Question

Water is flowing through a cylindrical pipe of cross- sectional area 0.09 π
m-2 at a speed of 1.0 m s-1. If the diameter of the pipe is halved, then find the speed of flow of water through it.​

Answer 1

Answer : The speed of the flow of water will be 4m/s.

Explanation:

Area of pipe ( A1 ) = π × r² = 0.09π m². ( given )

Speed of the flow ( V1 ) = 1 m/s. ( given )

Now according to given condition,

Area of the pipe ( A2 ) = π ×( r/2)²

= π × r²/4

= A1 / 4 ( since π × r² = A1 )

Speed of the flow (V2) = ?

Now by using the continuity equation ,

∴ A1 × V1 = A2 × V2

∴ ( A1 × V1 ) / A2 = V2

∴ A1 × 1 × 4 / A1 = V2 ( substituting the value)

∴ V2 = 4 m/s