Which of the following statements regarding flow net are true? (1) Flow lines and equipotential lines intersect orthogonally. (2) Number of flow channels determine discharge. (3) Head loss is constant across flow lines. (4) Valid for both laminar and turbulent flows.
- A1, 2 and 3 onlyCorrect
- B2, 3 and 4 only
- C1, 3 and 4 only
- DAll of the above
Solution
Concept
Properties of Flow Nets and Validity of Laplace's Equation
Formula
q = k × H × (Nf / Nd) Δh = H / Nd
Step-by-step solution
1. Statement (1) is correct: Flow lines and equipotential lines always intersect at right angles (90°). 2. Statement (2) is correct: Discharge (q) is directly proportional to the number of flow channels (Nf). 3. Statement (3) is correct: The head drop between any two successive equipotential lines is equal and constant (Δh = H / Nd). 4. Statement (4) is incorrect: Flow nets rely on Darcy's law (Laplace equation Δ²h = 0), which is valid only for laminar flow through soil, not turbulent flow. 5. Therefore, statements 1, 2, and 3 are correct.
Explanation
Flow lines and equipotential lines intersect each other orthogonally (at 90°). The rate of discharge is directly proportional to the number of flow channels (Nf). The head loss per potential drop is constant (Δh = H / Nd). Flow nets are derived using Laplace's equation which assumes Darcy's law is valid, meaning flow nets are valid ONLY for laminar flow, not turbulent flow.
Why the other options are wrong
B: Incorrect because statement 1 is true and statement 4 is false. C: Incorrect because statement 4 is false. D: Incorrect because statement 4 is false.
Shortcut
Darcy's law is valid ONLY for laminar flow. Any option containing Statement 4 is incorrect, leaving Option (A) as the only correct choice.
Common mistake
Correct answer: A) 1, 2 and 3 only