Discussion Forum



1)

A spray gun is shown in the figure where a piston pushes air out of the nozzle. A thin tube of uniform cross-section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out.

 For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1mm respectively. The upper end of the container is open to the atmosphere.

2632021254_m9.JPG

 

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


A) $\sqrt{\frac{\rho_{a}}{\rho_{l}}}$

B) $\sqrt{\rho_{a}\rho_{l}}$

C) $\sqrt{\frac{\rho_{l}}{\rho_{a}}}$

D) $\rho_{l}$

Answer:

Option A

Explanation:

$p_{1}-p_{2}=\frac{1}{2}\rho_{a}v_{a}^{2}$

 2632021653_m11.JPG

$p_{3}-p_{2}=\frac{1}{2}\rho_{l}v_{l}^{2}$

p3= p1

   $\therefore$     $\frac{1}{2}\rho_{l}v_{l}^{2}$= $ \frac{1}{2}\rho_{a}v_{a}^{2}$

          $\Rightarrow$           $  v_{l}=\sqrt{\frac{\rho_{a}}{\rho_{l}}}v_{a}$

     $\therefore $     Volume flow rate  $\propto  \sqrt{\frac{\rho_{a}}{\rho_{l}}}$