Question

The cylindrical tube of a spray pump has a cross-section of $8c{m}^2$, 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 $0.15mmi{n}^{-1}$, the speed with which the liquid is ejected through the holes is

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

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 $v=\frac{8\times 10^{-4}\times 0.15}{40\times 10^{-8}\times 60}=\frac{8\times 15}{4\times 6}$
$=5m{s}^{-1}$