Question

A horizontal pipe widens from a radius of 0.120 m to 0.260 m. If the speed of the water is 2.00 m/s in the smaller pipe, what is the speed in the larger pipe (in m/s)?

Answer 1

Radius of the smaller pipe = R₁ = 0.12 m

Cross-sectional area of the smaller pipe = A₁ = R₁²

Speed of water in the smaller pipe = V₁ = 2 m/s

Radius of the larger pipe = R₂ = 0.26 m

Cross-sectional area of the larger pipe = A₂ = R₂²

Speed of water in the larger pipe = V₂

By continuity equation,

A₁V₁ = A₂V₂

R₁²V₁ = R₂²V₂

R₁²V₁ = R₂²V₂

(0.12)²(2) = (0.26)²V₂

V₂ = 0.426 m/s

Speed of water in the larger pipe = 0.426 m/s