .6 {ms}^{- 1}$
D

$19 .7 {ms}^{- 1}$

Solution

According to Bernoulli's theorem,
$\begin{array}{l} P_{B} + hρg = P_{A} + \frac{1}{2} {ρv}_{A}^{2} (As v_{A} >> v_{B}) \\ 3 .10 P + 53 \times 660 \times 10 = P + \frac{1}{2} \times 660 v_{A}^{2} \\ \Rightarrow 2 .1 \times 1 .01 \times 10^{5} + 3 .498 \times 10^{5} = \frac{1}{2} \times 660 \times v_{A}^{2} \\ \Rightarrow 5 .619 \times 10^{5} = \frac{1}{2} \times 660 \times v_{A}^{2} \\ ∴ v_{A} = \sqrt{\frac{2 \times 5 .619 \times 10^{5}}{660}} = 41 m / s \end{array}$

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