Two water pipes of diameter (2 ~cm ) and (4 ~cm ) are separately connected to a main supply line. The velocity of flow of water in the pipe of (2 ~cm ) diameter is

Step-by-step solution

Diameter of first pipe, (d₁=2 ~cm ) ( ) Radius, (r₁=1 ~cm =10⁻² ~cm ) Diameter of second pipe, (d₂=4 ~cm ) ( r₂=2 ~cm =2 10⁻² ~m ) If (v₁ ) and (v₂ ) are the velocities of water in first and second pipe respectively, then according to principle of continuity, ( aligned & & A₁ v₁=A₂ v₂ r₁^2 v₁= r₂^2 v₂ & v₂ & = ( r₁ r₂ )^2 v₁= ( 10⁻² 2 10⁻² )^2 v₁ & & v₂= v₁ 4 v₁=4 v₂ aligned )