Difficulty: Medium
Correct Answer: 2.0 m/sec
Explanation:
Introduction / Context:
Flow nets are graphical solutions of Laplace’s equation used in seepage and potential flow. The spacing of streamlines and equipotentials encodes discharge per flow tube, enabling velocity comparisons between sections without direct computation of the velocity field.
Given Data / Assumptions:
Concept / Approach:
In a given stream tube, discharge q is conserved: q = v * A_tube. With constant thickness, A_tube ∝ s (streamline spacing). Therefore, v is inversely proportional to s. Halving the spacing doubles the velocity.
Step-by-Step Solution:
Verification / Alternative check:
Uniform net thickness and equal potential drop ensure the stream tubes carry the same discharge; the inverse proportion confirms the result.
Why Other Options Are Wrong:
(a) and (b) ignore the reduced spacing; (d) and (e) exaggerate the change beyond the inverse-spacing rule for the given ratios.
Common Pitfalls:
Comparing sections across different potential drops; reading spacing obliquely rather than perpendicular to streamlines; neglecting varying thickness in 3D scenarios.
Final Answer:
2.0 m/sec
Discussion & Comments