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Figure shows a crude type of atomizer. When bulb A is compressed, air flows swiftly through tube BC causing a reduced pressure in the particles of the vertical tube. Liquid rises in the tube, enters BC and is sprayed out. If the pressure in the bulb is $P_{a} + P,$ where $P$ is the gauge pressure and $P_{a}$ is the atmospheric pressure, $ν$ is the speed of air in BC, find how large would need to be to cause the liquid to rise to BC. Density of air $= 1.3 kg / m^{3}$

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$\frac{P + ρ gh}{\sqrt{0.65}}$

$\frac{Phpg}{\sqrt{0.65}}$

$\frac{P \sqrt{h ρ g}}{0.65}$

$\frac{P}{h ρ g \sqrt{0.65}}$

answer is A.

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Detailed Solution

Absolute pressure in bulb= gauge pressure + atmospheric pressure $= p_{g} + p_{a}$

Using Bernoulli’s equation

$p_{a} + p = p_{BC} + \frac{ρ_{a} V^{2}}{2}$

$ρ_{a}$ is the density of air

$p_{BC} = p_{a} + p - (\frac{1.3}{2}) v^{2}; p_{BC} = p_{a} - ρ gh$

So equating these two values for $p_{BC},$ we get

$v = \frac{P + ρgh}{\sqrt{0.65}}$

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