Flow Through Pipes MCQ with answer and solution

Concept

The Hardy Cross method is based on two principles: the sum of inflows and outflows at any junction is zero, and the algebraic sum of head losses around any closed loop is zero.

Formula

ΔQ = -Σ(h_f) / Σ(n × |h_f / Q|), where h_f = k × Qⁿ

Step-by-step solution

1. Assume an initial distribution of flows in the pipe network such that the continuity equation is satisfied at each junction. 2. Calculate the head loss in each pipe using a formula like Darcy-Weisbach or Hazen-Williams (h_f = k × Qⁿ). 3. Calculate the algebraic sum of head losses around each closed loop (Σh_f). 4. Calculate the flow correction (ΔQ) for each loop using the formula ΔQ = -Σh_f / Σ(n × |h_f / Q|). 5. Apply the correction to the assumed flows and repeat the process until the head loss in each loop is negligible (balanced).

Explanation

The Hardy Cross method is an iterative procedure used to determine the flow rates in a network of pipes where the head loss around any closed loop must sum to zero. It balances the head losses by applying successive corrections to initial assumed flows until the continuity and energy equations are satisfied.

Why the other options are wrong

A: Discharge is measured using devices like venturimeters, orificemeters, or pitot tubes. B: Pressure head at a point is calculated using the energy equation (Bernoulli's) once flows are known, but the method's primary function is balancing. D: Hardy Cross is specifically for closed conduit (pipe) networks, not open channel flow.

Shortcut

Remember: Hardy Cross = Loop balancing (Head loss) or Junction balancing (Discharge). Most competitive exams focus on the loop balancing aspect (Σh