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 $m/min$, then the speed with which the liquid is ejected through the holes is:

• A. 50 m/s
• B. 5 m/s
• C. 0.05 m/s
• D. 0.5 m/s

Answer 1

Answer: (B)

5 m/s

Using Law of Continuity,

$A_1{v}_1=A_2{V}_2$

$A_1=8c{m}^2=8\times {10}^{-4}$

$v_1=\frac{0.15}{60}=2.5\times {10}^{-3}{ms}^{-1}$

$A_2=40\times {10}^{-8}{m}^2=4\times {10}^{-7}{m}^2$

Using above theorem,

$8\times {10}^{-4}\times 2.5\times {10}^{-3}=4\times {10}^{-7}\times v_2$

Velocity at holes $=5{ms}^{-1}$