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. $50\, m \,s ^{-1}$
• 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,
(area} A $\times$ ( velocity v)= constant
$\therefore $ For tube, $\left(8 \times 10^{-4}\right) \times\left(\frac{0.15}{60}\right)=A_{1} v_{1}$
For holes, $\left(40 \times 10^{-8}\right) \times v=A_{2} v_{2}$
As $A_{2} v_{2}=A_{1} v_{1}$
$\therefore 40 \times 10^{-8} \times v=\frac{8 \times 10^{-4} \times 0.15}{60}$
or $v=\frac{8 \times 10^{-4} \times 0.15}{40 \times 10^{-8} \times 60}=\frac{8 \times 15}{4 \times 6}$
$=5 \,m \,s ^{-1}$