Question

A horizontal pipe, 10 cm in diameter, has a smooth reduction to a pipe 5 cm in diameter. If the pressure of the water in the larger pipe is 8.00*10^4 Pa and the pressure in the smaller pipe is 6.00*10^4 Pa, what is the flow speed of the water (in m/s) in the smaller pipe?

Answer 1

Density of water = = 1000 kg/m³

Pressure of the water in the larger pipe = P₁ = 8 x 10⁴ Pa

Diameter of the larger pipe = D₁ = 10 cm = 0.1 m

Cross-sectional area of the larger pipe = A₁ = D₁²/4

Speed of flow of water in the larger pipe = V₁

Pressure of the water in the smaller pipe = P₂ = 6 x 10⁴ Pa

Diameter of the smaller pipe = D₂ = 5 cm = 0.05 m

Cross-sectional area of the smaller pipe = A₂ = D₂²/4

Speed of flow of water in the smaller pipe = V₂

By Continuity equation,

A₁V₁ = A₂V₂

(D₁²/4)V₁ = (D₂²/4)V₂

D₁²V₁ = D₂²V₂

(0.1)²V₁ = (0.05)²V₂

V₁ = 0.25V₂

The pipe is horizontal therefore the larger and smaller pipe are at the same elevation.

By Bernoulli's equation,

2x10⁴ + 31.25V₂² = 500V₂²

468.75V₂² = 2x10⁴

V₂ = 6.53 m/s

Flow speed of water in the smaller pipe = 6.53 m/s