Question

A water hose 2 cm in diameter is used to fill a 20 litre bucket. If it takes 1 minute to fill bucket with watch velocity it leaves the hose ,

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

Answer 1

The correct option is C 106 cm/s

Given,

Area, $A=\frac{\pi d^2}{4}=\frac{\pi }{4}{\left(0.02\right)}^2$

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

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

$\dot{V}=Av$

$v=\frac{\dot{V}}{A}=\frac{{10}^{-3}}{3}\times \frac{4}{\pi {\left(0.02\right)}^2}=1.06m{s}^{-1}=106cm{s}^{-1}$

Hence, velocity of water leaves hose is$106cm{s}^{-1}$.