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 liquid flows inside the tube with a speed of $0.15mmi{n}^{-1}$ , the speed with which the liquid is ejected through the hole 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,
$av=constant$
$\therefore Fortube,\left(8\times {\left(10\right)}^{-4}\right)\times \left(\frac{0.15}{60}\right)=a_1{v}_1$
$Forholes\left(40\times {\left(10\right)}^{-8}\right)\times v=a_2{v}_2$
$\therefore a_1{v}_1=a_2{v}_2$
$\therefore 40\times 10^{-8}\times v=\frac{8\times 10^{-4}\times 0.15}{60}$
$⟹v=\frac{8\times 10^{-4}\times 0.15}{40\times 10^{-8}\times 60}=5m{s}^{-1}$