Question

A water hose 2 cm in diameter is used to fill a 20-liter bucket. If it takes 1 minute to fill the bucket, then the speed v at which the water leaves the hose is,

• A. 150 cm/s
• B. 70 cm/s
• C. 100 cm/s
• D. 106 cm/s

Answer 1

Answer: (D)

106 cm/s

Given , $d=0.02⟹r=0.01$

Area = $\pi r^2=\pi {0.01}^2$

Volume rate of flow, $V=\frac{V}{t}=\frac{20L}{60}=\frac{{10}^{-3}}{3}{m}^3{s}^{-1}$

Volume rate of flow = Cross-Section Area x Velocity of Flow

$\frac{dV}{dt}=\dot{V}=Av$

$v=\frac{\dot{V}}{A}==\frac{{10}^{-3}}{3}{m}^3{s}^{-1}\times \frac{1}{\pi {0.01}^2}=1.06m/s=106cm/s$

Hence, velocity of water leaves hose is $106cm/s$