Question

A fluid flowing through a pipe of diameter 450 mm with velocity 3 m/s is divided into two pipes of diameters 300 mm and 200 mm. The velocity of flow in 300 mm diameter pipe is 2.5 m/s, then the velocity of flow through 200 mm diameter pipe will be 

1. 2.5 m/s
2. 5.55 m/s
3. 7.25 m/s
4. 9.56 m/s

Answer 1

Correct Answer - Option 4 : 9.56 m/s

Concept:

According to continuity, the liquid flow rate will be conserved.

Q₁ = Q₂ + Q₃

In a pipe, flow rate is given by

Q = AV

Calculation:

Given V₁ = 3 m/s, D₁ = 450 mm, V₂ = 2.5 m/s, D₂ = 300 mm, D₃ = 200 mm;

From continuity,

D₁² V₁ = D₂² V₂ + D₃² V₃

⇒ 450² × 3 = 300² × 2.5 + 200² × V₃

⇒ V₃ = 9.56 m/s