If you squeeze the handle of a spray bottle (figure), you cause air to flow horizontally across the opening of a tube that extends down into the liquid almost to the bottom of the bottle. If the air i

Question

If you squeeze the handle of a spray bottle (figure), you cause air to flow horizontally across the opening of a tube that extends down into the liquid almost to the bottom of the bottle. If the air is moving at 50.0 $m / s$ , what is the pressure difference between the top of the tube and the atmosphere? Assume that the density of air is $ρ = 1.20 kg / m^{3}$ . If your answer is 250X (in Pa) fill value of X.

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TestHub · Accepted Answer

Bernoulli pressure drop at the tube opening:
$Δ p = \frac{1}{2} ρ_{air} v^{2}$
$Δ p = \frac{1}{2} (1.20) (50.0)^{2} = 1500 Pa$
The question asks for X when the pressure difference is 250X Pa:
$250 X = 1500 \Rightarrow X = 6$

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