Statement (I): In Hardy Cross method, a trial distribution of discharges is made arbitrary. Statement (II): The continuity equation must satisfy at each junction.
- ABoth Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
- BBoth Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)Correct
- CStatement (I) is true but Statement (II) is false
- DStatement (I) is false but Statement (II) is true
Solution
Concept
In Hardy Cross method, assumed flows are arbitrary but must satisfy continuity at every junction; then they are corrected loop by loop.
Formula
Δ = -Σ(r Qn) / Σ(n r Qn-1); for Darcy n = 2, so Δ = -Σ(r Q2) / Σ(2 r Q)
Step-by-step solution
1. In Hardy Cross method, we first assume flows in all pipes. This trial distribution is arbitrary, so Statement (I) is true. 2. The assumed flows must satisfy continuity at each junction (inflow = outflow). So Statement (II) is true. 3. Statement (II) is a condition on the trial flows. It does not explain why the trial flows are arbitrary. 4. So both statements are true, but (II) is not the correct explanation of (I). Answer: B.
Explanation
The first trial flows in the Hardy Cross method can be chosen freely. They must still obey continuity at every junction. Continuity is a rule the trial flows must follow, not the reason they are arbitrary.
Why the other options are wrong
A: (II) is a condition, not the reason for the arbitrary choice. C: (II) is true, continuity is always required. D: (I) is true, the initial flows are assumed arbitrarily.
Shortcut
Arbitrary flows + continuity condition = two separate true facts, so choose B.
Common mistake
Choosing A because both statements are about the same method.
Correct answer: B) Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement (I)