Question 437: Properties of Matter

Question

A spray gun is shown in the below figure where a piston pushes air out of a 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 1 mm, respectively. The upper end of the container is open to the atmosphere.

Accepted Answer

For horizontal flow, Bernoulli's theorem becomes
$${P \over \rho } + gh + {1 \over 2}{v^2} = k'$$
$$P + {1 \over 2}\rho {v^2} = k$$ (h = 0)
Between points 1 and 2 :
$${P_1} - {P_2} = {1 \over 2}{\rho _a}v_a^2$$
Between points 2 and 3 :
$${P_3} - {P_2} = {1 \over 2}{\rho _l}v_l^2$$
Since, P
1
= P
3
, we have
$${1 \over 2}{\rho _l}v_l^2 = {1 \over 2}{\rho _a}v_a^2$$
$${{{v_l}} \over {{v_a}}} =\sqrt {{{{\rho _a}} \over {{\rho _l}}}} $$

Answer

$\sqrt{\frac{\rho_a}{\rho_{\ell}}}$

Answer

$\sqrt{\rho_a \rho_{\ell}}$

Answer

$\sqrt{\frac{\rho_{\ell}}{\rho_a}}$

Answer

$\rho_{\ell}$

Properties of Matter

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