The diameter of a main pipe is 30 cm and it branches into two pipes | Civil UPSC ESE Exam Solution 2021

Civil UPSC ESE Exam Solution 2021

UPSC ESE Exam Solution 2021 for Civil Engineering UPSC ESE 2021 GS Paper 1 download exam paper from telegram https://telegram.me/civil_experiences

A network of pipes conveying water to a city has the following specifications. The diameter of a main pipe is 30 cm and it branches into two pipes of diameters 20 cm and 15 cm respectively. If the average velocity in the main pipe is 2.5 m/s and the average velocity in the 20 cm pipe is measured as 2 m/s, what is the velocity in the 15 cm pipe?

[A] 8.84 m/s
[B] 7.44 m/s
[C] 5.84 m/s
[D] 6.44 m/s

ANSWER= [D] 6.44 m/s

Detailed Explanation

From the continuity equation

(πD₁²/4)V₁ = (πD₂²/4)V₂ + (πD₃²/4)V₃

? D₁²V₁ = D₂²V₂ = D₃²V₃

? V₃ = (D₁²V₁ – D₂²V₂)/D₃² = (D₁/D₃)² V₁ – (D₂/D₃)² V₂

? V₃ = (30/15)² × 2.5 – (20/15)² × 2

? V₃ = 4 × 2.5 – (4/2.25) × 2 = 6.44 m/s

? V₃ = 6.44 m/s

Civil UPSC ESE Exam Solution 2021