In the Hardy Cross method of network analysis, which of the following conditions must be satisfied for each closed loop? (i) The algebraic sum of pressure drops around a closed loop must be zero. (ii) The flow entering a junction must be equal to the flow leaving the same junction. (iii) The flow velocity must be uniform across all pipes in the loop. (iv) The pressure at every node in the loop must be equal.
- AOnly (i)
- B(i) and (ii)Correct
- C(iii) and (iv)
- D(i), (ii), (iii) and (iv)
Solution
Concept
Hardy Cross method loop conditions
Formula
Σ Q = 0 (nodes); Σ hf = 0 (loops)
Step-by-step solution
1. Hardy Cross method applies two physical laws to analyze closed pipe loops: 2. Conservation of energy requires net head loss around any closed circuit to equal zero [sum(hf) = 0], satisfying (i). 3. Conservation of mass requires inflow to equal outflow at each junction [sum(Q) = 0], satisfying (ii). 4. Velocities and pressures vary across the loop according to pipe diameters and head losses. Answer: B
Explanation
In the Hardy Cross iterative method for pipe networks, two physical criteria must be satisfied for each closed loop: the algebraic sum of head losses around the closed circuit must equal zero [sum(hf) = 0] by conservation of energy, and the algebraic sum of inflows and outflows at every node must equal zero [sum(Q) = 0] by continuity.
Why the other options are wrong
A) Incomplete because junction continuity (ii) is also an essential governing condition. C) False because pipe velocities and nodal pressures vary with friction loss and pipe diameter. D) False because statements (iii) and (iv) violate hydraulic principles.
Shortcut
Hardy Cross loops: sum(hf) = 0 (loop energy) and sum(Q) = 0 (node continuity).
Common mistake
Assuming velocities or pressures are equal at all loop nodes.
Correct answer: B) (i) and (ii)