Water flows through a hose pipe whose internal diameter is (4 ~cm ) at a speed of (1 ~ms ⁻¹ ). If water has to emerge at a speed of (4 ~ms ⁻¹ ), then the diameter of the nozzle should be

Step-by-step solution

Internal diameter for hose pipe, (d₁=4 ~cm , r₁= d 2 = 4 2 =2 ~cm =2 10⁻² ~m ) Speed of water through hose pipe, (v₁=1 ~ms ⁻¹ ) Speed of water through nozzle, (v₂=4 ~ms ⁻¹ ) Diameter, (d₂= ) ? According to principle of continuity, ( array llll & A₁ v₁=A₂ v₂ & r₁^2 v₁= r₂^2 v₂ & r₂^2= r₁^2 v₁ v₂ r₂^2= (2 10⁻² )^2 1 4 & r₂^2=10⁻⁴ & r₂=10⁻² ~m r₂=1 ~cm array ) ( ) Diameter of nozzle, (d₂=2 r₂=2 1=2 ~cm )