Two pipes of same length and diameters d and 2d are connected in series. The diameter of equivalent pipe of same length is
- AGreater than 2d
- BBetween 1.5d and 2d
- CBetween 1.2d and 1.5d
- DLess than 1.2dCorrect
Solution
Concept
Dupuit equation
Formula
L/D⁵ = L₁/d₁⁵ + L₂/d₂⁵
Step-by-step solution
1. The equivalent pipe has the total length 2L: 2L/De⁵ = L/d⁵ + L/(2d)⁵ = (L/d⁵)(33/32). 2. De⁵ = 64/33 d⁵ = 1.94 d⁵. 3. De = 1.940.2 d ≈ 1.14 d, which is less than 1.2d.
Explanation
The smaller pipe dominates the resistance.
Why the other options are wrong
The equivalent diameter is far below 2d.
Shortcut
De ≈ 1.14 d.
Correct answer: D) Less than 1.2d