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 the liquid flows inside the tube with a speed of $0.15 \,m.min^{-1}$, the speed with which the liquid is ejected through the holes is

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

Answer 1

Answer: (C)

According to equation of continuity,
av = constant
$\therefore $ For tube, $(8 \times 10^{-4} ) \times \left( \frac{0.15}{60} \right) = a_1 v_1$
For holes, $\left(40 \times10^{-8}\right) \times v = a_{2}v_{2} $
$ \therefore a_{2} v_{2} =a_{1} v_{1} $
$\therefore 40 \times10^{-8} \times v = \frac{8 \times10^{-4} \times0.15}{60}$
$ \Rightarrow v= \frac{8 \times10^{-4} \times0.15}{40 \times10^{-8}\times60} $
$ =5 \,m/s $