Question

The cylindrical tube of a 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 $0.15 \, m \, m i n^{- 1}$ , the speed with which the liquid is ejected through the hole is

• A. $50 \, m \, s^{- 1}$
• B. $5 \, m \, s^{- 1}$
• C. $0.05 \, m \, s^{- 1}$
• D. $0.5 \, m \, s^{- 1}$

Answer 1

Answer: (B)

According to equation of continuity,
$av=constant$
$\therefore \, \, \, For \, tube, \, \left(8 \times \left(10\right)^{- 4}\right)\times \left(\frac{0.15}{60}\right)=a_{1}v_{1}$
$For \, holes \, \, \left(40 \times \left(10\right)^{- 8}\right)\times v=a_{2}v_{2}$
$\therefore \, a_{1}v_{1}=a_{2}v_{2}$
$\therefore \, \, 40\times 10^{- 8}\times v=\frac{8 \times 10^{- 4} \times 0.15}{60}$
$\Longrightarrow \, v=\frac{8 \times 10^{- 4} \times 0.15}{40 \times 10^{- 8} \times 60}=5 \, m \, s^{- 1}$