Q. The cylindrical tube of spray pump has a cross-section of 8$\ {cm}^{2}$, one end of which has 40 fine holes each of area $10^{- 8}\ m^{2}$. If liquid flows inside the tube with a speed of ${0.15\ m\ min}^{- 1}$, the speed with which the liquid is ejected through the hole is
A) $50\ {ms}^{- 1}$
B) $5\ {ms}^{- 1}$
C) $0.05\ {ms}^{- 1}$
D) $0.5\ {ms}^{- 1}$
Explanation
(b) According to equation of continuity,
$av = constant$
$\therefore\ \ \ For\ tube,\ \left( 8 \times 10^{- 4} \right) \times \left( \frac{0.15}{60} \right) = a_{1}v_{1}$
$For\ holes\ \ \left( 40 \times 10^{- 8} \right) \times v = a_{2}v_{2}$
$\therefore\ a_{1}v_{2} = a_{2}v_{1}$
$\therefore\ \ 40 \times 10^{- 8} \times v = \frac{8 \times 10^{- 4} \times 0.15}{60}$
$\Longrightarrow \ v = \frac{8 \times 10^{- 4} \times 0.15}{40 \times 10^{- 8} \times 60} = 5{ms}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.