If the density of air is $ρ_{a}$ and that of the liquid $ρ_{l}$ , then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

\sqrt{\frac{ρ_{a}}{ρ_{l}}}

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\sqrt{ρ_{a} ρ_{l}}

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\sqrt{\frac{ρ_{l}}{ρ_{a}}}

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ρ_{l}

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Solution

The correct option is A $\sqrt{\frac{ρ_{a}}{ρ_{l}}}$
Pressure at point in nozzle $\Rightarrow P$

$P = P_{0} - \frac{1}{2} ρ_{a} V_{1}^{2}$ ...(1)

$P = P_{0} - \frac{1}{2} ρ_{l} V_{2}^{2} - ρ_{l} g h$ ...(2)
Equation (1) and (2)
$\frac{1}{2} ρ_{a} V_{1}^{2} = \frac{1}{2} ρ_{l} V_{2}^{2} + ρ_{l} g h$
Neglecting the terms $r_{e} g h$
$V_{2} = \sqrt{\frac{ρ_{a}}{ρ_{l}} V_{1}}$
Rate of liquid flow $= A V_{2}$
$= A V_{1} \sqrt{\frac{ρ_{a}}{ρ_{l}}}$
Rate of liquid flow $\propto \sqrt{\frac{ρ_{a}}{ρ_{l}}}$

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If the density of air is ρa and that of the liquid ρl, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

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If the density of air is $ρ_{a}$ and that of the liquid $ρ_{l}$ , then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to