Which of the following statement(s) is/are true? (i) The Hydraulic Gradient Line (HGL) represents the total energy of a flowing fluid per unit weight (ii) Leakage detection uses the HGL by identifying abnormal drops in pressure profiles; a sudden, steeper slope in the HGL indicates significant pressure loss at a leak location
- AOnly (i)
- BOnly (ii)Correct
- CBoth (i) and (ii)
- DNeither (i) nor (ii)
Solution
Concept
Hydraulic gradient line in leak detection
Formula
HGL = z + p / γ; TEL = z + p / γ + v2 / (2g)
Step-by-step solution
1. Total Energy Line (TEL) represents total fluid energy (datum + pressure + velocity head). 2. Hydraulic Gradient Line (HGL) represents piezometric head only, making statement (i) false. 3. Concentrated pipe leakage causes localized high friction head loss, steepening the HGL slope at the breach, making statement (ii) true. 4. Therefore, only statement (ii) is true. Answer: B
Explanation
Statement (i) is false because the Hydraulic Gradient Line (HGL) represents piezometric head (elevation head plus pressure head), while the Total Energy Line (TEL) accounts for total energy including velocity head. Statement (ii) is true because significant pipe leaks cause abrupt localized head loss, resulting in an abnormal drop and steeper downward slope in the HGL.
Why the other options are wrong
A) Statement (i) is false because HGL excludes velocity head. C) Statement (i) is false, so both statements cannot be true. D) Statement (ii) is correct regarding HGL leakage detection.
Shortcut
Total energy = TEL; Piezometric head = HGL. Steep drop in HGL indicates pipe leak.
Common mistake
Confusing HGL with TEL by assuming HGL includes kinetic velocity head (v²/2g).
Correct answer: B) Only (ii)